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CHAPTER -1INTRODUCTION

______________________________________________________________________________Multi scale decompositions have shown significant advantages in the representation

of signals, and they are used extensively in image segmentation [15] and de noising [68].In this paper, we will mostly deal with the modeling of the wavelet transform coefficients ofcolor Images and its application to the problem of segmenting noisy images. Wavelets haveemerged as an effective tool for this problem as they provide a natural partition of the imagespectrum into multistate and oriented sub bands. Moreover, statistical modeling is mucheasier to perform in the transform space rather than on the original image pixel values

because of its energy compaction property. Image segmentation is a fundamental problem inimage processing and image analysis. It provides a partitioning of the image in regionswhich should ideally represent Meaningful objects.

However, certain types of images, for instance, medical images or remote-sensingimages may contain noise which can originate in the input device (scanner or digital camera)sensor and circuitry, or in the unavoidable shot noise of an ideal photon detector. Thepresence of image noise is generally considered undesirable as it damages image details andit affects the tasks of human interpretation and image analysis. It also causes under or over-segmentation problems, which degrade the performance of automatic image segmentationalgorithms in general. An obvious approach to overcoming the above problems is to performnoise reduction and segmentation separately. Much literature has been produced recentlydescribing the application of image segmentation to de noised images [9, 10]. Imagedenoising and segmentation can also be incorporated into a unified framework where apriori knowledge gained from the de noising process is used to aid the image segmentation.For example, a multi scale segmentation algorithm using a shrinkage function and anadaptive threshold for noise removal in conjunction with watersheds was presented in [4,11]. Edge information and Noise was modeled by chi distributions.

The likelihood of the coefficient being related to an actual edge was calculated usingBayes theorem. The threshold value was assigned manually which makes it impossible toobtain an optimal result as the threshold is the key factor to control the number of segmentedregions. In the past decades, many researchers have applied Statistical techniques combinedwith wavelet transform for image denoising [7, 1214], and image segmentation [2,15].

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Some of the state-of-the-art statistical models for noise free Sub band data includegeneralized Laplacian [1618], Normal inverse Gaussian [19], Gaussian scale mixture[20,21], Bessel K forms [22], bivariate Laplacian models [7] and so forth. These approacheshave improved the denoised and segmentation results of different image modalities.

In Recent work, we showed that successful statistical image processing algorithmscan be developed if they take into consideration the actual heavy-tailed behaviour of mostreal-life signals [6, 23]. Specifically, we have shown that wavelet decompositioncoefficients of images are best modelled by symmetric alpha-stable (SaS) distributions [2].Compared with SaS distributions, the proposed Cauchy model possesses a closed-formexpression for the probability density function (PDF) which leads to an analytical expressionfor the maximum a posteriori (MAP) equation in the image denoising process. This iscomputationally more efficient than the previous MAP method [24]. As a special case of theSaS family, the Cauchy distribution can also provide a good model for natural images [24]and, as we show in this paper, it allows for a simpler implementation of image segmentationalgorithms. In this paper, a novel statistical image segmentation technique for noisy images

based on wavelet transform and Cauchy density is presented. Fig. 1 illustrates the blockdiagram of the proposed image segmentation algorithm. An input image described by theRGB colour space is decomposed into multiple resolutions using the dual-tree complexwavelet transform (DT-CWT) [25]. A noise reduction approach in the wavelet domain isdeveloped relying on the bivariate Cauchy density, through which we are able to capture theheavy-tailed nature of the data as well as the inter-scale dependencies of waveletcoefficients.

The overall segmentation process consists of three components. In the initial texture

segmentation, all the three colour bands are employed as there is an important correlationbetween the image bands. First, the image is roughly segmented into textured and non-textured regions using the bivariate model parameters which are obtained from the denoisingprocedure. Multi scale segmentation is then applied to the resulting regions to partition theimage into a set of relatively homogeneous regions.

Finally, a region merging method is applied to the over-segmented image, in whichthe region similarity is measured by the KullbackLeibler distance (KLD) between twoCauchy models corresponding to the adjacent segments over the RGB colour bands. Thesethree components are efficiently combined together to perform a superior segmentation for

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noisy images. The innovative aspects of this work consist of the following: First, the image

denoising and segmentation are combined into a single framework to perform imagesegmentation for noisy images. The proposed algorithm estimates the model parameters inthe denoising stage, which are later used through the segmentation stage. Second, theproposed Cauchy distribution formulations provide a more efficient MAP solution than theexisting approach [24]. Third, the interdependencies between the colour channels are takeninto consideration in the texture segmentation in order to provide a precise texture map.Finally, the methodology presented in this paper can be seen as a general framework forsegmentation of noisy colour images. This framework has the potential to be adapted foreventual use with different denoising and segmentation modules as appropriate.

