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Introduction To Image Processing In BiologyWS-2014/15 Uni-Konstanz (1-March-2015)

Optimal Edge-Based Shape Detection

Waleed AbrarUni-Konstanz

Abstract:-

Object detection is always a classical problem in image

processing and people are always looking for betterways to detect the objects and to improve the

performance of already developed algorithms for

detection.

This paper tried to bridge the gap as to find

the optimal way for 2-d object detection based on the

fundamental principles of object detection, which isedge detection, and as edge detection is the base stone

for object detection, whose high level application are

object recognition. So to optimize the process of object

detection we need to optimize the process of edge

detection.

This report summarize the report regarding optimal

based edge detection, how do they achieved their goalswhat are the preconditions for their algorithm to work.

And this report also covers the pros and cons of this

paper according to my perspective. This report also

covers evaluation of their work and future developments

in this field as it is relatively an old paper

Keywords

Edge Detection, Derivative of Gaussian (DOG), Double

derivative of Exponential function (DODE), Profiling,

Filtering, Smoothing operators

1.

Motivation:-

All edge base shape detection methods are effected by

the same problem that some information is lost duringthe process of edge formations or we can say edge

detection. Because the parameters are not defined based

on looking at the stats of the signal fidelity and the

algorithms are not smart enough to choose the optimal

parameters based on the distortion of the original signal.

So mostly the parameters are chosen globally, so theydidnt present the true picture of the scenario so author

of this paper decided to address that issue and come up

with optimal parameters to finally bridge the gap

generated at the lowest possible level of imageprocessing.

2 Introduction:-

Fig: 1 Showing Lenna on the left and edges on the right

Lets look at the picture above you can see that even if

we removing most of the pixels from the left image we

can still understand the content of the picture (on the

right) like this picture is of a lady who is wearing a hat

and more, so we can easily conclude that edges in fact

represent the most interesting areas of the image.

Research in the field of human eye suggest that human

peripherals at the lowest possible level are also working

on principles of edge processing that helps us recognize

and categories things after wards and build the

connections.[1]

Now let me explain the Regions or

contours R that give us the description about the edges.So a Region R is a set of connected (4 or 8 or n

connectivity) pixels that have the same neighbors or

relatively same neighbors.

Fig: 2 showing concept of 4 and 8 connectivity [2].


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So you can see from the above figure that if the pixels are

same as compared to the central pixels then those pixels

are considered to be in the Region R if one or more

pixel in R thats different from the rest of the pixels then

those pixels are called and boundary pixels.

Now you have understood the concepts of boundary so

edges are mostly the candidates from the boundary

regions, Sometime whole boundaries are considered as

edges but in some cases some thresholding throws a little

bit of those pixels.

There are many types of Edges some of the important one

are Roof edge, step edge and ramp edge. Step edges are

the ideal edges because they are good in localization and

they exist mostly in test images. I will explain the

Localization and detection in next section. Roof edge is

basically, when pixels are converging from dark to grey

and then instead of bright they turn dark again. Ramp

edges are mostly what we deal with in most of the images

as instead of a sharp change in the image its from dark to

less dark and eventually ending up to bright pixels or vice

versa. Following figure show different types of edges

explained above with their orientation.

Fig: 3 Different types of Edges along with Orientation [3].

Normally there are two problems that relates to the

process of Edge extraction. Edge detection and edge

localization. To detect the shape optimally we need to find

out the optimal way for not only finding the edges but also

to localize the edges which mean how to represent, some

of the properties attached to the edges are its length, width

and thickness.

First derivative gives if there exist an edge or not but the

problem is there is a little bit of noise then the edge

detection via this process is nearly impossible. See figure

below [1]

The first column represent 4 signals with little bit of

Gaussian noise. First row has the Step edge, the ideal so

detection with the first derivative is the best and so is the

localization. But as you can see from the rest of the rows

as soon as the noise is added to the system the process

edge detection and localization is nearly impossible.

Mostly DOG (Derivative of Gaussian) or DOB

(Derivative of Box) are used for the detection and

localization process. But the author of this paper hascome up with quantitative measures that the DODE

(Double derivative of Exponential function) gives better

results than both of them. And to get the better detection

we need optimal parameters for de-noising the image.

3 The Procedure of Optimal based shape

detection:-

One dimensional smoothing operator:

Step 1:-

Where F is the output frequency, the procedure is done

for one dimension smoothing operator which was later

extended to multiple dimensions, In the last equation one

can easily see that we need to find the optimal h for

both the values of X(edge ) along with the additive noise

N.

MSE (Mean squared error in term of frequencydomain can be represented as)


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Step 2:-

Where =Radian Frequency Represent the distortion from the equilibrium

position.

