Fast Wavelet-Based Multiresolution Image Registration on aMultiprocessing Digital Signal Processor

Hao Wu, Yongmin Kim

Image Computing Systems Laboratory, Department of Electrical Engineering, Box 352500,University of Washington, Seattle, WA 98195

ABSTRACT: Image registration is a fundamental task in image pro- the images are most similar to each other. Most current researchcessing. It is used in matching two or more images taken at different on image registration is focused on two aspects of this searchtimes, from different imaging modalities, or from different viewpoints. process: the similarity measure and the search strategy.One of the obstacles in achieving practical acceptance of image regis- Among the various similarity measures that exist, the cross-tration techniques is their computational complexity, which results in correlation coefficient is the most frequently used [1,2,4,7,13,14].a long response time. In this article we present a fast multiresolution

A far more computationally efficient similarity measure based onimage registration algorithm using wavelet transform for the transla-the sum of absolute differences between the pixels on the twotional and rotational alignment of two-dimensional images. In particu-images was proposed by Barnea and Silverman [22]. Venot andlar, a novel approach to determine the algorithm parameters to bal-Leclerc [4] introduced two similarity criteria based on signance the registration accuracy and computational requirement is also

described. We implemented this algorithm on a PC-based multimedia changes: the deterministic sign change (DSC) criterion and theand imaging system using a multiprocessing digital signal processor. stochastic sign change (SSC) criterion. Applications of theseThe algorithm is capable of achieving a subpixel registration accuracy similarity measures could be found in their later work on photo-reliably under various noise levels. The multiresolution algorithm im- graphic images [6] and medical imaging [10]. More recently,plemented on this desktop system was able to register two 256 1 Chiang and Sullivan [23] proposed a new similarity measure256 images in 466 ms, which is 40 times faster than the uniresolution called coincident bit counting (CBC), which is based on theexhaustive search approach. q 1998 John Wiley & Sons, Inc. Int J Imaging

number of matching bits between the corresponding pixels ofSyst Technol, 9, 29–37, 1998two images.

Key words: image registration; wavelet; multiresolution; multi- Common search strategies include decision sequencing andprocessing DSP; multimedia; imaging system multiresolution techniques. Barnea and Silverman [22] intro-

duced a search technique called the sequential similarity detectionalgorithm (SSDA). The multiresolution search strategy analyzesI. INTRODUCTIONimage data at several coarser resolutions, thus making the number

Image registration plays an important role in a number of applica- of computations tractable [24]. Oghabian and Pokropek [7] de-tions where images with relative spatial transformations need to veloped a multiresolution algorithm to register sets of MR im-be compared to extract further information. Applications can be aging (MRI), positron emission tomographic (PET), and singlefound in the areas such as medical imaging [1–11], remotely photon emission computed tomographic (SPECT) images. Mallatsensed data processing [12–15], motion estimation [16], docu- [29] developed a new technique to provide efficient multiresolu-ment imaging [17], and automated inspection [18,19]. For exam- tion image representations based on the wavelet transform. Djam-ple, Van den Elsen et al. [1] developed a correlation-based auto- dji et al. [14] used this technique for registration of remotelymatic registration technique to match computed tomographic

sensed satellite image data. Unser and Aldroubi [25] performed(CT) and magnetic resonance (MR) brain images. Le Moigne

registration and statistical analysis of PET brain images using the[13] described an image registration method that allows the com-

wavelet transform.bination of data from coarse-resolution and fine-resolution sen-

Even though quite a few registration techniques are theoreti-sors in satellite imaging. Casey and Ferguson [17] described an

cally well developed and have demonstrated their feasibility inintelligent form processing system where image registration is

many application fields, their fast implementations have not beenessential in extracting data from the fields in a form. A lot of effort

well addressed. Le Moigne [13] implemented a multiresolutionhas been dedicated to developing image registration methods, and

registration algorithm on a single instruction multiple datatwo extensive surveys [20,21] have been published recently.(SIMD) parallel computer, the MasPar MP-2. The MasPar MP-Given a priori knowledge about the transformation between2 is a fine-grain, massively parallel computer with 16,384 pro-the images, the registration process is an ordered search over allcessing elements arranged in a 128 1 128 matrix and connectedallowed transformations to find the transformation under whichby an 8-nearest neighbor interconnection network. It registerstwo 512 1 512 images in 10 s. Van den Elsen et al. [1] and Tran

Correspondence to: Y. Kim and Sklansky [5] discussed the possible implementation of their

q 1998 John Wiley & Sons, Inc. CCC 0899–9457/98/010029-09

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Table I. Performance of 2D image registration algorithms on different computer systems.