Fig. 1 Framework of the algorithm Dotted box shows the image segmentation process

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CHAPTER -2COLOUR IMAGE DENOISING WITH CAUCHYDISTRIBUTION

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In this section, our goal is the design of a statistical estimator that recovers the signalcomponent of the wavelet coefficients in noisy colour images by using a bivariate Cauchysignal prior to distribution. In order to be able to implement a noise removal processor, setsof noisy wavelet coefficients can be defined as the sum of the clean signal and noise. Thesignal component is modeled according to a bivariate Cauchy distribution with zero locationparameter, whereas the noise component can be modeled as a zero-mean Gaussian randomvariable.

2.1 CAUCHY DISTRIBUTIONThis subsection is intended to provide a brief introduction on the Cauchy

distribution. The Cauchy distribution is a special case of the SaS family. Unlike SaSdistributions [26] that lack a compact analytical expression for the PDF, the univariateCauchy distribution has the PDF defined as

Where d is the location parameter, specifying the location of the peak of thedistribution, and g is the dispersion of the distribution which determines the spread of thedistribution around its location parameter. In the region merging stage, we estimate theregion features using a symmetric Cauchy density function with zero mean (d 0). Fig. 2illustrates that the histogram of detail coefficients in a particular subband is fitted by theestimated Cauchy model in comparison with the fitted generalized Gaussian distribution(GGD) [27]. By examining the graphs, the subband coefficient distribution decays slowly onboth tails. The Cauchy model provides a better fit on these heavy tails than the generalizedGaussian model. This has been verified by the KLD to measure the difference between twoprobability distributions. The smaller value indicates a better fit. As the KLD of the Cauchymodel is 0.003 whereas the KLD of the GGD is 0.066. The bivariate isotropic Cauchy

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distribution is a member of the family of multidimensional isotropic stable distributions[26], whos PDF can be written as

Where the location parameters are assumed to be zero as our further developmentsare in the framework of wavelet analysis. This model used in both the denoising andsegmentation stages achieves superior results by not only capturing the heavy-tailedbehavior of the subband marginal distribution, but also the strong statistical dependenciesbetween wavelet coefficients at different scales.

2.2 STATISTICAL PROCESSOR FOR NOISE REDUCTIONThe 2-D wavelet transform is a powerful tool, providing a natural arrangement of

image wavelet coefficients into multi scale and oriented sub bands and allowing the study ofeach subband separately. Specifically, unlike the histograms of images in the spatial domain,wavelet coefficients of images will always be characterized by unimodal, symmetric andheavy-tailed distributions. In this work, we use a three-scale DT-CWT [25] with sixorientations, which is able to provide approximate shift invariance and directional selectivitywhile preserving the usual properties of perfect reconstruction and computational efficiency.

In [24], the authors proposed a Bayesian technique for removing noise from digitalimages. They designed a MAP estimator relying on the bivariate alpha-stable distributions.The authors of [24] derive a shrinkage function by minimizing a Bayesian risk to optimizethe subband statistics. The parameters are estimated using maximum likelihood methodfrom noisy observations. Here, we propose a new image denoising approach that is aparticular case of [24]. Being based on Cauchy model, it significantly improves thecomputational efficiency, for example, solving the estimation problem using a closed-formexpression for the MAP equation. As our main objective is to design a segmentationalgorithm, it is desirable to use a faster denoising approach before the segmentation task.