As you can see from 2 is using absolute values for theangular frequencies which is later divided into both veand positive part. After wards 1 is subtracted from the

angular frequencies because of the Amplitude values. For

MSE output 2we continue with the absolute values.And () and () are spectral densities of Xand N

Step 3:

Apply Wiener filter to minimize criterion function which

is demonstrated below

Step 4:

As we have the step edge and the white noise so

applying the values from the frequency domain we have

the optimal filter as defined below.

Where:

d =

= magnitude of step edge

= Phase shift of cosine signals

Step 5:

Extending the one dimensional smoothing operator to

two dimensions

4

Extension of Optimal smoothing filter to

arbitrary shapes and Profiling Responses:-

The author of the paper modelled intensity changes at an

object boundary as a step function (where the changes

are rapid) and some of the assumptions for the models

are that the boundary smooth or simply a connected

contour.

Let image be represented as -

-- (A)

Here D is simply a connected region representing the

shape before moving

Following is a flow diagram of connected component

analysis used is the paper firstly its for a pixel that

doesnt belong to background

The algorithm starts by giving the image (I) as an input

function then each of its pixels are scanned .Then each

pixel are checks to see if they dont belong to background

Then their neighbours are checked for component

initialization if neighbour is already labeled then assign

parent label to new pixel if not assign new label during

the first iteration.

Component relabeling step and re classification


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Shuffling of pixel labels continue until all pixels are

labelled and no pixel are left which are not added to the

list

The below example elaborate the process for more

understanding of the process.

Initial step:-

Fig: 4 Binary images to show the working of CCA algorithm

Segmentation and initialization step:-

This first row and column tell about the index

values of the stored label initially we start withcopying a new matrix equally to size of given

image and initializing all with zeros except the first

element

I cant explain all the iteration steps hers so just

describing the output result where are pixels are labelled

according to the connectivity. Its like a water flow and

strong regions are connected with the same region number

Final step:-

All regions of the image are assigned the labels according

to the connectivity. So now moving on with the rest of

the procedure where we left at (A)

The boundary C =D be parameterized as

Which explain mostly the intensity differences and l is

the level function. Then the Shape operator is inserted in

position and the responses are collected at the centroid of

the operators then maximum response is chosen as an

indication to the presence of the particular shape.

Fig: 4 Response profiles of shapes

0 1 2 3 4

0 1 0 0 0 0

1 1 1 0 0 0

2 0 1 1 0 0

3 0 1 1 0 0

4 0 1 0 0 1

0 1 2 3 4

0 1 0 0 0 0

1 0 0 0 0 0

2 0 0 0 0 0

3 0 0 0 0 0

4 0 0 0 0 0

0 1 2 3 4

0 1 2 2 2 2

1 1 1 2 2 2

2 3 1 1 2 2

3 3 1 1 2 2

4 3 1 2 2 4


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6 Major Applications of Optimal edge based

Shape detection:Some Major application for this optimal based shape

detection are already mentioned in the paper I will

mention them but I will extend them to the biological

perspective as the seminar is dealing with a major part in

biology for that so I read couple of other papers [4] and

[5] .

1) Cars Detection from Areal images:Its can detect the shape of cars and categorize

them which in turn help us in looking forparking space problem, like rather to expand the

area or not is there is enough space or not.

2) Optimal face Detection:-Instead of tracking the whole face which might be

computationally inefficient we can work or

particular shapes in image like eyes eyebrows andnose and based on their position categorize a face

or a non-face which is way efficient and can

remove some restriction about orientation noise aswe are looking for targeted features as explained

in the paper.

3) Contour Detection and active Contours:-As the author have shown that the algorithm work

really well for edge localization which is biggest

problem in fine detailed image as edges are

overlapping and make no sense. So using this

technique will solve those problems as thistechniques use the optimum filtering so all the

representation is preserved as shown in figure 13

of paper.

4) Selective object tracking :-We can use the knowledge of profiling to track

efficiently any object as any object has someorientation and that orientation can fall into any

category of shape which can be added to the

algorithm to lower the problem of false alarms

which is a big worry in object detection.

5) A synthetic Genetic Edge DetectionProgram[6]:-A genetic circuit such as one mentioned in the

paper is using special engineered light sensors toget the light between light and dark regions andduring the process of diffusion the tracking become

really difficult so using thins algorithm can

enhance some of the problems created during

transfusion or diffusion of the substance and one

can track the moment accurately because detection

here is not a big deal, localization is important.