Author Image Size Processor Performance

Tran, 1992 [5] 512 1 512 MicroVAX II GPX 240 minVan den Elsen, 1995 [1] 256 1 256 HP 9000 Model 715 190 minCosta, 1994 [8] 256 1 256 SUN SpracStation 1 10 minOghabian, 1991 [7] 256 1 256 MicroVAX II 6–7 minMedioni, 1991 [18] 640 1 640 Mercury array processor 5 minVenot, 1988 [6] 256 1 256 AP 120B array processor 2–5 minLe Moigne, 1995 [13] 512 1 512 MasPar MP-2 10 s

algorithms on parallel-structured hardware to speed up the execu- direction, resulting in four subband images: Xll , Xlh , Xhl , and Xhh .Xll is a coarse version of the input image X . Xlh , Xhl , and Xhhtion time, but none of such implementations and their results

have been reported so far. Performance of image registration emphasize the image features in the horizontal, vertical, and diag-onal directions, respectively. The filtering and downsampling pro-on various computer platforms as reported in the literature is

summarized in Table I. cess can be recursively applied to the low-resolution subband Xll

until the desired resolution level is reached.Selection of the multiresolution algorithm parameters is ofgreat significance to the registration accuracy and execution timeof the algorithm. However, systematic research results on this B. Multiresolution Registration Algorithm. The flow of our

2D multiresolution registration algorithm is shown in Figure 2.issue are seldom found in the literature. Chetverikov and Lerch[26] studied the choices of the multiresolution algorithm parame- A reference image R(x , y) and an input image I(x , y) to be

registered with the reference image are input to the algorithm.ters. Their experiments used computer-generated binary contourimages, which limited their applicability in applications using Both R(x , y) and I(x , y) are of the same image size. This image

size becomes the finest resolution of the images. We model thegray-level images.In this article, we introduce a multiresolution two-dimensional rigid transformations between the reference and input images

with a rotation around the center of the image in the range [0u,(2D) image registration algorithm using wavelet transform andan experiment protocol to determine the algorithm parameters. u] and a translation in the range [0T , T] in both x and y directions.

Here, [0u, u] and [0T , T] specify the rotation angle and transla-The experiment results and the performance of the algorithmimplemented on a high-performance programmable parallel digi- tion limits, respectively.

The algorithm begins with computing the pyramidal wavelettal signal processor (DSP) (Texas Instruments TMS320C80) arepresented. decomposition of both the reference and input images using

QMFs up to the level L . The lowpass images at each resolutionlevel are denoted as Ri and Ii , i √ [1, L] , for the reference andII. METHODSinput image, respectively. These lowpass images together with

A. 2D Pyramidal Wavelet Decomposition. Grossmann andthe images at the finest level R(x , y) and I(x , y) , i.e., R0 and I0 ,

Morlet [27] introduced wavelets as functions generated from oneform a pyramidal representation used in our image registration

single function (mother function) c by dilations and translationsalgorithm.

of the form Ca ,b( t) Å [1/√aC(( t 0 b) /a)] , a √ R/ , b √ R , At the coarsest level of the pyramid (level L) , the reference

where a is a positive real scaling parameter and b is a real shift image RL and the input image IL are compared at all possibleparameter. Meyer [28] showed that there exist special choicesof wavelets C whose translations and dilations, Cj,k( t) Å 20j /

2C(20jt 0 k) , j , k √ Z , constitute an orthonormal basis of avector space of measurable, square-integrable 1D signals.

Mallat [29] showed that a multiresolution representation of asignal can be computed by decomposing the signal using a wave-let orthonormal basis. He also showed that wavelet decompositionmay be accomplished with a pyramidal algorithm based on con-volutions with quadrature mirror filters (QMFs). Figure 1 illus-trates the pyramidal decomposition of a 2D image by cascadingtwo 1D wavelet transforms along the x and y axes. Let HV be thediscrete lowpass filter with impulse response hU n and GV be thehighpass mirror filter with impulse response g

V n . The 2D imageX is first filtered along the horizontal direction by convolving theimage data with filters HV and GV , resulting in lowpass- and high-pass-filtered images. These two resulting rectangular subbandimages are then downsampled by a factor of two (dropping everyother filter output) along the horizontal direction. Next, both Figure 1. Pyramidal wavelet decomposition of a 2D image using

QMFs.subband images are filtered and downsampled along the vertical

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to be 8 bits /pixel. Higher-order filters like D6 usually result inbetter quality approximations at the cost of more computations.

