Matlab Graphic User Interface for image

segmentation using Markov random fields and

entropy estimation with parallel processing.

Osvaldo Gutierrez Mata

Instituto Tecnol6gico Superior de Fresnillo Fresnillo, Zacatecas, Mexico

osvaldo _gtz _ mt@hotrnail.com

Alejandro Serna Dominguez

Instituto Tecnol6gico de Lazaro Cardenas Lazaro Cardenas, Michoacan, Mexico

serna _841 O@hotmail.com

Ismael de la Rosa', Jesus Villa, Efren Gonzalez

Unidad Academica de Ingenieria Electrica Universidad Aut6noma de Zacatecas

Zacatecas, Zacatecas, Mexico *

ismaelrv@ieee.org

Abstract-In this work it is presented, described and tested a new Matlab Graphic User Interface (GUI) for image segmentation of degraded images using two probabilistic techniques, Markov random fields (MRF) and nonparametric

entropy estimation. This GUI was created in order to integrate a

series of steps needed for the segmentation process into a single

visual environment to aDow an easier handling of input images and saving of results. It is also used a powerful utility of the Matlab software concerning to paraDel processing, with the aim

of reduce the computational time because of the high time

consumption of this kind of algorithms. Results show a very satisfactory performance of this tool, allowing us to make this task easier and faster.

Keywords - image segmentation; Markov random fields; entropy estimation; graphic user interface; parallel processing.

I. INTRODUCTION

Segmentation of degraded images is a problem that has been widely studied, and a very useful approach that have helped significantly to solve it, is the use of Markov Random Fields (MRF) within a Bayesian framework [1-8], since MRFs allow to pose this kind of problems as statistical estimation problems where the solution is going to be estimated from a degraded image, that is, the observed data. The basic idea of these methods is to construct a Maximum A Posteriori (MAP) estimate of the probability density function (pdf) corresponding to the image model in order to find the maximum of such distribution, which provides the estimated image closest to the real one.

The classic MAP estimator is defined by:

= argmax{p(xIY)} XEl\{

= argmax{logp(ylx) + logg(x)} xEl\{

(1)

= argmin{-logp(ylx) -logg(x)}, xEl\{

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where g(x) is a MRF function that models the prior information of the phenomena to be estimated as a probability distribution, }1.{ is the set of image elements capable to maximize p(xly) and p(ylx) is the likelihood function from y given x [9].

In [10] it was introduced a new proposal of MRF for image segmentation, called semi-Huber potential function. In this paper it was addressed the problem of segmenting images degraded with Gaussian noise. Some other MRF models reported in the literature (Generalized Gaussian MRF [4], Welsh and Tukey potential functions [11,12]) were taken as a reference in order to prove the results obtained with that new proposal, finding that they were consistent with respect to those obtained with the other models, standing out the advantage that the proposed model contains a lower number of parameters to be tuned to obtain the desired segmentation according with the image type to be processed.

Nevertheless, in some applications the noise is nonGaussian or unknown, and with this previous approach the model is not able to identifY the nature of the degradation factor, thus the results are not good. In that sense, in [13-16] a new approach was introduced to deal with other kinds of noise. In [10], the first term in the MAP estimator was defined as a quadratic function of the differences between real and observed data, because the noise considered was Gaussian. But in this new context (nonGaussian), it is assumed a limited knowledge about the noise pdf, pee) = p(ylx), and the likelihood term is estimated starting with the data itself by means of a nonparametric entropy estimate, resulting in the new MAP Entropy Estimator (MAPEE).

The general form of this new estimator is presented here for quick reference:

XMAPEE = arg TJr {HA (Pn,h(eE)) -logg(x)} , (2)

where

(An HA(f) = - LA

/(X) logf(x) dx, (3)

and g(x) is the same as in (1).

