IT 13 074

Examensarbete 45 hpDecember 2013

Artifacts handling and DBS electrodes localization in the CT/MRI brain images

Amir Motevakel

Institutionen för informationsteknologiDepartment of Information Technology

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Artifact handling and DBS electrodes localization inthe CT/MRI brain images

Amir Motevakel

In the DBS surgical treatment the location of the electrodes has direct influence onthe success rate of treatment. Considering the fact that MRI imaging is not compatiblewith metal, post-operative CT images should be used to locate the electrodes onpre-operative MRI images which contain information about soft tissues. It isimpossible to locate them directly since the area around the electrodes on the CTimage has been corrupted due to the blockage of x-ray by them. This work attemptsto precisely estimate the position of the DBS electrodes inside the brain by means ofimages gathered from the CT-scanner and MRI device. In order to do this, all types ofpossible CT artifacts and the physics behind has been carefully studied and a state ofthe art research on MAR techniques has been performed. Apart from hardware MARtechniques and also methods which are applicable only by having the model of thegantry (Cylindrical scanner assembly) and raw data, after the formation of the image itis not possible to completely recover all lost intensity levels without exposing theresult to the risk of secondary artifact as well as electrode dislocation which might beminor yet critical for this application.

Considering the latter, a novel technique named junction method developed. Insteadof eliminating the artifacts, the method takes advantage of them, considering the factthat they are signatures of the electrodes. To achieve this, first the brain extractedfrom the whole image by defining a brain mask. Later the edges are intensified byapplying a Gaussian convolution followed by a second measure of the secondderivative of the image along all directions. Next all lines are detected by the Houghtransform and after filterations the intersections of interest are specified.

In the second part of this project, state of the art research on multi-modality medicalimage registration techniques was carried out. Advantages and disadvantages of eachmethod in relation to this specific case were studied. Registration technique selectioncould not be done without investigation of all types of discrepancies which might existbetween two image modalities; therefore discrepancies are being discussed. NonrigidAffine registration algorithm suggested along with logarithmic contrast enhancementand Gaussian smoothening as preprocessing steps, based on experiences performedon an available image set. The mutual information, an information-theoretic criterionused as the measure of registration with the help of calculation of a joint histogram ofthe two modalities. All the algorithms starting from CT images to MRI images areimplemented in Matlab software and the resulting image shows a close matching.

Tryckt av: Reprocentralen ITCIT 13 074Examinator: Philipp RümmerÄmnesgranskare: Lars OestreicherHandledare: Alexander Medvedev

All our knowledge begins with the senses, proceeds then to the understanding, and ends with reason. There is nothing higher than reason.

The Critique of Pure Reason

Immanuel Kant (1724 - 1804)

Acknowledgements

This is a Master Thesis submitted in partial fulllment of the requirementsfor the degree of Master of Science in Embedded Systems to the Departmentof Information Technology, Uppsala Universiy, Uppsala, Sweden.

I would like to thank my supervisor, Prof. Alexander Medvedev who pro-vided me the opportunity to do this project. Also I would like to thank Dr.Lars Oestreicher for reviewing my master thesis.

Further I would like to thank Dr. Philipp Rummer, programm director forMaster’s programm in Embedded System at Uppsala university, for his guid-ance and encouragement he demonstrated during my Master’s studies atUppsala university. Also I need to thank all my lecturers and researchers inUppsala university who shared their knowledge with me.

Also I would like to thank Uppsala University for providing me all the soft-ware and hardware necessary for the project.

Sincere thanks to my friends and my family who gave me courage and supportthroughout my Master’s studies.

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Contents

Popularvetenskaplig introduktion (Popular intro. in Swedish) 1

Background 1

I Artifact handling in CT scan images 5

1 Background: CT scanning 61.1 Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Image formation . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 CT scanner types . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Artifacts in CT 132.1 Physics-based Artifacts . . . . . . . . . . . . . . . . . . . . . . 132.2 Patient-based Artifacts . . . . . . . . . . . . . . . . . . . . . . 172.3 Scanner-based Artifacts . . . . . . . . . . . . . . . . . . . . . 19

3 Localization of the DBS electrodes 223.1 Image analysis reduction of CT artifacts caused by metallic

objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.1 Normalized method . . . . . . . . . . . . . . . . . . . . 233.1.2 Three phase method . . . . . . . . . . . . . . . . . . . 233.1.3 Incorporating intermediate image method . . . . . . . 24

3.2 Proposed method: Localization of electrodes by incorporatingartifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Brain mask . . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Detection of straight lines . . . . . . . . . . . . . . . . 303.2.3 Selecting the main intersections . . . . . . . . . . . . . 34

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II Registration of MRI and CT images 38

4 Classification of registration methods 414.1 Supervised registration . . . . . . . . . . . . . . . . . . . . . . 414.2 Fiducial methods . . . . . . . . . . . . . . . . . . . . . . . . . 434.3 Automatic registration . . . . . . . . . . . . . . . . . . . . . . 43

4.3.1 Registration measure . . . . . . . . . . . . . . . . . . . 434.3.2 Registration transformations . . . . . . . . . . . . . . . 474.3.3 Interpolation . . . . . . . . . . . . . . . . . . . . . . . 48

5 Proposed registration method 505.1 Implementation of geometric transformations . . . . . . . . . . 515.2 Medical images file formats . . . . . . . . . . . . . . . . . . . . 54

6 Discussion and Conclusion 56

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List of Figures

1 An early-stage stereotactic device . . . . . . . . . . . . . . . . 32 Targets of DBS electrode insertion in the brain . . . . . . . . . 3

1.1 Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Inelastic scattering effect . . . . . . . . . . . . . . . . . . . . . 71.3 Elastic scattering effect . . . . . . . . . . . . . . . . . . . . . . 71.4 The Beer-Lambert law illustration . . . . . . . . . . . . . . . . 81.5 Back-projection example of a round object . . . . . . . . . . . 91.6 Result of a deblurring filter. . . . . . . . . . . . . . . . . . . . 91.7 A first generation CT scanner . . . . . . . . . . . . . . . . . . 101.8 A second-generation CT scanner . . . . . . . . . . . . . . . . . 101.9 A third-generation CT scanner . . . . . . . . . . . . . . . . . . 111.10 A fourth-generation CT scanner . . . . . . . . . . . . . . . . . 111.11 Conventional CT scan versus Spiral CT scan . . . . . . . . . . 12

2.1 Cupping effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Cupping effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Streak artifact . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Partial Volume example of round acrylic rods . . . . . . . . . 172.5 Photon starvation artifact . . . . . . . . . . . . . . . . . . . . 182.6 Patient Movement Artifact in CT image of head . . . . . . . . 202.7 CT image of a water-filled phantom shows ring artifact . . . . 21

3.1 Beam hardening in a round object vs. a non eccentric object . 253.2 Beam hardening resulted from a metallic object . . . . . . . . 263.3 Comparison between intermediate-image and prior methods . 273.4 Post-operative CT scan of the brain . . . . . . . . . . . . . . . 293.5 The head mask . . . . . . . . . . . . . . . . . . . . . . . . . . 313.6 Brain image after applying Laplacian of Gaussian convolution

operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.7 The Hough transform of the processed CT brain image . . . . 33

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3.8 Images of some of the lines detected by Hough transform inthe CT image of the brain (before applying the criterion) . . . 34

3.9 Detected streak lines on a CT image . . . . . . . . . . . . . . 353.10 Marked intersections on the image of the brain . . . . . . . . . 363.11 Different imaging planes with a same centre point . . . . . . . 39

4.1 Overlaid MRI and CT images of the brain before registration . 424.2 Joint histogram of the two registrations of MRI images of the

brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3 A comparison between rigid and Affine registrations . . . . . . 49

5.1 The algorithm for registration of CT/MRI brain images . . . . 51

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ABBREVIATIONS

1-D 1 dimentional2-D 2 dimentional3-D 3 dimentionalAR Augmented realityCBR Closing by reconstructionCT Computerized tomographyDBS Deep brain stimulationDOF Degree of freedomET Essential tremorFOV Field of viewGpi Globus pallidus internusHU Hounsfield unitIGS Image guided surgeryMAR Metal artifact reductionMI Mutual informationMRI Magnetic resonance imagingOBR Opnening by reconstruction OCD Obsessive compulsive disordersPSA Posterior subthalamic nucleus PD Parkinson's diseaseSE Structuring elementSTN Subthalamic nucleusVIM Ventral intermediate nucleus of thalamus

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Popularvetenskaplig introduktion (Popular introductionin Swedish)

Det huvudsakliga malet for det har examensarbetet ar att utveckla en algo-ritm for att bestamma den exakta positionen for DBS elektroder i hjarnan.MRI bilder ar inte kompatibla med DBS elektroder pa grund av de starkamagnetiska falten som skapas. Innan operationen av elektroderna utfrs tasMRI-bilder och sedan CT-scan med elektroder pa plats i hjarnan. Plac-eringen av elektroderna maste definieras med avseende pa mjukdelar runtdem. Den forsta delen av projektet ar att hitta elektrodernas lage fran MRI-bilderna och i den andra delen hitta samma plats i CT-scan bilderna medavseende pa hjarnans anatomi.