The rotation involves both the spatial transformation and thegray-level interpolation. Bilinear interpolation provides a goodbalance between the computation cost and the smoothness of therotated image compared to the other interpolation techniques suchas nearest neighbor and cubic convolution. The similarity mea-sure based on the minimum sum of the absolute differences be-tween the pixels in the two images has been demonstrated byBrown [20] and Barnea and Silverman [22] to be computation-ally simpler than the correlation measure, and is used in ouralgorithm.

Our multiresolution image registration algorithm requires theuser to input the following parameters: translation limits [0T ,T] , rotation angle limits [0u, u] , the coarest resolution level L ,and the search range parameters Du and Dt . The algorithm wasimplemented on the Texas Instruments TMS320C80-based multi-media system MediaStation 5000 [31] at the Image ComputingSystems Laboratory of the University of Washington. TheTMS320C80 is a fully programmable multiprocessor with morethan 2 billion operations/s, (BOPS) computing power designedas a next-generation digital signal processor (DSP) [32,33].

C. Algorithm Parameter Estimation. Our multiresolutionregistration algorithm has three variable parameters: the coarestresolution level L and the search range parameters, Du and Dt .A large L means faster execution since the registration starts witha small image size which results in less computation for both theFigure 2. Flow chart of the multiresolution image registration algo-image interpolation and the similarity measurement. However,rithm.the discrimination between the reference and input images be-comes less reliable and even undetectable at coarse resolutionlevels when many relevant features are severely blurred owingto the lowpass filtering nature of the decomposition process. Therelative positions using a predefined similarity criterion. At this

resolution level, the possible relative positions are combinations same tradeoff applies to the choice of Du and Dt . Small Du andDt values lead to less computation in interpolating the image andof rotation in [0u, u] and translation in [0T /2L , T /2L] along

both x and y directions. The best transformation parameters found measuring the similarity at the risk of missing the best registra-tion. Therefore, the judicious choice of these parameters is ofat this level producing the maximum similarity measure are de-

noted as (uL , tx ,L , ty ,L) . importance to the balance of the registration accuracy and compu-tational cost. The goal of our study here was to find the largestAt the next higher-resolution level ( level L 0 1), the search

for the best registration is performed with a greatly constrained possible starting level L and smallest search range parametersDu and Dt , such that when these parameters are used in ourset of transformation parameters with rotation in [uL 0 Du, uL /

Du] and translation in [2tx ,L 0 Dt , 2tx ,L / Dt] for x and [2ty ,L 0 algorithm, the output is essentially the same as that of the conven-tional registration using exhaustive search.Dt , 2ty ,L / Dt] for y . Du and Dt are called the search range

parameters for rotation and translation, respectively. The result If we start registration from a certain resolution level K andthe differences between the best transformation parameters atof the search at level L 0 1 is used for the search at the next

higher level of resolution L 0 2. This process is iterated until adjacent resolution levels are always within a certain range de-noted by DuK and DtK , then K is qualified to be a starting resolu-the finest scale corresponding to the original image resolution is

reached. The best transformation parameters (u0 , tx ,0 , ty ,0 ) are tion level, and DuK and DtK can be used as Du and Dt . Thelargest K found in this way and the associated DuK and DtKoutput as the registration parameters to establish the geometric

correspondence between the given reference image and the input are then used as the starting resolution level and search rangeparameters in our algorithm.image.

The QMFs used for wavelet transform are specified by a set Given a set of images from an imaging source, we can system-atically study the coherence of the best transformation parametersof numbers called wavelet filter coefficients. Here, we restrict

ourselves to a class of wavelet filters constructed by Daubechies between the adjacent resolution levels as summarized in the fol-lowing experiment protocol. This protocol has been implemented[30]. In this class of wavelet filters, D4 is the simplest and most

localized member with only four coefficients. D4 was chosen in in the C programming language on a SUN SparcStation 20.this study for the QMFs for fast execution of the decomposition,since the shorter the filter size, the less the computation cost. The 1. Select one reference image from the data set.

2. Generate a set of random transformation parameters (u*,current implementation of D4 wavelet requires the input images

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Table II. Registration results with the Lenna image.

Known Transformation Registration Error

Test No. u tx ty du dtx dty

1 0.4 9.5 7.4 0.2 0.1 0.22 9.7 9.1 2.8 0.1 0.1 00.23 05.7 5.0 02.6 00.1 00.2 0.24 1.0 1.2 11.6 0.0 0.0 0.05 13.4 04.5 5.3 0.0 00.1 0.16 09.8 1.2 0.0 0.0 0.0 0.07 6.1 09.3 03.4 00.1 00.3 00.28 08.2 9.0 07.1 0.2 00.2 0.39 00.1 012.8 05.8 0.1 0.2 0.0

10 011.3 0.0 08.5 00.1 0.2 00.1

The starting resolution L is 3 where the image size is 64 1 64. Du Å 47 andDt Å 2 pixels. The final step size in the parameter space at the finest resolutionlevel is 0.27 for the rotation and 0.4 pixels for the translation.

for rotation and [015, 15] pixels in both x and y directions fortranslation.