For the realization of experiments performed in works [10, 13] it was used the MATLAB software, a computing environment intended for project development that require a huge amount of mathematical computations and its corresponding graphical visualization. This software integrates numerical analysis, matrix computation, signal processing and some other features in an easy to use interface. At University as well as in Industry, MA TLAB has become a widely used tool for solving complex mathematical problems in a variety of areas such as computation, numerical calculation, algorithm development, automatic control, statistics, among others [17].

In those works, the tests were performed in an elementary way in the sense that most of the preprocessing steps, before segmentation, were made separately; namely, the image had to be read within the program execution; every time we wanted to change the model parameters or the image, we had to do that from the program code list and then run the program; to generate and save the noisy image we had to use a separated script; every parameter combination that was used had to be written in a notebook; after segmentation, to observe the computation times, we had to go to other window in the screen, and if we wanted to save the segmented image, we had to proceed from the figure window; but mainly, if we wanted to use a different model or approach, we needed to open a different set of scripts for each one. All these things together with the enormous time and computation resources consumption gave rise to the need of create a graphic user interface that could integrate all the necessary actions for the processing in the same visual environment, that enables to open and save images directly from it, select the kind of noise to add, and select also the model or approach to work with. Additionally, it was thought to use a very valuable modality of MA TLAB, the parallel processing, in order to reduce computation times; experimental results show a significant processing time reduction. And finally, to avoid the use of a notebook for the record of the parameter values and times of computation every time the process is executed, this interface can generate a database in MS Excel with the parameter values and times of computation for each processing.

The rest of the paper is as follows: section II introduces the three MAP estimators that were included in the graphic interface, one for each MRF model, the Generalized Gaussian, the Welsh and the semi-Huber functions. Section III describes all the fields of the graphic interface and the function of all the interactive buttons that it contains. Section IV presents some comparative results about computation times using parallel processing with respect to simple processing; and finally in section V, some conclusions are exposed.

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II. MAP ESTIMATORS

A. Generalized Gaussian MRF MAP estimator.

The MAP estimator for the Generalized Gaussian MRF (GGMRF) is given by

XMAPgg = arg min {LIYS -xslq XEX SE§

+ (Jq'J....P L bsrlxs -XrIP} . (4) {s,r}EtC

The first term of (4) corresponds to the log-likelihood and the second one is the GGMRF; s is the site of interest, r corresponds to the local neighbors, § is the set of sites in the image and ( is the set of cliques (pairs of neighboring pixels in this case); bsr is a constant that depends on the distance between pixels s and r. For the case of Gaussian noise, q = 2; 0', A and p are the parameters to be tuned for the segmentation process, where 1 ::; p ::; 2.

B. Welsh MAP estimator.

The MAP estimator for the Welsh potential function IS

defined as:

XMAPwel = arg min {LIYS -xsl2 XEX SE§

+1.. (11 L bsr<l>1(X) + (1 {s,r}EtC

- 11) L bsrp2(X))} , (5) {S,r}EtC

where 11 is the granularity control parameter, cp\(x) = e2 with e =

(xs - xr),

(6)

and k is a positive scale parameter for edge preservation. In this case A, 11 and k are the parameters to be tuned.

C. Semi-Huber MAP estimator.

The MAP estimator for the semi-Huber potential function is given by the equation:

XMAPsh = ar�E�in{LIYs -xsl2 + A L bsrP1(X)} (7) sE§ {s,r}EtC

where p\(x) is the named semi-Huber potential and is defmed as:

�� ( 4<1>1 (X) ) P1 (X) = "2 1 + �� - 1 . (8)

Here, �o > 0 is a constant value and is the only one parameter to be adjusted during the segmentation process. cp\(x) is the same as in the Welsh case.

III. GRAPHIC USER INTERFACE (GUI)

For the design and creation of the GUI for image segmentation based on MRFs and entropy estimation, it was used the GUIDE (Graphical User Interface Development Environment) tool of a demo version of MAT LAB R2012.