Forskning har gjorts for att reducera artefakter fran metaller i CT-scan bilder.Ingen metod kan dock aterstalla forlorade intensitetsnivaer helt. I dennaapplikationen kan dessa metoder infora sekundara artefakter som forsvararpositionsbestammandet av elektroderna. Darfor har en ny teknik, vilkennamnsgav till Junction method, utvecklats for applikationen.

Artefakterna har skapats av elektroderna men istallet for att forsoka elimin-era artefakterna, anvands de for att lokalisera dem. Resultaten nar metodenhar tillampats pa bilder tagna fran patienter med implanterade elektrodervisar att metoder fungerar.

I den andra delen av projektet, for att korrelera varje punkt pa MRI-bildertill CT-scan bilder, har olika registreringsmetoder studerats. Efter att hastuderat flera typer av deformationer och variationer som kan handa i ochmellan MRI och CT-bilder sa kravs en registreringsteknik som innefattar ennon-rigid Affine transformering.

Background

An efficient and developing surgical treatment for many neurological dis-eases is Deep Brain Stimulation (DBS). The effectiveness of this method hasbeen proved for the treatment of essential tremor (ET), Parkinsons disease(PD), Dystonia, Chronic pain, Obsessive-compulsive disorders (OCD) andtreatment-resistant depression. However there might be some side effectsresulting from such a stimulation. To provide an overview of the diseasesmentioned above, a short description of the important ones is given below.

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Essential tremor is the most common neurological disorder and it may affectas many as 10 million people in just United States of America alone. It is20 times more prevalent than Parkinson’s disease [1]. Although the exactmechanism behind it is still unknown to researchers, it is a disease thataffects the central nervous system. There is no absolute cure for it but somemethods reduce the symptoms by using medications or by DBS surgery. ETcan take away the quality of life from the victims therefore DBS can bringback joy to their lives. Symptoms appear in the form of shaking when theperson moves their hands or some other parts of the body. It usually affectsonly certain parts of the body, including the hands, arms, face, voice, jawand less commonly the legs (walking ability balance). It can cause significantinconvenience to the patients due to the social and functional embarrassmentthat usually occur in daily life activities for such a patient. As many as 85percent of the patients with ET reported that this disease affected theirlifestyle in certain ways. Social phobia resulted from negative reactions ofindivisuals intensify the symptoms of disease [2], hence social awareness ofsuch an issue becomes important.

In Parkinson’s disease the motor symptoms which cause movement of musclesresult from the death of dopamine-generating cells in a region of the mid-brain, but the cause of this cell death is still unknown to science. Early inthe course of the disease, the most obvious symptoms are movement-related.These include shaking, rigidity, slowness of movement and difficulty withwalking and gait. Later, cognitive and behavioural problems may arise.

Dystonia is a neurological movement disorder, in which involuntary musclecontractions cause slow repetitive movements or abnormal postures. Thiscan be be combined with tremor or other neurologic features. The diseasecan affect either only certain muscles or the whole body. The cause of thedisease might be genetic, or there may be other unknown sources [3].

Procedure of DBS

The electrodes responsible for generating electrical field implant inside thebrain by Stereotactic surgery. An image of the device used for this shown inFigure 1 1. Later the electrodes connect to a battery-operated pulse genera-

1Same device has been used in radiosurgery which pioneered in 1951 by Lars Leksell andthe physicist and radiobiologist Borje Larsson by using the Uppsala University cyclotron;

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Figure 1: An early-stage stereotactic device devised by surgeon, physician, LarsLeksell (1907-1986) at Lund university, Sweden in 1949.

tor in order to produce chronic stimulation. The common areas in the brainwhere is the target of electrode placement for treatment of PD, is subthala-mic nucleus (STN) or internal segment of globus pallidus (GPi) and in case ofET ventral intermediate nucleus of thalamus (VIM) or posterior subthalamicnucleus (PAS). Figure 2 illustrates these targets in an image of the brain.

The efficiency of DBS significantly depend on the spatial distribution of the

Figure 2: An illustration of the targets of DBS electrode insertion [4].

this widely used method named ”stralkniven” (the ray knife) by the inventor, Lars Leksell.

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electric field in relation to the brain anatomy. This electric field is a functionof the placement of electrodes in the brain hence it is crucial that those werein the exact intended position [4].

This work attempts to find the precise position of the electrodes inside thebrain based on the images gathered by the CT-scanner and later on MRI im-ages. The information about electrode position is used later for tuning of thestimulation. This can not be accomplished directly since the post-operativeCT-images are heavily corrupted due to the presence of metallic objects.This fact necessitates a study of the mentioned artifacts and possibilities fortheir elimination or alleviation before attempting electrodes localization. Theprerequisites of studying the nature of the artifacts resulting from metallicobjects are in understanding of the physics behind the CT-scan device andthe imaging process in it.

Tools used

For development and visualization of this project, the following tools hasbeen used.

Matlab

The environment used for developing the algorithm is Matlab version 2013a.The image processing toolbox functions also used for developing algorithms.

Dicom viewer

To extract and export slices from Dicomfiles, Dicom viewer from Philips hasbeen used.

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Part I

Artifact handling in CT scanimages

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Chapter 1

Background: CT scanning

To enable handling of artifacts in CT images, it is essential to understandthe cause of those which consequently are the interactions of x-ray in thebody and later through the whole process of image formation inside the CTscanner.

1.1 Physics

After an x-ray beam enters the body of the subject of medical imaging, anumber of interactions cause its attenuation and deflection. Following is anoverview of them.

Photoelectric effect

An x-ray photon gives all its energy to an atom which ejects an electron.Other x-rays are emitted isotropically (fluorescence).

Figure 1.1: Photoelectric effect

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Inelastic (Compton) scattering

An x-ray photon gives part of its energy to an electron then is deflected andcontinues its trajectory with a different energy (inelastic scattering). Figure1.2 illustrates this interaction.

Figure 1.2: Inelastic scatter, (E2 < E1)

Elastic (Rayleigh) scattering

The x-ray wave induces a vibration of the electron of the matter. The x-ray keeps the same energy (elastic scattering). Figure 1.3 illustrates thisinteractions.

Figure 1.3: Elastic scattering effect, (E2 = E1)

The x-ray exiting the object has experienced all the mentioned interactions.A monochromatic x-ray beam with wavelength λ and intensity I0 passingthrough a uniform material is attenuated exponentially, according to theBeer-Lambert law (Eq.1.1).

I = I0 exp(−µL) (1.1)

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Figure 1.4: Beer-Lambert law defines the attenuation of an incident x-ray withenergy level I0 and the attenuated output x-ray with energy level I when passingthrough an object with thickness l and linear attenuation coefficient µ.

µ is the linear attenuation coefficient of the material for the wavelength λ. Itis also a function of the density of the material (β) and the atomic number ofthe material (Z) (equation 1.1). Linear coefficient µ, can be calculated using(1.2):

µ =4π

λβ[cm−1]. (1.2)

1.2 Image formation

Formation of CT images is a three phase process: 1. Generation of rawdata (scanning) 2. Forming the digital image (reconstruction), 3. Filteringthe result. During the scan phase a fan shaped x-ray beam is scanned aroundthe body.

A complete image is formed by rotating the x-ray source around the subjectof scan. All projected x-rays at every angle add up together by applyingback-projection theory. Based on back-projection theory, a 2-D image ofan object can be created by superimposing the views from different angels.Figure 1.5 shows this.

The back-projection method has some side effects as well. First problem isthat it produces an image that has a higher density in the centre. This isdue to the fact that many different images are being overlapped in this area.Consequently, the resulting image is severely blurred. This effect comes fromthe overlapping of the Fourier-transformed images around the low frequencyregion. To control these effects, it is clear that a filter is needed during the

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Figure 1.5: Back-projection example of a round object

reconstruction of the projections.

Figure 1.6: Result of a deblurring filter.

1.3 CT scanner types

Based on the architecture and settings of the instrument, it is possibleto have different types of scan and consequentially different type of imagereconstruction methods. The principle is the same for all but further stepsmight be different. To have a better understanding of x-ray tube1 and de-tector arrangements, following is an overview of CT-scanner types.

In first generation scanners, finely collimated x-ray beam (pencil-beam) wasused. It is only one detector in this scanner type and the gantry and thedetector perform a translate-rotate motion. 180 translations with 1 degreerotation between translates were executed. The scan time was 5 minutes andit was only possible to take images of the head [5].

In the second-generation scanners, the x-ray beam was collimated to a 10-degree fan, which encompassed an array of 8 to 30 radiation detectors, ratherthan the previous pencil beam with only a single detector. Although the

1The source of x-ray

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Figure 1.7: Simplified illustration of the scanning sequence of first generation CTscanner devices (1973. (Courtesy of Philips healthcare).

second-generation scanner also used the complicated translate-rotate me-chanical motion, the fan beam permitted multiple angles to be obtainedwith a single translation across the patient. The fastest second-generationCT units could achieve a scanning time of 18 seconds per slice. The im-age quality was substantially improved. In addition, the cumbersome waterbag was omitted on this and subsequent CT scanners. However, the second-generation units had definite speed limitations resulting from the inertia ofthe heavy gantry, as well as the use of the complicated translate-rotate mo-tion.