A. Registration Error Analysis. First, to validate our algo-Figure 3. 512 1 512 1 8-bit Lenna image. rithm and quantitatively measure the performance of the algo-

rithm, experiments using Lenna in Figure 3 as the reference imagewere performed. Transformation parameters found by the regis-tration algorithm are compared to the known transformation con-

t*x , t*y ) from a uniform distribution over the parameter sisting of rotation u ( in degrees around the center of the image)space specified by [0u, u] and [0T , T] pixels in both x and translations tx and ty ( in pixels in the x and y directions) .and y directions for the rotation and translation, respec- Table II shows the results obtained with 10 tests with the transfor-tively. Apply the transformation to the reference image. mation parameters randomly selected from a uniform distribution

3. Decompose both the reference and the transformed refer- over the parameter space. du, dtx , and dty are the differencesence image up to level L using D4 wavelet. between the transformation found by the algorithm and the known

4. Perform an exhaustive search at each resolution level i Å transformation. The results indicate that the errors for the esti-0, L , and record the best transformation parameters (ui , mated angle of rotation and translations do not correlate with thetx ,i , ty ,i ) using the minimum sum of absolute difference actual rotation and translation, and they tend to spread aroundcriterion. zero evenly. In all the 10 cases that we have considered, the

5. Calculate and record Dui Å ui01 0 ui , Dxi Å tx ,i01 0 2tx ,i maximum translation difference is 0.3 pixels and the maximumand Dyi Å ty ,i01 0 2ty ,i , i Å 1, L . rotation angle difference is 0.27.

6. Repeat Steps 2–5 for different transformation parameters. Second, to investigate the robustness of our multiresolutionIn our experiment, 150 different sets of parameters areused.

7. Repeat the above for other reference images in the data setTable III. Registration results with the Lenna images while the whiteand accumulate Dui , Dxi , and Dyi , i Å 1, L .Gaussian noise with two different standard deviations is added.

Registration ErrorIII. RESULTSs Å 100 s Å 255A sequence of experiments were performed to verify the perfor-

mance of the multiresolution registration algorithm and evaluate Test No. du dtx dty du dtx dtythe algorithm parameter estimation approach. The images used

1 0.2 0.1 0.2 0.2 0.1 0.2in the experiments are the 512 1 512 1 8-bit Lenna image and2 00.1 0.5 00.2 00.1 0.5 0.8256 1 256 1 8-bit MR brain images. The MR images were3 0.1 00.2 0.2 0.1 00.4 0.2acquired using a General Electric Signa 1.5-T (GE Medical Sys-4 0.0 0.4 0.0 0.0 0.4 0.2

tems, Waukesha, WI) whole-body scanner. The parameters for 5 0.0 0.1 0.3 0.0 0.1 0.3T1-weighted images were pulse repetition time (TR) of 500 ms 6 0.0 00.4 0.6 0.2 0.4 0.6and echo time (TE) of 17 ms. The field of view was 22 1 22 7 0.1 00.1 0.0 0.0 00.3 0.0cm. The acquired data were originally 12 bits /pixel and then 8 0.2 0.6 0.7 0.2 0.6 0.7

9 00.1 0.4 0.4 00.1 0.4 0.4transformed to 8 bits /pixel using the window and level values10 00.1 00.2 0.1 00.1 00.4 0.1of 256 and 128, respectively, as suggested by the physicians

examining the images. For all the experiments in this article, we The pixel values are clipped to 0 (for all negative values) or 255 (for all valuesexceeding 255). The same algorithm parameters are used as in Table II.assume that the parameter space is specified by [010, 10] degrees

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Figure 4. Three 256 1 256 1 8-bit magnetic resonance images selected for the algorithm parameter estimation experiments.

registration algorithm in the presence of noise, we performed the These images were used as the reference images in the experi-mental protocol described in Section IIC. The experimental re-same experiments as in Table II while adding white Gaussian

noise with a standard deviation of s to the transformed Lenna sults of Dui , Dxi , and Dyi , i Å 1, L , with a starting resolutionlevel L Å 4 are plotted from Figures 5–7. These histograms ofimage. The results are summarized in Table III. The first observa-

tion is that the estimated parameters become less accurate as the the differences of the best transformation parameters betweenadjacent resolution levels are used in selecting the right startingnoise level is increased, which is to be expected. When the stan-

dard deviation of the Gaussian noise is 100, the maximum transla- resolution level and search range for the algorithm parameters.We start with analysis of Dui , i Å 1, 4. Du4 records thetion difference increases to 0.7 pixels from 0.3 pixels. However,

even under a very severe noise condition where s is 255, the difference between the best rotation angle at resolution Levels 4and 3. Figure 5(a) shows that Du4 ranges from 0107 to 107 withalgorithm remains robust with the largest error õ0.8 pixels and