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2.2.1 MAP ESTIMATION OF CAUCHY SIGNALS IN ADDITIVEWhite Gaussian noise: We assume the original image is contaminated with signal-

independent additive white Gaussian noise. A wavelet transform of the noisy input yields anequivalent additive white noise model in the transform domain [16, 28]. We should note thatthe DTCWT introduces inevitable intra-scale correlations between wavelet coefficientsbecause the basis vectors of the transform cannot all be orthogonal to each other, and so thenoise is only approximately white in the transform domain. Consequently, in each of the sixorientations and for every two adjacent decomposition levels, sets of noisy waveletcoefficients can be written as the sum of the transformations of the signal and the noise

Where yl,u and yl+1,u are the noisy observations of child and parent waveletcoefficients at the lth decomposition level and uth orientation subband, l 1, 2, 3, u 1, 2, .. ., 6. X l,u and xl+1,u are noise-free wavelet coefficients at the current and coarserdecomposition level, respectively. el,u and el+1,u refer to the Gaussian noise at the adjacentscales. We process the real and imaginary parts of the complex wavelet coefficientsseparately, so yl,u and yl+1,u are real numbers referring to the real part or the imaginary partof the coefficients. This is also the same for xl,u, xl+1,u, el,u and el+1,u. The above set ofequations can be written in vectorial form as

where y = (yl , yl+1), x = (xl , xl+1), e = (el , el+1), and for simplicity we suppressthe orientation index because the denoising process will be applied to all the coefficientsacrossthe orientations. The signal and noise are modeled by the bivariate isotropic Cauchyand Gaussian distributions, respectively, (see Appendix). The MAP estimator of x giventhe measured coefficients y can be easily derived as being

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2.2.2 SIGNAL PARAMETERS ESTIMATION IN NOISYObservations: In this subsection, the methods used to estimate signal and noise

model parameters are described, which are the crucial steps in the denoising process. First,we find the level of noise. As proposed in [30, 31], a robust estimate of the noise standarddeviation s is obtained using the median absolute deviation (MAD) of coefficients at thefinest decomposition level

It is worth noting that the above equation only works if the input noise is white.Significant correction factors are needed for the lower-frequency sub bands if the noise has aspectral slope, for example, is pink or band limited. For the purpose of bivariate Cauchymodel parameter estimation from observed data, a method based on empirical characteristicfunction has been proposed by Achim et al. [29]. The derived equation is given by

Where s denotes the noise standard deviation. W y(v) is the empirical characteristicfunction [29] for observation y. In principle, v can be any non-zero value. However, in orderto reduce the overall variance of the estimate, we chose to average the results from theestimates corresponding to many possible choices of v. As the PDF of the measuredcoefficients y is the convolution between the PDFs of the signal x and noise components e,the associated characteristic function of the measurements is given by the product of thecharacteristic functions of the signal and noise. Mathematically, this corresponds to

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CHAPTER -3IMAGE SEGMENTATION ALGORITHMS

______________________________________________________________________________In the previous section, an image denoising method using bivariate Cauchy

distribution was developed in the wavelet transform domain. As our segmentation algorithmis implemented in the wavelet domain, the model parameters obtained from the denoisingstage can be used in the segmentation stage without reconstructing the clean images backinto the pixel domain. This section describes a multi scale (multi scale in this context refersto applying various window sizes to the image in order to capture the colour and texturefeatures.) Image segmentation algorithm as shown in the dotted box of Fig.1. The mainalgorithm can be divided into three parts:

First, the input image is crudely segmented into textured and non-textured regionsafter applying the image denoising to each colour band in the RGB colour space. Amultiscale segmentation is then performed over the resulting regions according to the localtexture characteristics. Finally, a statistical region merging approach is developed bycalculating the KLD as the statistical measure of similarity between the neighboringsegments. A preliminary version of this methodology has been already reported in [2, 32].The difference of the method presented here is that a Cauchy distribution is applied tosegmentation of noisy images.

3.1 INITIAL TEXTURE SEGMENTATIONInitial texture segmentation aims to produce a rough segmentation map with only

textured and non-textured regions. Therefore the different image regions can be processedindividually rather than globally. In [33], the authors showed that there is an importantcorrelation between the image colour bands. Specifically, an image discontinuity from oneband is likely to occur in at least some of the remaining bands. In order to capture thisinterband correlation, the texture segmentation is applied to all image bands separately toobtain a texture map per image band. Then the joint texture map is generated by a specificrule. As the RGB colour space is widely used in image segmentation algorithms, thisrepresentation is employed in this step to acquire the multivalued data of the colour images.In Section 2, the clean signal is approximated by bivariate isotropic Cauchy distribution(see also Appendix), which provides an attractive model of both the non-Gaussian statistics