Figure 1.8: Simplified illustration of a second-generation CT scanner. There is asmall number of beams (approximately 8 to 30) in a narrow fan configuration withthe same translate-rotate motion used as in the first generation machines. Eachlinear traverse produces several projections at differing angles, one view for eachx-ray beam. (Courtesy of Philips healthcare).

The major difference between the third and fourth-generation rotationalscanners is the motion of the detectors. In the third-generation system, the

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Figure 1.9: Simplified illustration of the third-generation CT scanners. There is alarge number of x-ray beams (approximately 500 to 700) in a wide fan configuration.Both the x-ray tube and the detectors rotate. (Courtesy of Philips healthcare).

Figure 1.10: Fourth-generation CT scanner. There is an intermediate number ofx-ray beams (approximately 50 to 200 ) in a wide fan configuration with a rotatingx-ray tube and a stationary circular array of approximately 600 to 2400 detectorssurrounding the patient. (Courtesy of Philips healthcare).

x-ray tube and detector array are mounted opposite one another and pivotaround the patient in a single rotational movement during which the viewsare acquired. In fourth-generation systems, the detector array is a stationarycircle, and only the x-ray tube rotates through a circle within the array. Asmany as 1,200 to 2,400 detectors may be used, compared with 500 to 700 inthird-generation units.

Both third and fourth-generation scanners can obtain individual slices in 2to 4 seconds. A variation on the fourth-generation design was the ”ultrafast”CT scanner. Designed by Douglas Boyd and collaborators at Imatron for thepurpose of imaging the heart, this unit has no moving parts and can acquirean image in as fast as 17 ms. By successively steering a small focal-spot sizeelectron beam at four fixed tungsten target rings, the heart can be imagedwithout moving the patient and virtually free of motion artifacts.

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In third-generation type, the patient is scanned one slice at a time. Thex-ray tube and detectors rotate for 360 degrees or less to scan one slicewhile the table and patient remain stationary. This slice-by-slice scanning istime-consuming, and therefore efforts were made to increase the scanning oflarger volumes in less time. This notion led to the development of a techniquein which a volume of tissue is scanned by moving the patient continuouslythrough the gantry of the scanner while the x-ray tube and detectors rotatecontinuously for several rotations. As a result, the x-ray beam traces a patharound the patient. Some manufacturers call this beam geometry ”SpiralCT” while others refer to it as ”Helical CT” [6]. Figure 1.11 shows the con-cept.

Figure 1.11: A: Conventional CT scan, B: Spiral CT scan. ()Courtesy of NationalCancer Institute (imaging.cancer.gov))

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Chapter 2

Artifacts in CT

In computed tomography (CT), the term artifact is applied to any sys-tematic discrepancy between the CT numbers in the reconstructed imageand the true attenuation coefficients of the object. CT images are inherentlymore prone to artifacts than conventional radiography because the image isreconstructed from something on the order of a million independent detectormeasurements. The reconstruction technique assumes that all these mea-surements are consistent, so any error of measurement will usually reflectitself as an error in the reconstructed image [7].

Two main sources which are the reason of artifacts are physical propertiesand human factor.

2.1 Physics-based Artifacts

Physics-based artifacts arise from the physics of x-ray and effects they havewith respect to characteristics of the subject of imaging.

Beam Hardening

X-rays produced in an x-ray tube (the source of x-ray in a CT-scanner device)cover a spectrum of various x-rays with different energy levels; hard x-rayshave more energy. Accordingly when a spectrum of x-rays enter the matter,hard x-rays attenuate less than soft x-rays. The result of this is an increase

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in mean energy of output rays. The result can cause so called Cupping aswell as Streak artifacts.

Cupping Artifacts

X-rays passing through the centre of a large object become harder than thosepassing through the edges of the object due to the greater amount of materialthe beam has to penetrate. Because the beam becomes harder in the centre ofthe object, the resultant profile of the linear attenuation coefficients appearsas a ”cup”. Figure 2.1 shows CT number profiles obtained across the centreof a uniform water phantom.

Figure 2.1: Cupping effect: CT number profiles obtained across the center of auniform water phantom without calibration correction [7].

Streak artifacts

The second type of artifact relating to beam hardening are dark streaks andbands between dense objects in an image. As an example in dental imaging,this type of artifact can be seen between two implants located in the same jawthat are in close proximity to each other. This occurs because the portion of

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Figure 2.2: Cupping effect: CT number profiles obtained across the center of auniform water phantom after calibration correction [7].

the beam that passes through both objects at certain tube positions becomesharder than when it passes through only one of the objects at other tubepositions. Figure 2.3 is an example of this.

To overcome this, filtration by using a physical attenuator, calibration cor-rection and software correction has been used when it comes to imagingbony regions. Another approach can be done by operator, either by patientrepositioning or gantry tilting.

Partial Volume

This artifact can happen when a dense object with high CT number locatedoff-centre, protrudes pathway into the width of x-ray beam. The algorithmsused in CT data reconstruction assume that the object is completely coveredby the detector at all view angles, and that the attenuation is caused by theobject only. When this situation does not occur, reconstructed CT imagescan contain a truncated-view artifact. Figure 2.4 addresses this issue.

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Figure 2.3: Streak artifact in CT-guided abdominal biopsy [7].

Photon starvation

When the x-ray passes through a long and non-symmetrical object, theamount of photons received in a range of specific angels would be less thanthe rest and this decrease the signal to noise ratio of the detector signal. Thereconstruction process has the effect of intensifying the noise which leads tostreaks in the photo. This phenomenon can be seen in Figure 2.5.

Increasing the current of x-ray tube solves the problem but the patient wouldbe exposed to excessive amount of radiation which is not desirable. A methodto suppress the extra radiation is called milliamperage modulation. Mil-liamperage modulation allows enough photons to be generated to overcomeattenuation resulted from widest part of the body.

Adaptive filtration, another method to enhance photon-starved images, smoothesthe attenuation profile in wide areas. This is a multidimensional adaptivetechnique developed for use on multi-section scanners.

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Figure 2.4: Partial Volume example of three 12-mm-diameter acrylic rods sup-ported in air parallel to and approximately 15 cm from the scanner axis [7].

Undersampling

One of the key factors to produce a CT image is the number of projections.Considering the back-projection theory, less projection leads to less accurateestimation of the curves and relatively small objects. In such a case an effectknown as view aliasing happens in which fine stripes appear to be radiatingfrom the edge, but at a distance from a dense structure. Stripes appearclose to the structure are more likely caused by under-sampling within aprojection, which is known as ray aliasing.

2.2 Patient-based Artifacts

Patient-based artifact addresses a type of artifacts resulted from any probableabnormality related to the body of the patient such as movement of patientduring the scanning process.

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Figure 2.5: Photon starvation in imaging of the chest area [7]. In the widest area,specialy where there are more bony parts, significantly less amount of x-ray reachthe detector

Metallic objects

Metallic objects in the scan field cause severe streak artifacts. Since thedensity of the metal is far higher than the bodily organs, this leads to in-complete attenuation profiles. When scanning denser parts of the body suchas bony organs, additional artifacts due to beam hardening, partial volumeand aliasing are likely to compound the problem.

Attenuation of metallic objects artifacts

This can be done in two different ways: avoidance by operator or by soft-ware methods.

Avoidance by operator: Patients must remove all metal objects such asjewellary unless there are non-removable items, for instance dental fillings,prosthetic device, surgical clips and DBS electrodes. In some cases, it mightbe possible to use gantry angulation to exclude metal inserts from scans ofnearby anatomy. When it is impossible to scan the required anatomy withoutincluding metal objects, increasing technique, especially kilovoltage may helpto have a better result.Software Corrections: Usefulness of metal artifact reduction software islimited since although streak artifacts further from the metal implants areremoved, there still remains a loss of detail around the metal which is oftenthe main area of diagnostic interest. Beam hardening correction softwareshould also be used when scanning metal objects to minimize the additionalartifacts due to beam hardening. This method will be discussed in depth

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later.

Patient Motion

This type can be due to voluntary motion of the patient or because ofinvoluntary motion of patient’s bodily organs. The artifact resulted frommotion called misregistration artifact. Because of the relatively long acqui-sition times (compared to conventional radiography) and volumetric imageacquisition, motion artifacts are more probable to happen. Small motionscause image blurring and larger displacements produce artifacts that appearas double images or ghost images (Figure 2.6). Involuntary or unconsciousmovements of the body of patient such as respiratory motion of diaphragm,when the gastro-intestinal system processes the food hence movements of themuscles in the colon and finally shakes of the body organs in ET (essentialtremor) patients all can be the cause of this type of artifact. The effect ofmovement of the patient can be different if the movement was continuousor if it was a one time displacement. In the latter, the ghost image is morepronounced while the other type causes more blurring effect.