0.27 for translation and rotation, respectively. a standard deviation of 6.77. This means that the best rotationangle at resolution Levels 4 and 3 are not well correlated. Conse-quently, no matter what rotation angle has been found by anB. Estimating Algorithm Parameters. Three representative

slices shown in Figure 4 were selected from the MR data set. exhaustive search at the resolution Level 4, another exhaustive

Figure 6. Histogram of the differences between the best translationFigure 5. Histogram of the differences between the best rotationangles in two adjacent resolution levels: (a) Du4 Å u3 0 u4 ; (b) Du3 Å in x direction in two adjacent resolution levels: (a) Dx4 Å tx ,3 0 2tx ,4 ;

(b) Dx3 Å tx ,2 0 2tx ,3 ; (c ) Dx2 Å tx ,1 0 2tx ,2 ; (d) Dx1 Å tx ,0 0 2tx ,1 .u2 0 u3 ; (c) Du2 Å u1 0 u2 ; (d) Du1 Å u0 0 u1 .

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C. Execution Time on TMS320C80. The performance of ourmultiresolution algorithm implemented on TMS320C80 is a func-tion of the image size, the starting resolution level L , and therotational and translational search ranges, Du and Dt . The execu-tion times on TMS320C80 for 256 1 256 and 512 1 512 imageswith different starting resolution levels and different Dus and Dtsare shown in Figures 8–11. Registration with a starting resolutionLevel L Å 2 begins with an exhaustive search with an image sizeof 64 1 64 and 128 1 128 for 256 1 256 and 512 1 512 images,respectively. The execution time increases nearly linearly withDu and Dt regardless of the starting resolution level. For 256 1256 images, the slopes are about 80 ms/degree of rotationalsearch range increase and 260 ms/pixel of translational searchrange increase, while for 512 1 512 images, the slopes are 300ms/degree and 1300 ms/pixel for rotation and translation, respec-tively. These findings suggest that an increase in the translationalsearch range is more than three times computationally expensivecompared to an increase in the rotational search range. It is inter-esting to observe that the execution time difference between twostarting resolution levels remains relatively constant with respectto Dus and Dts. When the same set of Du and Dt is used, theexecution time difference between starting resolution Levels 1and 2 is approximately 400 and 2300 ms for 2561 256 and 5121512 images, respectively. For 512 1 512 images, the D4 waveletdecomposition for two levels (128 1 128 image size) for thereference and input image takes 23.8 ms each. The executionFigure 7. Histogram of the differences between the best translationtimes for image transformation and similarity measurement atin y direction in two adjacent resolution levels: (a) Dy4 Å ty ,3 0 2ty ,4 ;

(b) Dy3 Å ty ,2 0 2ty ,1 ; (c ) Dy2 Å ty ,1 0 2ty ,2 ; (d) Dy1 Å ty ,0 0 2ty ,1 . different resolution levels are summarized in Table IV. It takeslonger at resolution Level 2 than Level 1 owing to the exhaustivesearch performed at a starting resolution Level L Å 2. Also,

search would be necessary not to miss the best rotation angle atthe finer resolution. Therefore, Level 4 does not qualify to be astarting resolution because the discrimination between the refer-ence and input images becomes too blurred to provide meaningfulinformation on the best rotation angle. The same argument is truefor Level 3 even though the standard deviation of Du3 is 4.57,which is smaller than 6.77 owing to an improved spatial resolu-tion. Level 2 serves as a qualified starting resolution level sinceDu2 falls into a range of {4.07, as shown in Figure 5(c) . Thisrange leads to a search range of 47 to reduce the number ofpotential rotation angles at resolution Level 1 without the risk ofmissing the best rotation angle. Similar reasoning applies to thetranslation variables. From Figures 6 and 7, we can see that thedifference between the best translation at adjacent resolution lev-els is no more than {2 pixels. Therefore, a search range Dt of2 pixels can be specified as the search goes from one resolutionlevel to the next finer resolution.