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and the property of persistence across scales in a wavelet decomposition. The modelparameter g represents the dispersion of the distribution, which is similar to the variance ofthe Gaussian distribution [26]. Textures can thus be characterized by a set of g valuesestimated locally. Therefore the parameter g corresponding to the noise-free coefficients isused in this stage to estimate the texture features within the original image. Therefore thefeature value Tc(x, y) in the c colour band at the pixel location (x, y) is defined as

Where i is the index of ith subband. c denotes the index of the image colour band, c [{R_band, G_band, B_band}. Compared with the previous work [2], in which the subbandcoefficients were modeled by SaS distributions, and the parameter estimation wasimplemented in a square-shaped neighborhood for each reference coefficient, our newapproach takes advantage of using the bivariate model parameters yielded from the noisereduction process thus reducing the computational cost. In order to obtain a uniformcharacterization of texture, median filtering [34] is employed on Tc(x, y) within eachsubband to filter out the texture associated with transitions between regions. Finally, a two-level K-means algorithm is used to assign the pixels to textured and non-textured regions. Apixel is then classified as textured if the proportion of the number of the sub bandsbelonging to the textured region is above a threshold P. Our experiments show that a valueof P 0.5 is a good choice for thresholding colour images. Compared with [32], thethreshold can be adjusted to the type of image. This property is useful for the segmentationalgorithm to handle not only natural images, but also images obtained using othermodalities.

The test image is corrupted by additive white Gaussian noise with standarddeviation s 45, and the peak signal-to-noise ratio (PSNR) which indicates that the imagecontains a large amount of noise. From the figure, we can see that these three maps not only

share some common areas in the textured regions, but also include some different areas ineach map. Some of the areas are misclassified to the textured regions because of thepresence of the heavy noise. Hence, it is impossible to obtain accurate textured and non-textured region boundaries from single band texture segmentation. A joint texture map isconsidered for the whole image which incorporates all the meaningful information from the

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different colour bands. In order to integrate all the texture features extracted from theseparate colour bands into one texture map, we set the following rules:

If pixel Q belongs to a textured region in all the three colour bands, Q isassigned to a textured region.

If pixel Q belongs to a textured region in any two among the three colourbands, Q is assigned to a textured region.

Otherwise, pixel Q is classified to a non-textured region.The original idea behind this rule comes from a criterion for producing a joint region map in

[35]. The basic method consists in integrating two separate region maps from differentsource images into a joint map for image fusion via a union operation. We adapt this rule toRGB colourbands using a majority rule based on the existing correlations between the RGBcomponents.Fig. 4a shows the joint texture map generated using the above rules. In addition,we show the texture segmentation results using the monochrome component of the colour

image with the same denoising process in Fig. 4b or the original coefficients without noisereduction in Fig. 4c.

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The texture map on the original clean image using Cauchy model is also shown inFig. 4d as a ground-truth image. It can be seen that the new approach generates the mostsimilar result to the one on the clean image and less degraded by the noise contamination.Fig. 4b also confirms that the monochrome band does not provide sufficient textureinformation for this process.

3.2 MULTISCALE IMAGE SEGMENTATIONThe textured and non-textured regions are further segmented into relatively small

and homogeneous regions while retaining the boundaries between the two regions. Thedominant colors are first extracted based on peer group filtering [36] and the generalizedLloyd algorithm [37]. Then, the JSEG algorithm proposed by Deng et al. in [38] is used tominimize the cost associated with partitioning an image at different scales. A bigger windowsize is used for high scales which are useful for detecting texture boundaries, whereas lowerscales are employed in order to localize the intensity of colour edges. It is reasonable toapply the lower scales to the non-textured region which has a more or less homogeneoustexture, whereas higher scales are adopted for the textured region to find the textureboundaries. In contrast to JSEG, which does not take into account the local texturedifference between the image regions, the strength of this approach is that we are able toapply the multiscale segmentation simultaneously to the same image according to the localtexture characteristics.