2.3 Scanner-based Artifacts

The source of such artifacts is in the instrument and can occure due to thearchitecture of the device or any type misalignment in it.

Ring Artifact

In a third-generation (rotating x-ray tube and detector assembly) scanner,when one of the detectors is out of calibration, the detector will give a consis-tently erroneous reading at each angular position resulting a circular artifact.

There are more types of artifacts such as cone beam effect, stair-step artifacts,and Zebra artifacts which are less relevant to this survey.

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Figure 2.6: Patient Movement Artifact in CT image of head [7].

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Figure 2.7: CT image of a water-filled phantom shows ring artifact [7].

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Chapter 3

Localization of the DBSelectrodes

The first approach in order to localize the metallic objects in the brain issuppressing the artifacts to make the external objects distinguishable fromthe surroundings. The state-of-the-art methods for this purpose were studied.

Generally, the methods of reducing metal artifact can be categorized intotwo main groups, hardware-based methods and software-based methods.Hardware-based methods consist of incorporating two or more energy spectraand gantry angulation. Utilization of multiple energy x-rays helps to distin-guish between different materials in the sample considering the fact that theyhave different attenuation coefficient at different energy levels.

Multiple energy decomposition methods needs at least two x-ray spectra inorder to understand energy-dependent attenuation of the materials present inthe subject. Having this information provides a possibility of calculating theexact CT numbers regardless of beam hardening effect. Later these valuescan be directly used to distinguish between different materials. In gantryangulation method the scanning plane is not parallel to the canthomeatalline 1 as conventional CT scanning protocol. This helps to decrease theblockage of x-rays by metallic objects.

Software methods consist of iterative reconstruction algorithms, multiple-

1the line which connects eyes to ears

22

energy decomposition methods and sinogram based methods. Iterative re-construction techniques require a precise model of gantry, attenuation profileand the detectors. This makes this method instrument-dependent. The othermethod will be discussed in depth in the next section.

3.1 Image analysis reduction of CT artifacts

caused by metallic objects

After formation of the image in the scanner, the sinogram in-paintingmethod is the most overall efficient method in terms of practicality sinceit does not need to incorporate a dual-energy beam and is relatively compu-tationally simple. All the solutions which will be discussed later on are basedon this method. The idea is based on interpolation of non-corrupted part ofimage to extract artifact-affected parts. The simplest approach is a linearinterpolation [8]. Although the result of this approach is not so promising,this was selected as the base of further research that will be reviewed below.

3.1.1 Normalized method

In this method, the metal is first segmented in the image domain by thresh-olding. A 3-D forward projection identifies the metal trace in the originalprojections. Before interpolation, the projections are normalized based on a3-D forward projection of a prior image. These prior images are obtained byfor instance a multi-threshold segmentation of the initial images. The origi-nal raw data are divided by the projection data of the prior image and afterinterpolation, they are denormalized again. Simulations and measurementsare performed to compare normalized metal artifact reduction (NMAR) withstandard MAR with linear interpolation and MAR based on simple lengthnormalization [9].

3.1.2 Three phase method

The algorithm can be splitted into 7 steps. 1) Initial reconstruction fromthe original sinogram data; 2) Simple thresholding to identify high densityregions (e.g. metal) that can cause artifacts; 3) Delineation of correspondingregions in the original sinogram that are replaced using linear interpolation;4) Second reconstruction after the interpolation; 5) All pixels in the second

23

image that lie between 500 and +500 Hounsfield unit (HU) are replaced withthe mean of these pixels; 6) Rays in the sinogram through the metal areestimated a second time through forward projection of the segmented secondimage; 7) Third and final reconstruction.

To avoid the need for forward projection across the entire native field ofview (FOV) during step 6 above, a double-edged filter is applied in the 2-D Fourier transform (2DFT) space of the sinogram so that objects outsideof the reconstruction FOV are filtered out of the original sinogram. If kand p are the view angle and fan angle frequency variables, respectively, thedouble-wedge filter consists of setting to zero all frequencies in the 2DFT of

the sinogram for which | k

k + p| > R

L, where R is the reconstruction FOV

and L is the source-to-isocenter distance [10].

3.1.3 Incorporating intermediate image method

In this method attention is payed to segmenting the metallic object sinceit would be the base of further steps.

To have a better estimation of attenuation profiles some software such asXSPCECW2 and XCOM has been used. Since the eccentricity of the objectdirectly influences the beam hardening artifact, this has been taken intoaccount for simulation [11]. The result shows that in case of a circular cross-sectioned object there is no hardening artifact outside the object but inside(cupping artifact). As the shape drifts from the mentioned above, darkregions start to form along the long axis of the eclipse and bright regionsalong the short axis. Obviously, severity of these artifacts is proportional tothe ratio between long axis and short axis of the object (Figure 3.1).

The type of x-ray has also influence on the distribution of the artifact. Amonochromatic one has an almost even distribution in the middle while apolychromatic one cause a drop in the centre.

Because of this fact, beam hardening inversion cannot be done in the ordinaryway, for instance, the way which has been used for bone correction sincethe skull is almost round [12]. The method consists of first segmenting theartifact-affected region and later removing those parts in order to have actualdata in those regions. Certain facts are helpful in the process of segmentation:1) The artifacts are adjacent to metal pieces. 2) Amplitude of the artifactsdecreases as they get further from metal. 3) Local maxima through metal inprojection space correspond to dark artifacts.

24

Figure 3.1: Beam hardening in a round object (left) vs. a non eccentric object(centre and right) [11].

As the first step, the local extrema are identified and are later grouped byregion-growing, taking into account the distance from metal. For the localmaxima which are the result of superposition of the artifact and bone, aso-called discriminant curve is used to classify voxels.

As the matter of fact, the dark artifacts may be apart from metal when highCT-number organs are close. The third conclusion helps to find the localminima since they are correlated with local maxima. In this way even ifminima artifacts were separated from metal, still they would be detectable.

The first step is contouring the anatomy from surroundings, due to the factthat they can molest local minima. To segment the voxels of metal, the regiongrowing method was used. The voxels above 7000 HU are the region growingseeds. The maximum HU number of bodily tissues is less than 3000 HUtherefore the adjacent voxels above 3000 HU are added to the region as well.

25

Figure 3.2: Illustration of the formation of the beam hardening artifact for a metalobject with elliptical cross section [11].

This step follows by labeling each of segmented metal islands. The removal ofthe local maxima (caused by metal) done by closing-by-reconstruction (CBR)and respectively removing of minima (the artifacts resulted from presence ofmetal) by opening-by-reconstruction (OBR). CBR is a gray-scale dilationwith a certain structuring element followed by iterative erosion. OBR simi-larly performs gray-scale erosion followed by iterations of dilation. CBR andOBR eliminate the regions that are smaller than structuring element (SE),therefore the the size of SE should be two times bigger than the smallest pieceof the metal. As the next step, the resulting image is subtracted from themain image which mostly contains hard object, both bony organs and metal-lic objects. A distance-dependent thresholding helps to distinguish betweenanatomy and artifacts. The function of this thresholding is as follows:

Tdelta(x) = max(Te−aD(x), Tmin), (3.1)

D(x) is the value of the distance transform at location x and T , Tmin and a

26

are constants. In this case, T is chosen to be 5000 HU, a=0.05 and Tmin=100.These values are determined experimentally.

To recover positive artifact from bone, equation (3.2) can be used:

Ic(D) = (Imax − Imin)e−cD + Imin, (3.2)

where c is the curve parameter, Imax is the maximum value in the region andD is the distance. Imin is the minimum of the region values and an outlierbound of 200 HU (minimum CT number in artifact cluster).

The last step is deleting the dark artifacts. Assuming that the dark artifactscorrespond to local maxima, centroids and eigenvectors of negative labels arecomputed.

Figure 3.3: A comparison between intermediate-image method and prior methods[11].

This method has been tested on transverse-plane images from brain withdental filling and DBS electrodes. No test has been done on images fromsagittal or coronal planes where the shape of the electrodes would not beeccentric. Based on the provided sample images this algorithm applied on,the results are satisfying.

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Since the method is based on three main assumptions, any invalid general-ization of special cases or any possible compositional artifact resulted fromdifferent modifications on the images may subjects the results to systematicerror. Such an error leads to discrepancy between the related position ofthe metallic object and the actual position of them. A study on this matterwould define the degree of reliability of this method in regard to metallicobjects dislocation. Specially in case of multiple metallic objects, where theartifact from each of those superimposed on the others, this might violatethe assumptions which comprise the foundation of this method. Althoughthe amount of such an error might not be significant, in this applications itcan be critical.

Another question would be to what extent the structure around the metalartifacts has been preserved. Since in the generated image by CT-scan device,the information related to areas close to the metallic objects is corrupted, theonly possible option would be to change those values to gray-levels adjacenttissues in the brain. This can improve the perceptual quality of images butdoes not bring any added value to the structural details.