In summary, a starting resolution level of 2, 47 for the rotationangle search range Du, and 2 pixels for the translation searchrange Dt can be used as input parameters for the multiresolutionregistration algorithm to register MR brain images. For 256 1256 MR images used in our experiment, when the final step sizein the parameter space at the finest resolution level is 0.47 ofrotation and 0.4 pixels for the translation, our algorithm imple-mentation on TMS320C80 was able to register two images in Figure 8. Performance for 256 1 256 image registration with differ-466 ms, which is 40 times faster than the uniresolution exhaustive ent Du values while Dt Å 2 pixels. The final step size in the parametersearch approach, which took 18.6 s on TMS320C80 to obtain the space at the finest resolution level is 0.47 of rotation and 0.4 pixels

for translation.same registration results.

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Figure 10. Performance for 5121 512 image registration with differ-Figure 9. Performance for 256 1 256 image registration with differ-ent Du values while Dt Å 2 pixels. The same final step size in theent Dt values while DuÅ 47. The same final step size in the parameterparameter space at the finest resolution level is used as in Figure 8.space at the finest resolution level is used as in Figure 8.

has also been tried for registration of CT images and the similarowing to the finer step sizes as well as a large number of pixels, results were obtained. Therefore, we conclude that this algorithmit takes much longer at a resolution Level 0, taking 76% of the can be generalized to other imaging modalities such as X-rays,total execution time. PET, ultrasound, and satellite images.

IV. DISCUSSION AND CONCLUSIONS

In this article, we have presented a fast and robust algorithm toregister 2D images of the same scene with a rigid geometrictransformation (rotation and translation). According to the classi-fication scheme proposed by Van den Elsen et al. [21], ourmethod is classified as 2D, intrinsic, global, rigid, approximating,search-based, and automatic. Special attention has been given tothe determination of the algorithm parameters. We also carriedout an experimental evaluation of the algorithm and its implemen-tation on a powerful multiprocessing DSP, TMS320C80.

The closest related work was described by Le Moigne [13].Compared to her work, our approach differs in three ways. First,our search for the registration parameters was performed on thelow-resolution subband instead of the high-frequency subbands.Second, the minimum sum of absolute difference similarity crite-rion described by Barnea and Silverman [22] was used in ouralgorithm instead of a correlation measure. Third, our multiresolu-tion registration algorithm was implemented on a single DSP chipinstead of a massively parallel processor, the MasPar MP-2.

Our algorithm uses wavelet transform to obtain the multireso-lution representations of images and performs a coarse-to-fineimage registration. The algorithm is capable of achieving a sub-pixel registration accuracy as shown in Table II. Unlike otherimage registration techniques [1,9,13,15] based on features ex- Figure 11. Performance for 5121 512 image registration with differ-tracted from the reference and input images, only the gray-level ent Dt values while DuÅ 47. The same final step size in the parameter

space at the finest resolution level is used as in Figure 8.information is used in our registration algorithm. This algorithm

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Table IV. Execution times for image transformation and similarity measurement at different resolution levels.

Execution Time

Resolution Image Image SimilarityLevel Size Transformation Measurement Total

2 128 1 128 26 ms 269 ms 295 ms1 256 1 256 24 ms 98 ms 122 ms0 512 1 512 214 ms 995 ms 1309 ms

Dt Å 2 pixels and Du Å 47. The same final step size in the parameter space at resolution level L Å 0 is used as in Figure 8.

The results in Table III show that the algorithm is robust in given images from a specific application, applying this approachenables us to determine the algorithm parameters judiciouslythe presence of noise. Since a complete and rigorous study of the

noise in the images is quite difficult to perform, white Gaussian based on the statistical information on the differences of the besttransformation parameters between adjacent resolution levels,noise is assumed in this study. As expected, the accuracy of the

registration decreases when the noise level goes up as shown in thus eliminating any possibility of failure in our registration algo-rithm.Table III. However, when the standard deviation of the Gaussian

noise increases to 100 and 255, there is only a slight increase in Another distinctive contribution of this work is the implemen-tation of the multiresolution algorithm on a multiprocessing DSPthe registration error compared to that without any noise (Table

II) . This result is not too surprising if one considers the smoothing TMS320C80. By combining the fast image registration algorithmand the flexible and powerful Texas Instruments TMS320C80, itnature of the coarser-level approximations of the input images

via wavelet transform. The effect of the noise is almost impercep- takes only 466 ms to register two 256 1 256 MR images com-pared with the same multiresolution algorithm taking 55.3 s ontible at coarser levels of the multiresolution pyramid. This makes

the algorithm quite robust when the noise is present. a SUN SparcStation 20, which is 119 times faster, as shown inTable V. Table V also shows the detailed breakdown of theThe algorithm performs coarse-to-fine image registration, and

only the best transformation parameters are used in specifying the algorithm performance into the execution times of major mod-ules. Compared to the Le Moigne’s implementation of D4 waveletsearch space in the next finer resolution. Therefore, this iterative