Fig. 1 shows the appearance of the graphic interface created for this application.

.... = ... T.'''·'n ... DE IMAGENES

3

Fig. 1 Main window of the GUI created for image segmentation.

To make use of this interface, one should follow the sequence as it is shown in Fig.l. At the moment the application is running, the program 'reads' the number of cores available in the computer and updates the menu marked as number 1 in Fig.l, then one can select the number of laboratories to be connected to perform the parallel processing, it can be from zero to two times the number of physical cores; so the user can select how many labs he wants to connect having previous knowledge of the number of cores the computer is capable to use. If the selected number in the box is zero, the parallel processing is not performed.

Once the type of processing has been configured, one should load an image pressing the 'Abrir' button, marked as number 2. Fig. 2 shows when the browser window is open, then one can browse and select an image. The image format one can select can be JPG, BMP, TIFF or PNG.

When the image is loaded, it appears in the axes marked as number 3, and below button 'Abrir', it is shown the image size in pixels. After that, if the image is in gray scale, it is passed directly to axes number 4, otherwise, the image is previously converted to gray scale and then displayed.

tIokm.- .. r .... Ilo... !.k..-..'...-

�� -........ ... ....... .. _" ... ... '"

- -- - --==:II -=--=- -=-

Fig. 2 Browser window to select and load an image.

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After that, one should select the kind of noise from the menu number 5, possible options are: Gaussian, Salt & Pepper, Beta, Gamma and Uniform. Depending on the noise selected, some fields appear in the box number 6, as it is described next:

• For Gaussian noise, introduce sigma value (variance).

• For salt & pepper noise, introduce density value D, where 0 < D < 1.

• For Beta, Gamma and Uniform noise, introduce amplitude, A and B.

When the corresponding values for the noise source selected have been introduced, the button 'Insertar Ruido' (from the box number 7) should be pressed, immediately after this, in axes number 9 appears the image originally loaded with the noise added. The button 'Guardar' in box number 8 is used to open the browser window and select a path for saving the noisy image if desired; one can also choose the file format for the saved image from the same options as in the case of loading an image. Fig. 3 illustrates this operation. If the button 'Guardar' is pressed and there isn't an image in axes number 9, an error message is displayed and one cannot save any image.

DEIMAGENES --�

,:0 ,. � ,01 ViI

Figura 3. Browser window to save a noisy image.

With the selection of the kind of noise, one select implicitly the segmentation approach. If the Gaussian noise is chosen, then the simple MAP approach is indirectly selected and the box number 10 allows to choose between the three MRF models described in section II. The options displayed by the menu are: Cuasi-Huber, Generalized Gaussian and Welsh. But if any other kind of noise is selected, the MAPEE approach is indirectly selected, and the menu in box number 10 of Fig. 1 also allows to choose between the same three MRF models but within the new scheme for segmentation. The new options displayed are: Cuasi-Huber Kernel, Generalized Gaussian Kernel and Welsh Kernel.

Each one of the segmentation methods require different parameter values before starting; then, when a specific method is selected, in the space pointed by box number 11 appear the fields needed to introduce the required values, such as it is described next:

• Cuasi-Hubber and Cuasi-Huber Kernel require the Delta and Xo values.

• Generalized Gaussian and Generalized Gaussian Kernel require Sigma, Lambda, P and Xo values.

• Welsh and Welsh Kernel require Lambda, K, Mu and Xo values.

Because de segmentation process includes a minimization stage, it is required an iterative process of optimization to fmd the global minimum of the probability distribution that represents the region map. In this stage, the Levenberg­Marquartd algorithm provided in the optimization toolbox of MA TLAB is used and it requires an initial value (Xo) to start finding the solution.