3.2 Proposed method: Localization of elec-

trodes by incorporating artifacts

For this end, a novel approach has been developed in this project. In theproposed method, instead of eliminating the artifacts, they are preserved andincorporated into the estimation procedure, since they are caused by metallicobjects of interest.

The principle of this method is based on detecting the straight lines formedby streak artifacts and later finding the intersection of those. As will bediscussed later, the centre of the electrodes would be among these points.

3.2.1 Brain mask

To extract the brain from the whole image, the background and skullshould be removed, as otherwise they would interfere with the detection offree paths for drawing straight lines. In order to accomplish this, first the

28

Figure 3.4: A sample of CT image of the brain with presence of the electrodes andthe streak artifacts.

29

image is converted into a black and white image. To extract the head, allthe holes in the image are filled so the brain turns into a sphere without anyhole. Later, all the background is eliminated. The head is the biggest objectand if in the black and white image all the objects with a surface less thanthe size of the head are omitted, the rest is only the brain. To remove theinner uneven areas between background and brain, morphological opening isapplied.

The next step is creating a mask to remove the skull. Since the skull overlapswith the brain and also has the same intensity as some parts of the artifactsin the brain’s area, it is not possible to treat it as the background. Bythresholding the gray-scale image with a proper value, the skull and the mainstreak artifact are distinguished. Morphological opening has been applied tothe result of the previous part to eliminate the streak artifacts. After theprevious step, some parts of the skull area also get partially deleted and, toreform the shape, morphological opening has been performed. To eliminateany remaining parts of the artifacts, morphological closing with structuringelement of a disk has been performed. At this stage, the skull is a bigconnected object, and another deletion of areas that have surface under 200pixels can eliminate all the remaining parts of deleted objects. Consequentlythe skull has been separated but in some areas it has got thinner, due tovarious operations; to make sure that no part of the skull has been eliminated,a dilation with a structuring element of a disk has been performed.

By only applying the background mask and skull mask, there would still beone area that is not supposed to be there but still exists, and that is theskin and muscles outside of the skull. This is a band between skull andbackground that can be removed by deleting the parts with an area less thanthe area of the centre part of the mask. To extract the brain from the wholeimage, it is only necessary to apply the final mask to the gray-scale image,but this will be done after the step of inverting the image.

3.2.2 Detection of straight lines

In order to detect streak artifacts which are in the form of the thin andlong isosceles trapezoid, the edge of the regions should be detected. However,ordinary edge detection cannot be used due to the offset it introduces whenapplied over the streak artifact’s strips that have a form of two coupled-rampedges but not a line. The solution to this matter is first applying a Gaussianconvolution operator to smooth the image, and then a 2-D measure of the 2nd

30

Figure 3.5: The head mask is for eliminating the background from the image ofthe head.

derivative of the image intensity along all directions by Laplacian operator.The Gaussian function is given by:

h(r) = −e−r2

2δ2 ,

where r2 = x2 +y2 and δ is standard deviation. The second derivative of thisfunction with respect to r which represent the Laplacian is:

∇2h(r) = −[r2 − δ2

δ4]e−

r2

2δ2 .

After making the lines more distinguished in the image, the latter is invertedto make the dark part of the artifacts bright, since those pass through thecentre of the electrodes.

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Figure 3.6: Brain image after applying Laplacian of Gaussian convolution opera-tor. The lines became more pronounced after applying the operator.

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Figure 3.7: The Hough transform of the brain image after applying Laplacian ofGaussian convolution operator. The horizontal axis represents the angle of thelines and the vertical axis represents the distance from the center of the lines tothe center of the image. The final lines has been indicated by blue markers.

Feeding the image to the Hough transform returns the Hough transform ma-trix that contains all the possible straight lines in the image. Figure 3.7 is theHough transform graph. Obviously, there would be many straight lines in theimage, but not all lead to a correct result. After studying the statistics of thelines and carrying out experiments with various settings, optimal parametersare extracted. The parameters consist of length of the lines, relative anglebetween them and discontinuation. Although the parameters can preciselyaddress the target lines, the settings slightly differ among various images,hence they needed to be fine tuned. To filter out the main lines, a restrictionof minimum length is applied. But even in case of main lines, there are somediscontinuation due to the noise and fluctuations in the intensity levels along

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Figure 3.8: Image of some of the lines detected by Hough transform in the CTimage of the brain (without applying the criterion). Beginning and the end of thelines are defined by yellow markers.

them, thus a gap-filling function is also introduced to merge different lineswhich follow a same line equation. The discontinuation should not exceed acertain value, otherwise it would not be considered as a discontinuation. Forangle selection, voting has been applied. By this the most dominant angle ischosen wherever there is a group of lines with close angles.

3.2.3 Selecting the main intersections

The structure of the brain is such that it might be possible for the Houghtransform to find additional lines which are not a result of the artifacts froma metallic object. Therefore, to increase the robustness of the method, more

34

Figure 3.9: Detected lines projected on the initial image of the brain.

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criteria are assessed in this phase. The first criterion is the necessity of in-tersecting with the connecting line between two electrodes, consequently thisline should be detected before any further steps. The specific characteristicof such a line is its slope which is close to the horizontal level. The numberof total intersections decreases to a small number after applying this. In thetest image, this gives only 3 intersections (Figure 3.9). The second crite-ria is the proximity of the detected intersections to the centre of the brainwhere the DBS electrodes are expected to be seen. In Figure 3.10, the twointersections indicated with red markers are the intersections of interest.

Figure 3.10: Marked intersections of electrode lines with other lines on the brain’simage.

So far, the position of the electrodes on the two dimension plane has beendefined. To find the third dimension the entire stack is fed to the algorithmfrom the inferior to the posterior of the brain. The first slice which containsthe full artifacts of the electrodes would be the tip of the electrodes and since

36

the geometry of the electrodes is known, it is possible to find the center andend of it.

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Part II

Registration of MRI and CTimages

38

Various medical images taken at different times or by various modalitiescan provide different types of information. Since these images are not iden-tical they need to be aligned in order to create a common ground for fusingthe information in the images. This process is called image registration. Theimage that is the target of registration would be the fixed image and theother one that is transformed will be the moving image.

The necessity for multi-modal image registration increase with the availabil-ity of more medical imaging equipment to the clinic [13]. Monitoring theprogress of disease or medication, targeting and dosage adjustment in radio-therapy and panoramic image creation are only some of the applications.

MRI images contain information about soft tissues while CT images containbony structures. Hence, combining these two can provide all topological in-formation needed for the study of the DBS electrodes position. However,different position of sensors in CT and MRI machines, different position-ing of the patient, different image processing techniques used in differentmachines and different slice intervals and finally the possible movement ofpatient introduce discrepancies between images from these two different im-age modalities. Hence a high level of uncertainty is expected.

The position of the imaging subject with respect to the scanning plane influ-ence the result of registration. Although there is a standard head orientationin brain imaging, some variation is expected. Even if two slices might be froma same point in the center, the viewing angle might be different. This hasbeen illustrated in Figure 3.11. Clearly having similar viewing angle helps toavoid any error resulting from this issue.

Figure 3.11: Two different imaging planes with a same-location centre point.

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Images of a same subject gathered by the same imaging device can rathereasily be registered; such an example can be two CT images taken at dif-ferent stages of medication. However multi-modality image registration isnot a trivial task. The complication of such a process is proportional tothe difference between images. Same intensity distribution of images en-ables the user to apply simple intensity based methods while lack of sucha similarity forces to incorporate more advance methods. When it comesto more complicated algorithms, great attention should be paid to certainassumptions that constitute the base of the algorithm. It is quite probablethat the algorithm would be misled by topographical differences between theimage modalities and consequently produce wrong registration. Other po-tential problems consist of trapping in local minima during the repetition ofiterations and non-unique feature selection.

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Chapter 4

Classification of registrationmethods

In order to perform method selection for this application, an overview ofvarious methods will be provided in this chapter.

Registration methods can be classified into different groups based on variouscriteria. Generally the methods to register images can be divided into twomain groups, supervised or interactive and automatic. The interactive wayis less prone to dramatic misalignment while automated methods offer fasterprocess time. Depending on the case, any of these can be applied. Therefore,for instance, in radiotherapy treatment machines both options are available.

4.1 Supervised registration

This method is based on the operator competence at adjusting parameters inorder to achieve a satisfactory result. Parameters selection is done dependingon the type of expected misalignment between the two images. Translationand rotation are common parameters to adjust. In case of volumetric image,rotation and translation consist of pitch, yaw, roll and up-down, left-right,back-forward respectively.

As in any manual method, the reproducibility needs to be investigated. Aresearch on CT and MR pediatric treatment planning head images over anine month period showed that the standard deviation of the average totaltranslation and rotation were 0.39 mm and 1.7 degrees respectively, for the

41

same operator, and 0.58 mm and 2.8 degrees among different operators. Themaximum deviation was 1.1 mm and 4.1 degrees for same operator and 1.4mm and 5.8 degrees among different operators [14].