However, the current boundary locations between textured and non-textured regionsare not the actual boundaries because of the fact that K-means clustering can only segmentthe image into rough regions. Moreover, multiscale segmentation provides accurate resultsonly within the textured and non-textured regions. Consequently, a boundary refinementstep is employed to adjust the boundaries between the two regions. A pixel is assigned to theneighbor class that has the minimum D value using the following function.

where Dist. refers to the Euclidean distance measure, C0 and Cj are the dominant colourvectors of the current pixel and its jth neighbor segment, Sj 4 and Sj 8 are the numbers of 4-and 8-neighbour pixels belonging to the jth segment, while Dj 4 and D j 8 are the numbers of4- and 8-neighbour pixels belonging to the different classes of the jth segment. A and b

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represent the strength of the spatial constraint. Specifically, as a and b increase, a pixel ismore likely to belong to the class to which many of its neighbors belong. Thus, regionboundary smoothness is achieved. The influence of a and b on the boundary refinementprocedure is shown in Fig. 5. The result in Fig. 5d which is obtained using higher values of aand b has smoother boundaries compared to Figs. 5b and c. In addition, the originalsegmentation result without using such a spatial constraint is illustrated in Fig. 5a in whichthe boundries between the two types of regions are deteriorated by the boundary adjustmentstep.

3.3 STATISTICAL REGION MERGINGIn general, the result of applying the algorithm described in the previous sections

leads to over-segmentation. A statistical region merging method is implemented by usingCauchy density to appropriately model wavelet coefficients within the segmented regions.Equation (13) in the boundary refinement step shows that the similarity measure between theneighboring pixels is computed using the dominant colour difference rather than the texturefeatures. As a result, the textured and non-textured regions near the boundaries contain somepixels with different labels. For example, a textured region may include some non-texturedlabelled pixels. Therefore an approach to grouping the regions into two categories isdesigned. The segments with more than a given threshold percentage of their pixelsbelonging to the non-textured areas are categorized as non-textured segments, and theremaining segments are classified as textured segments.

Therefore segmented regions are considered individually rather than globally. Acorresponding merging criterion is provided for each category. The main difference lies inthe way the features are extracted within the regions. Non-textured segments are mergedbased on their dominant colour similarity. To achieve this, the Euclidean distance of thecolour histograms extracted from the neighboring non-textured

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Segments are calculated. For textured segments, region similarity is measured usingstatistical model parameters followed by computing the KLD. In [39], the authorsintroduced a statistical framework for texture image retrieval where the marginal density ofcoefficients is approximated by SaS distributions and texture similarity is measured bymeans of the KLD between model Parameters.

We here employ a univariate Cauchy model, whose PDF is defined in (1), tocharacterize the region properties. Subband wavelet coefficients in the textured regions aremodeled independently using the Cauchy distribution, where the model parameter can beobtained using the log absolute moment method proposed in [40]

Where R refers to the region. c is defined as the image colour band. (x, y) is themagnitude of the complex detail coefficient obtained from denoising process in the ithwavelet subband within the region R. It can be shown [40] that the derived equation is givenby

Where E [.] is the expectation function. As described in Subsection 2.2.2, g can alsobe calculated by using (10) with noise standard deviation s 0. Therefore the characteristicsof the region can be completely defined via only one parameter g. The statistical measure ofsimilarity between the neighboring textured segments is calculated by KLD. The KLDbetween two adjacent textured segments is given below

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Where s1 and s2 are the adjoining textured segments, c [ {R_band, G_band,B_band}, KLDc(s1, s2) is the similarity distance for each colour band, which is defined as

where g 1 and g 2 are the estimated model parameters of the neighboring segments,respectively. i denotes the index of the wavelet subband. The pair of regions with theminimum distance is merged until a maximum threshold of the distance is reached.Compared with the previous work [32] in which the segments are classed into threecategories, our two-category method offers comparable results with reduction incomputational complexity. Figs. 6b and c show the final merging results using Cauchy andGGD models, respectively. Clearly, the Cauchy model provides better results than GGD interms of human visual perception.

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CHAPTER -4EXPERIMENTAL RESULTS

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The experiments consist of two parts. The first part focuses on validating thedenoising performance. The second part intends to test the proposed segmentation algorithmon different images containing artificial and natural noise. The segmentation results dependon a number of tunable parameters: the window size for Cauchy parameter estimation, thespatial constraint parameters a and b in the boundary refinement process, the window size ofthe median filter and the region-merging thresholds.

For simplicity of implementation, we run experiments with square windows only.For all tested images, a window of size 11 11 was used to estimate the model parameter g.a 1.0 and b 0.8 were adopted throughout all experiments. The window size for themedian operator primarily affects the detection of textured and non-textured regions.Specifically, it needs to belarge enough to capture local texture characteristics, but notarbitrarily large in order to avoid border effects. In our experiments, the median filterwindow size was set to 23 23 pixels. Higher region-merging thresholds could lead tofewer number of segments. The default values of the thresholds were set to 0.4 for non-textured regions and to 0.6 for textured regions, respectively.