method is somewhat sensitive to the result of the full search at transform [13] on the MasPar MP-2 with 16,384 parallel pro-cessing elements, where four decomposition levels took 25.4 ms,the coarsest resolution level as demonstrated by Unser and Al-

droubi [25]. They also demonstrated that the multiresolution the same algorithm with four decomposition levels with a 512 1512 image on TMS320C80 takes 26.7 ms, demonstrating theapproach may not converge to the right registration parameters

if the best transformation parameters found at the coarest resolu- computing power of the TMS320C80 in image-processing appli-cations. Van den Elsen et al. [1] developed a feature-based corre-tion level are too far from the true ones. This problem is often

caused by the improperly chosen algorithm parameters: in partic- lation method to register MR and CT images. They stated thatthe major drawback of their method, which takes 3 h and 10ular, the starting resolution level. If the level is chosen to be too

coarse, the similarity measure may not be meaningful since the min to run on an HP 9000 series Model 715 machine, is thecomputational resources needed. Figures 8–11 show the perfor-relevant features presented on the reference and input images

are so blurred by the smoothing effect. To tackle this, we have mance of our multiresolution algorithm on a high-performanceparallel DSP, TMS320C80. This kind of computing power en-developed and presented an experimental approach to determine

the algorithm parameters including the starting Level L and the ables algorithms previously taking minutes or hours to be com-pleted in only a few hundred milliseconds or a few seconds, thussearch range parameters Du and Dt . This approach has also been

applied to other groups of images such as CT, PET, and satellite greatly facilitating the applications of various image registrationalgorithms. Furthermore, the fully programmable feature of theimages, and similar results were obtained. Thus, we conclude that

Table V. Detailed breakdown of algorithm performance into execution times of major modules for a 256 1 256 imageon TMS320C80 and SUN SparcStation 20.

Algorithm TMS320C80 SUN SparcStation 20

Wavelet decomposition 21 ms 4.2 s

Resolution Level 2 Image transformation 6 ms 0.8 s49 ms 6.9 s

Similarity measurement 43 ms 6.1 sResolution Level 1 Image transformation 8 ms 0.9 s

36 ms 5.2 sSimilarity measurement 28 ms 4.3 s

Resolution Level 0 Image transformation 75 ms 7.9 s360 ms 39.0 s

Similarity measurement 285 ms 31.1 sTotal 466 ms 55.3 s

The same algorithm parameters are used as in Table IV.

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of images: The multiresolution approach,’’ Photogram. Eng. RemoteTMS320C80 makes it a very flexible DSP on which differentSens. 59, 645–653 (1993).algorithms (e.g., image filtering, segmentation, compression) can

15. J. Flusser and Y. Suk. ‘‘A moment-based approach to registration ofbe implemented with high efficiency as it is for the image registra-images with affine geometric distortion,’’ IEEE Trans. Geosci. Re-tion. This type of multiprocessing DSPs would facilitate practicalmote Sens. 32, 382–387 (1994).acceptance of a wide range of image processing and computer

16. Q. Zheng and R. Chellappa. ‘‘A computation vision approach tovision applications because it provides a retargetable programma- image registration,’’ IEEE Trans. Imag. Process. 2, 311–326 (1993).ble solution for computationally intensive image-processing ap- 17. R. G. Casey and D. R. Ferguson. ‘‘Intelligent forms processing,’’plications with a constantly improving cost /performance ratio. IBM Syst. J. 29, 435–449 (1990).

18. G. Medioni and A. Huertas. ‘‘Automatic registration of color separa-REFERENCES tion films,’’ Mach. Vision Appl. 4, 33–51 (1991).

19. A. A. Rodriguez. ‘‘Image registration for automated inspection of 2D1. P. A. Van den Elsen, J. B. A. Maintz, E. D. Pol, and M. A. Viergever.electric circuit patterns,’’ SPIE Proc. 1384, 2–11 (1990).‘‘Automatic registration of CT and MR brain images using correlation

20. L. G. Brown. ‘‘A survey of image registration techniques,’’ ACMof geometrical features,’’ IEEE Trans. Med. Imag. 14, 384–396Comput. Surv. 24, 325–376 (1992).(1995).

21. P. A. Van den Elsen, E. D. Pol, and M. A. Viergever. ‘‘Medical image2. E. F. Fitchard and P. A. Narayana. ‘‘Two-dimension registration ofmatching—a review with classification,’’ IEEE Eng. Med. Biol. 12,magnetic resonance brain images,’’ Med. Phys. 21, 1333–133726–39 (1993).(1994).