In another comparison between manual and automated multi-modality (CT-MRI) image registration for brain tumors, manual registration showed highermisalignment between corresponding points compared to automated registra-tion using intensity matching [15]. It has been observed that larger struc-tures cause more errors. This comparison was based on fiducial methodsand 3 landmarks used in each method on 10 patients. The evaluation ofmethods was based on the amount of time spent and accuracy. Another im-portant outcome of this research is in intensity-based method, the precisionof selection of the landmarks has less impact on accuracy of the results.

Figure 4.1: Overlaid MRI (green) and CT (violet) images of the brain before reg-istration.

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4.2 Fiducial methods

In this method some area pairs are defined in both images as a referencefor registration. Later the software finds the transformation needed to alignthese areas. The number of the pairs should be 3 or more as they shouldform a triangle (not on a straight line). Identifying these points can be doneby an operator after the images were taken or by putting some landmarksinside the anatomy of the subject of imaging. The latter can provide thepossibility of an automatic method.

Decision about the positioning of the area pairs is the base of further stepsand therefore has a great influence on the accuracy of the method. Some fac-tors thar can be influential are the size of these areas, the geometric relationof them to each other as well as the surrounding areas, and the number ofthem.

Putting some landmarks before the imaging stage makes it possible to de-tect those as reference points. To enable the use of segmentation techniques,they should be distinguishable from other elements in the image. Clearlythis cannot be an option for every type of application but can be used as amethod for algorithm development.

4.3 Automatic registration

The base registration algorithm usually consists of iterative optimizationof transformation parameters based on some similarity measure and on someexit condition [16]. This method can be broken down into three main parts,(1) registration measure; (2) transformation and interpolation; (3) optimiza-tion; Overall optimality of the results is achieved by a good combination ofthese [17].

4.3.1 Registration measure

Registration based on image content can be divided into geometric ap-proaches and intensity approaches. Intensity based approaches match in-tensity patterns in each image using mathematical or statistical criteria. It

43

has been used extensively during previous years in various types of applica-tions [18]. They define a measure of intensity similarity between the fixedand the moving image and tune the transformation iteratively until the sim-ilarity measure is maximized. They assume that the images will be mostsimilar at the best registration. Measures of similarity consist of squareddifferences in intensities, correlation coefficient, measures based on opticalflow, and information-theoretic measures such as mutual information whichhas been used in this project.

Sum of Squared Differences

The simplest similarity measure is the sum of squared differences. It assumesthat the images are identical at registration except for (Gaussian) noise. Thisalgorithm works fine for applications in which images are identical and theonly difference can be in a part of the image such as a tumor. This algorithmemployed successfully for serial MR images of the brain [19].

Ratio-Image Uniformity

In Ratio-Image Uniformity, also known as Variation of Intensity Ratios (VIR),each pixel in the fixed image is divided by each pixel in the transformed im-age and this gives a ratio image, R. Later the normalized standard deviationof the ratio image is calculated in order to determine uniformity. It mightbe necessary to remove some parts of the image. This is initially developedfor PET images [20] and later extensively used for serial MR images of thebrain [21]. In the original application of PET-PET registration, it needed tosegment the brain.

Partitioned Intensity Uniformity

This technique was initially developed for MR-PET registration [22]. Theunderlying assumption of this method is that all pixels with the same MRintensity represent the same type of tissue. Therefore the correspondingintensities in the PET images should also belong to same tissues. Conse-quently, the method minimizes the normalized standard deviation of PETpixels gray-level for each MR gray-level. This method might need some pre-processing steps for instance to improve the success rate of this method inMR-PET registration, the extra-dural tissue should be removed [23].

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Joint histogram

Joint histogram is formed from two or more images. The number of im-ages defines the dimension of the histogram. The axes indicate the differentgray-levels (intensity levels) ranging from black (darkest level) up to white(brightest level). Each point represents the number of voxels with a particularcombination of intensities in the different spectral components [18]. In otherword, each point in the joint histogram represents the corresponding valuein two images. To have the joint probability distribution function (PDF)of intensities the joint histogram needed to be normalized. The most reli-able similarity measures calculated from the PDF are based on informationtheory.

Entropy

In information theory, the Shannon entropy h is a measure of the uncertaintyin a random variable [24]. For a distribution of the probability p on a the setx1, x2, ..., the entropy is defined as [25]

h(p) = −∑i≥1

pi log pi. (4.1)

More specifically, in image analysis, entropy is a measure of histogram dis-persion. A mono-level gray image has an entropy with only one element inthat specific gray level. On the contrary, an image with many gray levels hasan entropy with as many elements as the image has. By merging the entropyof two images, a joint entropy can be created. To follow this method thevalue of joint entropy in (4.2) should be minimized.

h = −∑i,j

PDF [i, j] logPDF [i, j]. (4.2)

Mutual information

As mentioned before, entropy is calculated based on a common part of theimages (p ∈ A∧B) and this part changes after each iteration of entropy min-imization. Therefore, the histogram that is the base for calculating the PDFalso changes. This phenomenon makes the latter method not reliable for all

45

types of applications, especially intra-modality registration. The solution tothis matter is another measure from information theory, mutual information(MI) [26] [27]. Mutual information goes one step further and normalizes thejoint entropy with respect to the partial entropies of the contributing signal.In image analysis, MI measures the change of the intensity of the histogram.

h(A) =∑i

(∑j

PDF [i, j] logk PDF [i, k]), (4.3)

h(B) =∑j

(∑i

PDF [i, k] logj PDF [j, k]). (4.4)

Then the mutual information of image A and B, MI(A,B) would be:

MI(A,B) = H(A) +H(B)−H(A,B). (4.5)

Figure 4.2: An example of the two registrations of MRI images of the brain. Eachaxis on the joint histograms represents the gray levels on corresponding images,between 0 and maximum value (white). The left diagram shows misaligned imagesand the right diagram shows a better alignment of the same images. Denser areashave a color closer to red, proportional to their density [28] .

As it can be observed, the registration algorithm tries to minimize the spar-sity of the joint histogram.

46

Typically intensity-based methods incorporate just a subset of pixels sinceit is not feasible to use all. Due to this fact and to avoid aliasing, the im-age might needed to be blurred as a preprocessing step. Another issue thatburdens the algorithm is bit-depth of pixels. Depending on modality, imagescan have ten, twelve or sixteen bits of intensity levels. Such a great numbermakes the calculations unnecessary heavy; hence intensity-levels can groupedinto a smaller number of sets called the bin. Furthermore, the image can besegmented. The latter can decrease the probability of misregistration bynarrowing the pixel selection subset to a certain region or certain character-istics. This is much dependent on the type of modality and body organ beingimaged. It is also possible to use higher order information derived from theintensity of pixels such as gradients. Consequently all these methods makealgorithms application-specific and the latest research trend in this field is togeneralize algorithms.

Geometric approaches build explicit models of identifiable anatomical ele-ments in each image. These elements typically include functionally importantsurfaces, curves and point landmarks that can be matched with their counter-parts in the second image. These correspondences define the transformationfrom one image to the other. The use of such structural information ensuresthat the mapping has biological validity and allows the transformation to beinterpreted in terms of the underlying anatomy or physiology [29].

4.3.2 Registration transformations

From the point of view of the type of voxels movement, registration meth-ods can be divided into two different groups, (1) rigid-body transformation;(2) deformable transformation. In the rigid transformation, maximum de-grees of freedom can be three in 2-D (along the x and y axis as well asrotation) and six in 3-D (along the x,y and z axis, pitch, yaw and roll) whilein the deformable this number increases dramatically. Therefore several sim-plified algorithms are proposed to overcome this complexity [30].

The rigid transformation has three degrees of freedom (DOF) in 2-D and sixDOF in 3-D. Transformations include translation and rotation.

47

Affine transformation

In geometry, an affine transformation or an affinity is a transformation whichpreserves straight lines (i.e., all points lying on a line initially still lie on aline after the transformation) and ratios of distances between points lying ona straight line. It does not necessarily preserve angles or lengths, but doeshave the property that sets of parallel lines will remain parallel to each otherafter an affine transformation.

Scaling transformation

This type is in between the rigid and the affine transformation. In this type,in addition to translation and rotation, scaling is also included. Scaling canbe along different axis and independent. For instance, it can be performedalong one of the axis or more. There is a specific type of scaling transforma-tion, named similarity, in which scaling along all axes is the same why theaspect ratios stays constant.

4.3.3 Interpolation

After transformation, pixels might migrate to a new position thereforefinding the gray value of a certain pixel at a non-integer-valued locationis necessary. Interpolation can be a relatively heavy computational task,especially for advanced types, therefore it would be a trade off between betterresults in terms of accuracy and sharpness of the image versus computationtime.

Common interpolation techniques applicable in this field ranging from simpleto hard are nearest neighbor, bilinear and bicubic. There are higher ordertypes which take into account more surrounding pixels such as spline andsinc interpolation. All non-adaptive techniques are prone to three types ofartifacts, edge halos, blurring and aliasing.