4.1 DENOISING PERFORMANCE

We compared the performance of the proposed denoising method (Cauchy Shrink)with a state-of-the-art approach that employs the generalized Laplacian prior for noise-freeSubband data and additive white Gaussian noise [33], referred to as Prob Shrink. Theauthors developed three wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. Among them, multivalued denoising is appliedto colour noisy images. Thus, it was chosen as a reference method for comparing with ourproposed algorithm. For the actual noise removal process, the authors in [33] adopted asimple shrinkage rule where empirical wavelet coefficients are multiplied with theprobability of containing a significant Noise-free component. For [33], we use theparameters that were reported by the authors to yield the best PSNR performance.

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A denoising method using the Cauchy model was also presented in [24]. Thedifference in the proposed algorithm with the work in [24] is that the presentation of theCauchy shrinkage function has a closed-form expression which leads to an analyticalexpression for the MAP equation, whereas in [24] the shrinkage function was implementednumerically with a less efficient MAP solution. The denoising results obtained fromCauchyShrink and ProbShrink are illustrated in Figs. 7b and c, respectively. From humanvisual inspection, it shows that they provide similar denoised images although our proposedmethod performs better than ProbShrink in terms of PSNR value. Table 1 lists the resultingPSNR values in comparison with those achieved by ProbShrink. Currently, the running timefor our method (which uses un-optimised Matlab code) is around 5 min on Intel Pentium43.00 GHz machines to process a 256 256 pixels test image, whereas the average CPUtime taken by

the existing MAP method [24] is reported to be about 17 min [13]. ProbShrink needsapproximately 18 s in the same conditions. We prefer to use the proposed denoising methodbecause it is an integral part of the whole segmentation framework. For example, theestimated model parameters are used in both the denoising and the segmentationcomponents of our algorithm. Hence, the entire process does not require the reconstructeddenoised image, and denoising and segmentation can be performed in a unified framework.

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4.2 SEGMENTATION RESULTS FOR NATURAL IMAGESIn this section, the influence of noise on the final segmentation is investigated. The

performance of the proposed method (called CauchySeg) tested on a variety of naturalimages is analysed. Our method is compared with three other reference methods, includingJSEG [38], Watershed [3] and Waveseg [4]. JSEG is an automated colour imagesegmentation approach which involves minimizing a cost associated with partitioning of theimage based on pixel labels. The notion of J-images is introduced with reference tomeasurements of local image homogeneities at different scales. A spatial segmentationalgorithm is developed to grow regions from the valleys of the J-images to achievesegmentation. JSEG examples shown here are optimized using the best option values viavisual inspection. Watershed is an unsupervised segmentation method consisting of twostages. The first stage extracts texture features from the subbands of the wavelet transform.A perceptual gradient function is proposed whose watershed transform provides an initialsegmentation.

The second stage consists in grouping together these primitive regions intomeaningful object via a spectral clustering technique. Watershed applies the region-depththreshold to the gradient surface that is set as 0.15 times the median gradient. Waveseg is amultiresolution technique for colour noisy image segmentation. A wavelet transform is first

applied to each colour channel. The watershed transform is then applied to the thresholdedmagnitudes at the coarsest scale to obtain an initial segmentation.

Finally, the inverse wavelet transform is used to project the initial segmentation tofiner scales until the full resolution image is achieved. For Waveseg, we use the defaultvalue 0.5, which was recommended by the authors as the adaptive threshold in the waveletshrinkage stage of their algorithm. Fig. 8 shows the segmentation results using the lizardimage contaminated with different amounts of noise. On inspecting Figs. 8c and d, it is clearthat CauchySeg provides robust segmentation results as the noise intensity is increased. Inboth images, the entire contour of the lizard is better extracted than by Waveseg where themain body of the lizard is segmented into a lot of small separated regions, whereas in JSEG,the bottom part of lizard is merged into the rock background. The watershed algorithmshown in Figs. 8i and j fails to detect the correct boundaries of the lizard because of thepresence of heavy noise. In addition, we compare CauchySeg with the same segmentationapproach but did not include any denoising mechanism. The results are displayed in Figs. 8a

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and d. It demonstrates that the proposed algorithm improves the final segmentation resultsby combining the denoising and segmentation components in an effective way.