22. D. I. Barnea and H. F. Silverman. ‘‘A class of algorithms for fast3. J. Noack and D. Sutton. ‘‘An algorithm for the fast registration ofdigital image registration,’’ IEEE Trans. Comput. 21, 179–186image sequences obtained with a scanning laser ophthalmoscope,’’(1972).Phys. Med. Biol. 39, 907–915 (1994).

23. J. Y. Chiang and B. J. Sullivan. ‘‘Coincident bit counting—a new4. A. Venot and V. Leclerc. ‘‘Automated correction of patient motioncriterion for image registration,’’ IEEE Trans. Med. Imag. 12, 30–and gray values prior to subtraction in digitized angiography,’’ IEEE38 (1993).Trans. Med. Imag. 3, 179–186 (1984).

24. R. L. Allen, F. A. Kamangar, and E. M. Stokely. ‘‘Laplacian and5. L. V. Tran and J. Sklansky. ‘‘Flexible mask subtraction for digitalorthogonal wavelet pyramid decompositions in coarse-to-fine regis-angiography,’’ IEEE Trans. Med. Imag. 11, 407–415 (1992).tration,’’ IEEE Trans. Signal Process. 41, 3536–3540 (1993).6. A. Venot, J. Y. Devaux, M. Herbin, J. F. Lebruchec, L. Dubertret,

25. M. Unser and A. Aldroubi. ‘‘A multiresolution image registrationY. Baulo, and J. C. Roucayrol. ‘‘An automated system for the registra-procedure using spline pyramids,’’ SPIE Proc. 2034, 160–170tion and comparison of photographic images in medicine,’’ IEEE(1993).Trans. Med. Imag. 7, 298–303 (1988).

26. D. Chetverikov and A. Lerch. ‘‘A multiresolution algorithm for rota-7. M. A. Oghabian and A. T. Pokropek. ‘‘Registration of brain imagestion-invariant matching of planar shapes,’’ Pattern Recog. Lett. 13,by a multi-resolution sequential method,’’ in IPMI ’91 Proceedings,669–676 (1993).1991, pp. 165–174.

27. A. Grossmann and J. Morlet. ‘‘Decomposition of Hardy functions8. W. L. S. Costa. ‘‘A maximum-likelihood method for PET emission/into square integrable wavelets of constant shape,’’ SIAM J. Math.attenuation image registration,’’ MSEE thesis, University of Wash-15, 723–736 (1984).ington, Seattle, WA, 1994.

28. Y. Meyer. ‘‘Principe d’incertitude, bases hilbertiennes et algebres9. S. D. Kugelmass, C. H. Labovitz, and E. A. Hoffman. ‘‘Cardiac imaged’operateurs,’’ Bourbaki Seminar, no. 662, 1985–1986.registration via global and local warping,’’ SPIE Proc. 1905, 75–81

29. S. G. Mallat. ‘‘A theory for multiresolution signal decomposition:(1993).The wavelet representation,’’ IEEE Trans. Patt. Anal. Machine Intell.10. M. Herbin, A. Venot, J. Y. Devaux, E. Walter, J. F. Lebruchec, L.11, 674–693 (1989).Dubertret, and J. C. Roucayrol. ‘‘Automated registration of dissimilar

30. I. Daubechies. ‘‘Orthonormal bases of compactly supported wave-images: application to medical imagery,’’ Comput. Vision Graphicslets,’’ Commun. Pure Appl. Math. 41, 909–960 (1988).Image Process. 47, 77–88 (1989).

31. W. Lee, Y. Kim, R. J. Gove, and C. J. Read. ‘‘MediaStation 5000:11. J. A. Correia. ‘‘Editorial: Registration of nuclear medicine images,’’Integrating video and audio,’’ IEEE Multimedia 1, 50–61 (1994).J. Nucl. Med. 31, 1227–1229 (1990).

32. K. Guttag, R. J. Gove, and J. R. VanAken. ‘‘A single chip multiproc-12. M. D. Pritt. ‘‘Automated subpixel image registration of remotelyessor for multimedia,’’ IEEE Comput. Graphics. Appl. 12, 53–64sensed imagery,’’ IBM J. Res. Dev. 38, 157–166 (1994).(1992).13. J. Le Moigne. ‘‘Towards a parallel registration of multiple resolution

33. J. Kim, Y. Kim, R. J. Gove, and J. Golston. ‘‘Performance evaluationremote sensing data,’’ Int. Geosci. Rem. Sens. Symp. 2, 1011–1013of a single-chip DSP-based multimedia system using the Abingdon(1995).

14. J. P. Djamdji, A. Bijaoui, and R. Maniere. ‘‘Geometrical registration Cross benchmark,’’ Opt. Eng. 35, 2905–2911 (1996).

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