Once the segmentation method has been selected and the corresponding parameter values have been introduced, everything is ready to start the segmentation process pressing the button 'Segmentar' shown in box number 12 of Fig. 1, and the functionality of the elements of boxes 1,2,5-8, 10-13, 16 and 17 is immediately disabled, the pointer of the computer changes to wait mode, in the space of box 15 appears the message 'En proceso', indicating that a segmentation process is being executed.

When the segmentation process ends, in the space of box 14 appears the computation time required, in seconds. Then the message in box 15 changes to 'Segmentacion terrninada', in axes number 16 appears the segmented image and all the elements that were disabled, turn to enable except that of box number 2. The button 'Guardar' in box 13 is for open the browser window and choose a path to save the segmented image in the desired file format (JPG, BMP, TIFF or PNG).

The button 'Guardar registro' in box 16 is for open the browser window and one can save a Microsoft Excel file with the record of the data generated during all the times the segmentation process was executed, including information of boxes 6, 10, 11 and 14, creating a sheet for each method used. The Excel file can be named as you want.

When the first segmentation process has started, the button 'Abrir' in box number 2 is disabled and the loaded image cannot be changed, but one can generate noisy images with different kinds of noise and perform as many segmentation processes as desired with the different methods available. The button 'Reiniciar' in box number 17 is for clear all the registers, images in all the axes, and for enable again the button 'Abrir' in box number 2.

IV. EXPERIMENTS AND RESULTS

In order to show the advantages of this new graphic interface for image segmentation using Markov random fields and entropy estimation with parallel processing, we present a series of experiments that consist of repeat some tests performed in [10, 13] with the same parameter values used in that works and compare the computation times. For this work, experiments were performed on an Acer laptop with Windows 7 operating system, an Intel® Core™ i5-2450M CPU @ 2.50 GHz and 6 GB of RAM because it was the computer available.

A first experiment consists of segment an image of the brain degraded with Gaussian noise, n�N(O, n(1�), into tree tissues: white matter, gray matter, and cerebrospinal fluid (CFS), but now using parallel processing into the new graphic

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user interface. N is the noise matrix that corrupts the image and (1� is the variance. The image size is 187 x 161 pixels. Fig. 4(a) shows the brain image with a noise level of (1� = 10, Fig. 4(b) shows the segmentation result obtained for the semi - Huber MRF model, Fig. 4(c) shows the segmentation result obtained for the Generalized Gaussian MRF model and Fig. 4( d) shows the corresponding to the Welsh MRF model. In Table I it can be seen the times of computation for each model, noting that with parallel processing, integrated in this new graphic interface, it occurs a considerable reduction in the computation time.

Fig. 4 Segmentation results obtained from the graphic user interface created for the brain image, (a) noisy image, (b) segmentation with semi - Huber MRF, ( c) segmentation with GGMRF, (d) segmentation with Welsh MRF.

TABLE I. COMPUTATION TIMES WITH AND WITHOUT PARALLEL PROCESSING FOR SEGMENTATION RESULTS OF FIG. 4.

Model Parameter values Time (sec)

Simple [10] Parallel

Semi - Xo AI 339.1406 95.5493 Huber 80 150 Generalized Xo cr Ie P 339.0461 95.6239 Gaussian 80 0.3 40 1.5

Welsh Xo Ie k I.l 334.0902 93.2310 58 10 10 0.5

From Table I it can be observed that computation times with parallel processing represents approximately 28% of the original ones, even though the computer used this time had less processing capacity due to a smaller number of cores in the CPU, compared with that used in the previous works. Again, it is due to the advantage of the parallel processing implemented.

F or a second test to prove the computation time reduction and the consistency of the segmentation results, we took the geographical image of the dam used in [10, 13], in this case the image size is 310 x 208 pixels. Fig. 5 shows the segmented image results for each model, where Fig. 5(a) is for the noisy image, Fig. 5(b) is the segmented image with the semi - Huber MRF, Fig. 5(c) is the segmented image with the GGMRF and Fig. 5(d) is the segmented image with the Welsh MRF. In the same way, Table II contains the numerical results

corresponding to the input parameter values and computation times obtained, where again, it can be seen that computation times were reduced very significantly. In this case, computation times with parallel processing represents approximately 26% with respect to the original ones.