6) Marine microorganism Monitoring [4]:-As microorganism are really hard to visualize and

so are equally hard to localize or detect, in this

paper they are using temperature changes to give

them more hints about the presence or absence of

microorganism, which can be given as a parameter

to the profile and once those best maxima are

found we can use them efficiently for tracking of

even micro organisms

7) Culture Study in bacterium semi-automatedimage analysis [5].

Initially I was not really sure if the algorithm can

really be used in this situation but as I progressed

.CCA (connected component analysis 9 part can

be used but not sure about the whole algorithm as

there are so many factors involved and the changes

are very slow per frame and I am not sure it might

approximate the minute change as they didnthappen which is not we want but with some

manual parameters which can be set by the user it

can be used in certain aspect.

7 Some limitation and a little comparison to

other methods:-

Limitation:-

This paper is doing most of its calculation on DODE

based on MSE and I have recently read this paper [7]

which elaborated the advantages and disadvantages ofusing MSE and in terms of image fidelity it can cause alot of problem, like even small or big changes can effect

MSE and it doesntreflect the true picture. For example

look at the picture below [7]

In the first column a is the reference image then some

noise and disorientation is added and its effect on MSE

is described like in 2 image from top left (b) MSE is 306and in last image of the first column the MSE is 309 then

look at the third from right image in the second column

we have and MSE of 308 and most astonishing result

was in the picture right next to it here the MSE is 694

.which indicate a high distortion but when we see the

image in almost similar to the original picture , so thisapproach of using DODE can in some situation not be

right to use.

-As some of the results are not extraordinary, especiallyin terms of detection of actual edges, once can improvethat performance and leave the localization as it is and

then those results could still match the performance of

this algorithm as it will compensate for edge localization


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Comparison to other methods:-

Last semester I worked with Igor in the field of

straight line detection[8] and I can say that lines canbe of more value than edges, whatever we do in theend we still need some kind of thresholding in caseof depending solely on edge detection because theremight be so many false alarms . The work of thatpaper was really wonderful as edges are detected

and based on criteria called line support region putin a category to form a line. Gradient orientation is

used for the first time to explain some majorchanges across the image.

The process of line formation is explained in theabove picture along with that process manyattributes related to edges which were missing inthis paper are utilized in the (Extraction of straight

line paper) some of these attributes are edge length, steepness, sharpness ,orientation and more.

Personally if you ask me I would not totally dependupon the information provided by the edges but the

profiling concept is the real deal which I thinkadded value to their work. I personally recommendHough transform extension for shape detectionbecause they are better in every aspect.

6 Future works:-As I have mentioned during my talk there are many

alternative to MSE it would be really interesting to extend

this algorithm to incorporate any new method other than

MSE and compute the results there might be a few

surprises waiting. And as far as the second

recommendation I am 100 % sure it would be amazing

and give results in positive side and reduce the problem of

false alarms during object detection in 2-d if we combine

the power of CW-SSIM [7] complex wavelet structuresimilarity index with the profiling concept explained in this

paper . It will definitely minimize the false alarms if not makethem zero.

Final Word:

Paper was really well written and I enjoyed reading it but

some of the figures are really hard to understand because

of the poor visibility and visualization method chosen by

the authors. I hope this report covers mostly all aspects of

the paper in detail and some other suggestions from my

side if some want to continue working in that domain.

7 References:-

[1] Ghosh, K., Sarkar, S., & Bhaumik, K. (2007). TheTheory of Edge Detection and Low-level Vision inRetrospect. INTECH Open Access Publisher.

[2]www.cs.auckland.ac.nz/courses/compsci773s1c/lectures/ImageProcessing-html/neighbourhoods.gif

[3]http://campar.in.tum.de/twiki/pub/Chair/TeachingWs05SegmentationRegistrationHauptseminar/02DoychevEdgesFeaturesHandout.pdf

[4] B. Zhang, G.S. Sukhatme, A.A. Requicha, Adaptivesampling for marine microorganism monitoring, in:

IEEE/RSJ International Conference on Intelligent Robots

and Systems, 2004.

[5] H. Daims and M Wagner, Quantification of

Uncultured Microorganisms by Fluorescence Microscopy

and Digital Image Analysis, Appl. Microbiol.

Biotechnol., 75, 23748 (2007).

[6] Tabor J, et al. A Synthetic Genetic Edge DetectionProgram. Cell.2009;137:12721281.

[7] Z. Wang and A. C. Bovik, Mean squared error: Loveit or leave it? A new look at signal fidelity measures,

IEEE Signal Processing Magazine, vol. 26, no. 1, pp. 98117, Jan. 2009.

Book consulted:-

Gonzalez, R. C., & Woods, R. E. (2002). Digital image

processing. Prentice Hall, 10, 12-23.


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