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Figure 4.3: A comparison between a rigid body registration including scaling (lefthand side image) versus affine registration (right hand side image).

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Chapter 5

Proposed registration method

In this project the goal is finding the counterpart of each point of MRIimages in the CT images. This gives the estimation of the position of eachpoint of the CT image in the MRI image. Hence the CT modality is themoving and MRI would be the fixed one. The general registration methodused for this part is an intensity-based method. For multi-modality registra-tion, mutual information based on the joint histogram should be used as theregistration measure since the intensity maps differ between the two modali-ties. To select a type of transformation, images from the two modalities havebeen studied. Later, both rigid and non-rigid registration is applied to theimages from the same slices. Both visual inspection of the results and theentropy numbers of registered and interpolated images indicated that a bet-ter alignment has been resulted from the non-rigid method. In the exampleshown in Figure 4.3, the entropy values related to non-rigid plus scaling andaffine registration methods were 4.4287 and 4.1821, respectively.

The base registration algorithm iteratively optimizes the transformation pa-rameters based on similarity measure and exit condition. As an optionalpre-processing step for registration and to achieve better results, histogrammatching can be performed. The algorithm is shown in Figure 5.1

Expected geometry discrepancies in this project are the geometry distortionin MR resulted from gradient nonlinearity and the imperfections in the B0field1 [31] and geometry distortion in CT due to bed speed and gantry tiltangle. Affine transformation supports all the functionality needed to handle

1The invariant magnetic field for creating magnetization

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Figure 5.1: The algorithm of the method for registration of CT/MRI images of thebrain for DBS application.

the expected deformations.

5.1 Implementation of geometric transforma-

tions

One of the problems in the field of robotics is the kinematic of the roboticarms, i.e. finding the movement of the robot at different joints. The verysame problem needs to be formulated in image registration. A combinationof several simple transformations forms a complex transformation needed forregistration of one image to another.

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An advance but yet convenient representation of transformations is matrixform. It has several advantages such as convenience of factoring a complextransformation into a set of simple transformations and similar representa-tion as in Matlab software. Some of the transformations are linear and someare not. This would be problematic when it comes to combining severaltransformations together. The solution to this incompatibility is having ahomogeneous coordinates by adding one dimension to all linear transforma-tions. Subsequently, all pixel coordinates need to be represented in 3-D. Itcan be done by adding a 3rd identical coordinate to the normal 2-D vectors.The resulting vector is as follows:

xy1

(5.1)

To translate the point (x, y) in 2-D to a new position (x′, y′) by adding thevector [f, g], the translation matrix would be

1 0 f0 1 g0 0 1

(5.2)

The result of multiplication of the rotation matrix for rotating (x, y) for αangle is

cosα − sinα 0sinα cosα 0

0 0 1

(5.3)

Scaling in the isotropic from does not change the aspect ratio of the im-age, however the general form of it supports anisotropic scaling as well. Inisotropic form, the scale factor along the x axis, s and the scale factor alongy axis s are equal. The following matrix is a representation of the scalingtransformation

52

sx 0 00 sy 00 0 0

(5.4)

.

Shear offsets a set of points, proportional to their distance from a certainaxis. This defines the related transformation matrix as

1 hx 0hy 1 00 0 1

. (5.5)

Clearly in case of applying several transformation, order of transformationsis important.

Calculation of joint PDF

To calculate the joint PDF for two images the following steps need to befollowed.

1) Define an a by b array JH[a,b] (floating point data type); 2) Reset allelements of JH to zero; 3) For every pixel p which belongs to both images(p ∈ A ∧ B ) calculate the intensity numbers A(p) and B(p), calculate theintensity partition numbers a and b related to A(i) and B(i); 4) Calculate∑

i,j JH[i, j]; 5) Calculate the PDF by normalizing the joint histogram:

PDF [a, b] =JH[i, j]∑i,j JH[i, j]

(5.6)

Since pixels have very diverse intensity levels and there is no added value inhaving a very fine step for calculating the joint histogram, the full range ofintensity levels is divided into 50 bins.

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Bilinear interpolation technique has been used. Bilinear interpolation is anextension of linear interpolation to 2-D and does three linear interpolationcalculations for each pixel. Due to a relatively low rate of pixel-intensitychange in the brain images, nearest neighborhood interpolation has also asatisfactory result for this part, yet delivers a slightly lower quality than theformer one.

5.2 Medical images file formats

There are variety of medical image formats and it seems inevitable tostudy them before performing experiments since different software and med-ical imaging devices use specific formats that are not necessarily compatiblewith each other. This matter is one of the unforeseen issues that can causedelays in research projects. The following is a brief overview of commonformats.

Digital Imaging and Communications in Medicine (DICOM)

The recent medical devices mostly produce files in DICOM format (*.dcm).The header of a file contains meta-data about device, settings, image infor-mation, patient information and some application-specific data. All this in-formation has to be set otherwise the related field would be empty. Regardingpatient confidentiality issue, some software provides a patient anonymizationfeature that allows to delete all patient information from a file. Dicom readersoftware can recognize the presence of a series of images in the same directoryand make a sequence out of them which can be observed in a series.

Nearly Raw Raster Data (nrrd)

The flexible nrrd format includes a single header file and image file(s) thatcan be separated or combined. A Nrrd header represents N-dimensionalraster information for scientific visualization and medical image processinghence recently has been used more in relevant software. However with someconvertors, the dicom files generated with the following machines can beconverted to nrrd file format. Philips scanner/software version combinations:Achieva 2.1.3.6, Achieva 2.5.3.0, Achieva 2.5.3.3, Achieva 2.6.1.0, Acheiva2.6.3.4, Intera 2.1.3.6, Intera 2.6.3.5, Siemens: Trio B13, Trio B15, Trio

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B17, Verio B15V, GE: SIGNA HDx14.0, SIGNA HDxt 15.0, DVMR 20.0M4,DVMR 20.1.

Neuroimaging Informatics Technology Initiative (NIfTI)

The NIfTI image format standard was designed for scientific analysis of brainimages. The format is simple, compact and versatile. The images can bestored as a pair of files (hdr/img, compliant with most analyse format view-ers), or a single file (nii).

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Chapter 6

Discussion and Conclusion

The state of the art overview on the possibility of elimination of streakartifacts resulting from metallic objects in the bodily organs when imagedby a CT-scanner showed that after the completion of the scanning processit is not possible to precisely recover all the altered pixel-intensities sincethose data have been lost during the image formation process. However itis possible to correct some of the corrupted intensity levels by applying acombination of various algorithms, but this cannot be an absolute reliableground for localizing the DBS electrodes inside the brain.

Although the resulting image from the Sinogram methods seems to be sat-isfying, it might be subject to modification due to secondary artifacts anddisplacement of the center of the mass of the electrodes in the image; thusit brings no added value for this application. Therefore, in the proposedmethod, it is suggested to locate the electrodes directly by studying the arti-facts resulting from them. Digital medical images contain more informationcompared to other types of data in computer systems and this makes pro-cessing them a relatively heavy task even for modern computers. In thejunction method, after finding the lines, further calculations are performedon these regions and not on the entire image; this makes the algorithm byfar more responsive compared to the methods in which the whole image dataare involved in all calculations.

Detecting the streak artifact’s lines is performed by considering the wholelength of the line. Therefore local fluctuations in the image cannot disturbit. In addition, the long length of lines help to reduce the angular freedom(play) of the lines. The latter is one of the error sources in estimating the

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electrode position.

In the available image-set, the thickness of each slice is 2.5 mm which meansthat the objects in the slice can be anywhere in this spatial volume. In otherwords, the object which is present in a specific slice can be somewhere be-tween the highest or the lowest points in the range. This factor can introducean estimation error up to 2.5 mm along the axis which is perpendicular tothe transverse plane.

This algorithm is able to estimate the position of the electrodes on an imageconstructed from only two projections from different angles. Evidently thisdramatically decreases the dosage of x-ray absorbed by the patient. Never-theless the combination of many projections and a high level of noise in theimage has a negative effect on the robustness of this method. To overcomethis an imaging protocol can be suggested.

Regarding the registration of CT-scan to MRI images, intensity-based reg-istration algorithms have a more general use than the other counterparts interms of intra-modality usages. An information-theoretic measure, mutualinformation, is incorporated to implement the non-rigid affine transforma-tion. Therefore, the scaling and shear capabilities of this transformationsupport mismatch of image sizes from different modalities as well as geomet-ric distortions. Although a higher order of transformations can provide moredegrees of freedom, they are more prone to invalid registration.

Regular image artifacts can be handled by the proposed method. Neverthe-less, specific artifacts resulting from the vibration of bodily organs demandtransformations with a higher DOF. The available MRI images set from thepatients with implanted electrodes have a significantly lower dynamic rangeand signal-to-noise ratio, making the task of registration more challenging.Better quality images can improve the accuracy of the registration.

In the field of image registration, quantitative verification is still an openquestion. However, reaching the global minima and avoiding local minimatraps can be used as a measure for assessing the algorithm. Since varia-tion in the input images can have a major influence on the performance ofthe algorithm, it is better to assess the algorithm with respect to a specificdataset.

