Segmentation of Restored Colour Texture Images Using MRF with Cellular Automata and Colour Block Matching 3D Algorithms

doi:10.21203/rs.3.rs-1622365/v1

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Segmentation of Restored Colour Texture Images Using MRF with Cellular Automata and Colour Block Matching 3D Algorithms

https://doi.org/10.21203/rs.3.rs-1622365/v1

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Role of texture segmentation is vital due to its diversified applications in image analysis and understanding. Noise is an integral part of measurements and affects the performance of segmentation algorithms. Recently, researchers have initiated the work on noisy textures to address automatic quality evaluation of fruits and vegetables, diagnosis of thyroid cancer images, recognition of facial expressions, texture-based image retrieval and texture analysis, after restoring the noisy images. With these motivations, benchmark images from the Prague and Brodatz texture dataset are tainted with salt pepper and Gaussian noise and restored using recent cutting edge performance algorithms. A novel Markov Random Field based approach using a custom Median filter is developed for segmentation of restored texture images. A maximum improvement of 16% segmentation accuracy for salt pepper noise with 70% noise density and 15.1% accuracy for Gaussian noise with variance 50 has been achieved over recent approaches on Brodatz textures. An improvement of 8% accuracy for Gaussian noise with variance 50 and 4.47% accuracy improvement for salt pepper with 70% noise density is achieved on Prague texture benchmark images. The proposed approach can be applied for satellite and medical image analysis, industrial applications, remote sensing.

Markov Random Fields

Noisy texture segmentation

Structural similarity index

Texture database

Segmentation of images is one of the mandated and crucial steps in analyzing the images while accomplishing the machine vision tasks for targeted performance. It has multiple applications in numerous fields such as image data retrieval, pattern analysis, industrial and medical image analysis, machine learning and various other areas. Segmentation of images is performed using various techniques and approaches such as thresholding, edge-based methods, clustering-based methods, level set method, parametric methods etc. Segmentation, based on Image Texture as a cue, is a perpetually popular research domain. Due to many texture attributes, researchers have not been able to converge upon a universal definition of texture, thus making the texture segmentation task as non-trivial. Haralick [21] define texture as repetition of grey levels in a neighbourhood and have categorized the texture as regular, irregular, coarse or fine. A strong correlation between human vision and texture has motivated various research activities in the domains of synthesis of textures, classification of textures and shape extraction using textures [16] leading to the applications such as 3D imaging, synthesis of natural scenes and computer graphics, extraction of surface shape from textures. Some of the texture analysis applications are diagnoses using X-ray images, retrieval of images from databases, weather forecasting, sea-ice imagery analysis etc.

An extensive literature review on texture segmentation, for the published work over the period of more than past three decades, segmentation of textures using Gabor filters with traditional classifiers [8, 9, 13, 25, 31, 41, 42] has been discussed, in majority. Segmentation of textured SAR and medical images using Markov Random Fields (MRF) have been proposed in [28, 29, 40, 41]. The color and texture-based image analysis is applied recently by researchers for medical image analysis [5, 6, 19, 39] industrial applications [17, 18, 34], remote sensing [49, 51], analysis of animal audio signals [36] and saliency estimation in the set of video frames and images [7]. All these researchers carried out experimentation on non-degraded noise-free texture images [23, 29]. However, noise is the important attribute that affects the performance of segmenting algorithms and also an integral part of measurements, thus making it imperative to test the noise robustness of segmenters for textures corrupted with additive Gaussian, Poisson, salt pepper and speckle noise, in several signal-to-noise-ratio (SNR) steps [33]. Identifying the due importance of noise in segmenting algorithms, as per the most recent literature [1, 12, 47], researchers have initiated the work on noisy textures to address noisy texture-based image retrieval and noisy texture analysis. They have used four texture datasets, namely, Outex, Broadatz, STex and Curet for experimentation. Though there are 30 plus texture datasets available globally as per [23, 33] for researchers to experiment with, the experimentation of noisy textures is not yet explored to a deeper extent by the researchers encompassing these datasets.