(a) (b)

Fig. 5 Segmentation results obtained from the graphic user interface created for the dam image, (a) noisy image, (b) segmentation with semi - Huber MRF, (c) segmentation with GGMRF, (d) segmentation with Welsh MRF.

TABLE II. COMPUTATION TlMES WITH AND WITHOUT PARALLEL PROCESSING FOR SEGMENTATION RESULTS OF FIG. 5.

Model Parameter values Time (sec)

Simple [10] Parallel

Semi - Xo "'0 713.5470 184.8699 Huber 90 60 Generalized Xo cr A. P 704.3832 186.5115 Gaussian 80 0.4 200 1.4

Welsh Xo A. k J.! 704.6216 184.4636 128 10 10 0.5

All the previous test were performed for the case of Gaussian noise corrupting the image. The following experiments consider the new approach presented in [13] for the case of impulsive noise (salt & pepper) as degrading factor, but in this case it is compared only the results for the semi -Huber MRF model because it was the only one used in that work and because it is more easy to tune. It is important to mention that although this work does not present experiments with other kind of degrading factors, in the graphic user interface introduced here, one has the possibility to choose from a variety of them ( including Gamma, Beta and Uniform noise distribution).

Taking again the same two images, Fig. 6 shows the segmentation result for the brain image, where Fig. 6(a) is the noisy image, degraded with a density of impUlsive noise of 0.15 (in a scale of 0 to 1) and Fig. 6(b) is the segmented image within the new approach of MAP Entropy Estimation. Fig. 7 shows the segmentation results for the dam image, where Fig. 7(a) is the noisy image as in the previous case and Fig. 7(b) is the resulting segmented image applying the MAPEE approach. Table III shows parameter values used during the processing

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and a comparative between computation times with and without parallel processing, for both images.

(n)

Fig. 6 Segmentation results obtained from the graphic user interface created for the brain image using the MAPEE approach with impulsive noise, (a) noisy image, (b) segmentation with the semi - Huber MRF.

Fig. 7 Segmentation results obtained from the graphic user interface created for the dam image using the MAPEE approach with impulsive noise, (a) noisy image, (b) segmentation with the semi - Huber MRF.

TABLE m. COMPUTATION TlMES WITH AND WITHOUT PARALLEL PROCESSING FOR SEGMENTATION RESULTS OF FIG. 6 AND FIG. 7

Parameter values Time (sec) Image

Xo l>o Simple [13] Parallel

Brain 90 110 457.9916 168.7192

Dam 80 0.4 957.1709 255.8809

As it was in the previous experiments, computation time reduction here is also very significant, parallel processing time in the case of brain image represents about 36% of the time taken with simple processing, and for the case of de dam image, it is about 26%.

V. CONCLUSIONS.

This new graphic user interface designed with parallel processing in MA TLAB allowed us to improve greatly various situations derived from the very important task of segmenting images degraded with noise. First of all, computation times during segmentation processes were reduced a lot; it remains to implement this graphic interface on a more powerful computer (with a greater number of cores, for instance) in order to check if computation times could be reduced even more. On the other hand we have now all the actions needed for segmentation of digi�l images integrated into a single environment so that, loading and saving images, adding different kinds of noise and

selecting the segmentation algorithm, can be done from the same window. Finally, it doesn't matter how many times we perform the segmentation process and how many times we modify the parameter values; at the end, we have the possibility to generate an MS Excel file with the registration of the data generated from all the executions of the segmentation process. Definitely, this tool came to alleviate a little an exhaustive and tedious work that we had to do before, giving us the ability to perform tasks faster and efficiently.

[I]

[2]

[3]

[4]

[5]

[6]

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