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Future work

Reduction of the thickness of slices in the imaging stage significantly im-proves the accuracy of the estimation of the position of the electrodes. An-other study that could improve the results is correlating the partial presenceof the electrodes in a slide with the amount of artifact it induced. A simu-lation of attenuation of Iridium with XCOM software can be a useful inputto this calculation. By achieving this, it would be possible to improve theaccuracy of estimation by software methods and reduce the total dosage ofx-ray delivered to the patient. Incorporating adaptive methods in the linedetection stage and specifically in order to tune the Hough transform param-eters will improve the robustness of the method against noisy and imperfectimages.

In regard with assessment of the accuracy of the position estimation, onereliable way is using a head phantom with embedded fiducial markers. Toavoid artifacts, plastic markers are suggested as a reference. With the helpof a neuroscientist, developing geometric approaches would be possible as analternative to intensity-based approaches in image registration. In the samemanner, it is also possible to compare the proposed registration method withfiducial-based methods side by side; this can reveal the advantages of eachmethod in terms of accuracy, robustness, and universality.

In some cases of DBS surgery, due to leakage of air inside the head, the rela-tive distances drift. This issue has direct influence on the result of registrationhence this should be taken care of in such a case. Possible solutions can besegmentation of those areas in order to isolate them from the process of reg-istration, masking the post-operative images with the help of pre-operativeimages and finally introducing landmarks as reference for registration.

Further proposals regarding DBS

This study can be helpful in understanding the correlation between thedistribution and strength of electrical field versus the efficiency as well as theside effects of the treatment. One of the best tools for study the distributionof electrical field is COMSOL software. Segmentation of the surroundingtissue around the electrodes in order to study the flux of the electrical fieldin various parts of the brain considering the type of tissues in each point is astep forward to improve the accuracy and validity of such a goal. In a longer

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perspective, all this information can facilitate the development of future andless-invasive types of surgery.

Further general proposals

Deriving a higher order of information either in the form of an image ora set of data from the subject of registration can be efficient in order toprovide generic or more accurate measures for registration. Intensity-basedalgorithms have been extensively applied to rigid transformations but thereis still much more space for work on non-rigid types of transformations.

With the combined view on the physical space and the medical imaging data,augmented reality (AR) visualization can provide perceptive advantages dur-ing image-guided surgery (IGS). The proposed algorithm is fast enough to beused in real-time applications even during the surgery in order to preciselynavigate the electrodes to the intended position by a surgeon manually or bya robotic arm.

In a more general sense, with today’s availability of significantly higher pro-cessing power in embedded systems, image registration can be used to in-crease in real-time the resolution, dynamic range, signal-to-noise ratio andFOV of relatively narrow-angle imaging sensors.

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Bibliography

[1] Essential tremor, Genetics Home Reference. June 2013.

[2] Kessler RC Asmundson GJ Goodwin RD Kubzansky L Lydiard RBMassie MJ Katon W Laden SK Stein MB. Roy-Byrne PP, Davidson KW.Anxiety disorders and comorbid medical illness. general hospital psychi-atry, 2008.

[3] Dystonias fact sheet. Technical report, Nationalinstitutes of health, U.SDepartment of health, 2012.

[4] Mattias Astrom. Modelling, Simulaltion, and Visualization of DeepBrain Stimulation. PhD thesis, Linkoping University, 2011.

[5] Masood Ahmed. Generation of CT scans. Technical report, Aga KhanUniversity Hospital Karachi, 2009.

[6] Development of CT imaging, Philips. Technical report, 2006.

[7] Julia F. Barrett and Nicholas Keat. Artifacts in CT: Recognition andavoidance1. Radiographics, 24(6):1679–1691, 2004.

[8] R. Hebel W. A. Kalender and J. Ebersberger. Reduction of CT artifactscaused by metallic implants. Radiology, 1987.

[9] Esther Meyer, Rainer Raupach, Michael Lell, Bernhard Schmidt, andMarc Kachelriess. Normalized metal artifact reduction (NMAR) in com-puted tomography. Medical Physics, 37(10):5482–5493, 2010.

[10] S. Mazin and N. Pelc. Metal artifact reduction algorithm for xray ctusing a threepass approach. Medical physics, 2009.

[11] Seemeen Karimi, Pamela Cosman, Christoph Wald, and Harry Martz.Segmentation of artifacts and anatomy in CT metal artifact reduction.Medical Physics, 39(10):5857–5868, 2012.

60

[12] Spital RD Joseph PM. A method for correcting bone induced artifactsin computed tomography scanners. 1978.

[13] Schlegel W Hartmann GH Sturm V Strauss LG Lorenz WJ Schad LR,Boesecke R. Three dimensional image correlation of CT, MR, and PETstudies in radiotherapy treatment planning of brain tumors. journal,1987.

[14] Jaap Vaarkamp. Reproducibility of interactive registration of 3D CTand MR pediatric treatment planning head images. JOURNAL OFAPPLIED CLINICAL MEDICAL PHYSICS, 2001.

[15] Smith R. Kassaee A. Sarkar A., Santiago RJ. Comparison of man-ual vs. automated multimodality (ct-mri) image registration for braintumors. JOURNAL OF THE AMERICAN ASSOCIATION OF MED-ICAL DOSIMETRISTS, 2005.

[16] Marco La Cascia Liliana Lo Presti Edoardo Ardizzone, Orazio Gambinoand Roberto Pirrone. Multi-modal non-rigid registration of medicalimages based on mutual information maximization. IEEE computersociety, 2007.

[17] Guang Li and Robert W. Miller. Volumetric image registration of multi-modality images of CT, MRI and PET. 2008.

[18] Milan Sonka and J. Michael Fitzpatrick. Medical image processing andanalysis, Handbook of Medical Imaging. SPIE Press.

[19] Soar EJ Oatridge A Young IR Bydder GM Hajnal JV, Saeed N. Aregistration and interpolation procedure for subvoxel matching of seriallyacquired MR images.

[20] J. C. Mazziotta R. P. Woods, S. R. Cherry. Rapid automated algorithmfor aligning and reslicing pet images. Journal of computer assisted to-mography, 1992.

[21] N. C. Fox P. A. Freeborough. The boundary shift integral: an accurateand robust measure of cerebral volume changes from registered repeatMRI. IEEE Transactions on Medical Imaging, 1997.

[22] S. R. Cherry R. P. Woods, J. C. Mazziotta. MRI-PET registration withautomated algorithm. Journal of computer assisted tomography, 1993.

[23] M. Y. Wang B. M. Dawant C. R. Maurer Jr. R. M. Kessler R. J. Maciu-nas C. Barillot D. Lemoine A. Collignon F. Maes P. Suetens D. Vander-meulen P. A. van den Elsen S. Napel T. S. Sumanaweera B. Harkness P.

61

F. Hemler D. L. G. Hill D. J. Hawkes C. Studholme J. B. A. Maintz M.A. Viergever G. Malandain X. Pennec M. E. Noz G. Q. Maguire Jr. M.Pollack C. A. Pelizzari R. A. Robb D. Hanson J. B. West, J. M. Fitz-patrick and R. P. Woods. Comparison and evaluation of retrospectiveintermodality brain image registration techniques. Journal of computerassisted tomography, 1997.

[24] Shunsuke Ihara. Information theory for continuous systems,. WorldScientific ISBN 978-981-02-0985-8, 1993.

[25] Keith Conrad. Probability distributions and maximum entropy, 2004.

[26] D. Vandermeulen G. Marchal F. Maes, A. Collignon and P. Suetens.Multimodality image registration by maximization of mutual informa-tion. IEEE Transactions on Medical Imaging, 1997.

[27] P. Viola H. Atsumi S. Nakajima W. M. Wells, III and R. Kikinis. Multi-modal volume registration by maximization of mutual information. Med-ical Image Analysis, 1996.

[28] Pierre-Malick; Migneco Octave. Darcourt, Jacques; Koulibaly. Exploringthe central nervous system: methodological state of the art. Alasbimn,2005.

[29] T. HARTKENS PhD W. R. CRUM, D. Phil and PhD D. L. G. HILL.Non-rigid image registration: theory and practice. The British Journalof Radiology, 2004.

[30] Max A. Viergever Josien P. W. Pluim, J. B. Antoine Maintz. Mutual-information-based registration of medical images: a survey. IEEE Trans.Med. Imaging, 2003.

[31] Stefan A. Reinsberg Simon J. Doran, Liz Charles-Edwards and Mar-tin O. Leach. A complete distortion correction for MR images: I. Gradi-ent warp correction. PHYSICS IN MEDICINE AND BIOLOGY, 2005.

[32] J. D. Leea W. C. Huanga S. T. Leeb C. T. Wub Y. N. Sunc C. H. Huanga,C. H. Hsieha and Y. T. Wud. A CT-ultrasound-coregistered augmentedreality enhanced image-guided surgery system and its preliminary studyon brain-shift estimation. Journal of instrumenttion, 2012.

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