The segmentation algorithm is tested on various colour images from the Berkeleydataset [41]. These images are artificially contaminated with different amounts of whiteGaussian noise for evaluation purposes. The human segmented images from Berkeleydataset benchmark [41]are used as ground truth. For the sake of fair comparison, we also perform CauchyShrinkimage denoising before applying JSEG and Watershed in order to assess the segmentationperformance.

The results of the six tested methods are illustrated in Fig. 9. As it can be seen fromFig. 9a, the salient object cheetah shown in the ground-truth image (Fig. 9m), is bettersegmented than by all other methods. For example, in Figs. 9e, g, i and k the cheetah ismerged into the grassland, Where as Fig. 9c even fails to capture the contour of the cheetah.The poor performance for that particular image is because of the fact that it contains similarbackground and foreground object as well as a large amount of noise. This proves that ouralgorithm can handle difficult image segmentation tasks.

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As a second example, demonstrates that our approach provides the most similarsegmentation to the ground-truth image (Fig. 9n) in comparison with the other testedmethods. On observing Figs. 9el, it can be seen that the noise-reduction process canimprove the segmentation performance. Our proposed algorithm has the advantage ofintegrating the denoising and segmentation algorithms into a single framework to performautomatic noisy image segmentation. This also reduces significantly the computationalcomplexity.

4.3 APPLICATION TO MULTISPECTRAL IMAGESIn Section 4.2, all the images used in the experiments were contaminated with artificialnoise. We also tested the algorithm with real data containing natural noise. Multispectralsatellite images were chosen for this purpose. There are several noise sources in

multispectral images, such as photonic noise, electronic noise, quantisation errors etc. It has

been proved that the additive Gaussian noise model is a realistic approximation for thesetypes of noise [42]. Fig. 10 shows the result for a multispectral image containing threebands. Segmenting a multispectral image is similar to the natural colour image segmentationproblem in that both types of images consist of multiple bands. Only a cropped region (448 448) of the image is chosen for this example, because the original image is large. Theareas showing the crop fields (right and bottom) and forest (left) in Fig. 10b are effectivelysegmented with smooth contours, whereas the over-segmentation problem occurs in Fig. 10c

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using Waveseg. It clearly demonstrates that our proposed method is robust for real imagedata as well.

The effectiveness of the proposed segmentation algorithm derives from threeaspects: First, the noise-removal processor based on the bivariate Cauchy distribution makesit possible to mitigate the noise while at the same time preserving fine image signal details.Second, the initial texture segmentation is able to generate a precise image texture map viaimproved texture feature extraction. Finally, the statistical region merging stage enhancesthe final segmentation results because it relies on an accurate statistical model and the KLD.All these three components are combined effectively to build a robust and efficient imagesegmentation framework.

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CHAPTER -5CONCLUSIONS AND FUTURE WORK

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We developed a novel image segmentation framework for noisy images based on theheavy-tailed Cauchy model that provides accurate description of the non-Gaussiandistribution of thewavelet coefficients [13, 24, 29]. Statistical analysis techniques are efficiently combinedwith low-level colour and texture features to perform the automatic segmentation. Thebivariate Cauchy distribution used in the noise-removal module has found to be moreefficient than the previously proposed MAP approach [24] in terms of computationalcomplexity with comparable noise mitigation performance. The texture segmentation is acrucial part of the overall segmentation method which is applied to all three image colourbands separately to obtain a precise texture map.

This is done by employing the bivariate model parameters corresponding to thedenoised wavelet coefficients. The main contribution of this work is that it provides anaccurate and reliable image segmentation algorithm for noisy colour image which integratesstatistical methods, denoising techniques and multiresolution analysis into a singleframework. A large number of examples are presented to show the high performance of theproposed algorithm, particularly in the presence of large amounts of noise. Future work willinclude the extension of the proposed method to the case of multidimensional data, such asvideo sequences contaminated with heavy-tailed noise. By including additional features, forexample, motion, the proposed methodology has the potential to solve some of thefundamental problems arising in the object tracking area. In addition, an interesting directionfor future work could be the adaption of the proposed segmentation methodology todifferent types of images, such as medical images.

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