As per recent literature [33] Prague texture benchmark offers potentially unlimited texture data for experimentation and it is developed to evaluate objective performance and ranking of texture segmentation algorithms and it contains largest variety of multi-class textures, that makes it the default choice of the researchers across the globe for relevant experimentation [29, 33]. As per state-of-the-art, more than 11 contemporary approaches of texture segmentation have been applied on the Prague texture dataset [29], though none of these algorithms used benchmark images degraded with noise. Many of the researchers have used Brodatz textures for experimentation as per the literature review, therefore proposed approach is also evaluated on color Brodatz texture benchmark images in [27]. In many of the real-life scenarios, salt pepper and Gaussian noise are the significant sources of corruption for texture images caused during acquisition, coding or transmission [3, 20, 48]. The researchers have also reported their work related to applications such as texture-based automatic quality evaluation of vegetables and fruits [4], diagnosis of thyroid cancer images [38] and recognition of facial expressions from the idea of the human face [43], after restoring the noisy images. As per literature review, most of the researchers focused on improvement in texture segmentation accuracy and real-world problem of noisy texture segmentation is not addressed to deeper extent. Our work on investigating the segmentation of noisy color textures from the Prague and Brodatz texture benchmark images, is thus duly motivated from such latest reported works of peer researchers round the globe. Proposed approach ensured unparallel performance with respect to rotational and scale variance although that has not been targeted as the immediate research concern.

In this work, texture images are degraded with salt pepper and Gaussian noise, respectively. Texture images degraded with Gaussian noise are restored using a colour block matching 3D (C-BM3D) algorithm due to its best restoration performance among the latest 14 algorithms [10, 11, 15, 30, 35], whereas, de-noising of texture images corrupted with salt pepper noise is achieved using a nature and bio-inspired algorithm, namely, Cellular Automata (CA) [14, 26] that being the best performing among 15 recent algorithms for this noise [14, 15, 35] and further it eliminates limitations of the Median filter and its variants, while preserving the edge information [14, 24, 32, 44].

A two-stage novel MRF segmentation algorithm using the custom Median filter is developed and used for segmentation of Prague texture images and Brodatz texture images. C-BM3D and CA restoration algorithms with the novel MRF based segmentation approach give better segmentation performance than deep learning-based approach using U-net in [27] on Brodatz texture benchmark images and recent texture segmentation algorithms in [29] and deep learning approach using fully convolutional network (FCNT) reported in [2] on Prague texture images, to compare with a few.

We could attain higher mean segmentation accuracy on tainted texture images than recent approaches evaluated on noise free texture images. This approach is evaluated on two color Brodatz texture benchmark images in [27], and accuracy achieved is higher on tainted Brodatz texture images than deep learning approach in [27], evaluated on noise free Brodatz texture benchmark images. Our segmentation accuracy achieved is higher by 16.04% for salt pepper noise with 70% noise density and it is higher by 15.10% than recent approaches for Gaussian noise with variance of 50 on 16-class Brodatz texture benchmark image. Our segmentation accuracy achieved is higher than the recent approach proposed by Kiechle et al. [29] for Prague benchmark images. It is higher than 8% for Gaussian noise with variance of 50 and it is higher by 4.47% for salt pepper noise with 70% noise density. Also, we could restore texture benchmark images in the Prague dataset and Brodatz texture benchmark images, degraded with salt pepper noise and Gaussian noise, with best performing algorithms viz. CA and C-BM3D, respectively, with an achievement of excellent mean values of performance metrics, structural similarity index (SSIM) and peak signal to noise ratio (PSNR). The proposed color texture segmentation approach can be applied for satellite, noisy texture-based retrieval and analysis, for river scene segmentation [51], diagnoses of breast [19] and prostate [5] cancer, analysis of radiographic images in dentistry [39], analysis of human hair and skin images useful for pharmaceutical and cosmetic industries [6], classification of fabrics, rocks and for inspection of aircraft surfaces, fruits, steel and wood [37].

The paper is further organized as follows: Restoration algorithms are discussed in Section-2. Segmentation problem formulation and segmentation approach are detailed in section-3. Experimentation and the obtained results are discussed in section-4. Section-5 reports the conclusion.

In this section, we will first elaborate the CA restoration algorithm, followed by the C-BM3D algorithm used for restoration of noisy texture images in Prague and Brodatz dataset.

2.1 Cellular Automata Restoration Algorithm

CA is a nature and bio-inspired algorithm with many applications in machine vision, image analysis and processing [14, 26]. In this work, it is used to restore texture images that are degraded with salt pepper noise. This algorithm decomposes the noise filtering task into an array of cells (pixels). The new state of a pixel at time instant t + 1 depends on the previous states at time instants t − 1, t – 2, t – 3, …, t – k. In this algorithm, the centre pixel in a 3 x 3 window is treated as the cell under processing. Zero boundary conditions are assumed for the CA algorithm for boundary pixels. Salt pepper noise affects the value of a pixel in the image lattice by replacing its value by a maximum (255) or a minimum (0) in the range of 0 to 255. Hence, two threshold values min_state= 0 and max_state= 255 are used for the states of the cell under processing.

Noise free and noisy cells (pixels) in the CA algorithm are identified using local rules based on the value of the cell under processing and the values of the cells in the neighbourhood. The value of a noisy cell is determined by estimating the mean of pixel values in the neighbourhood of that cell excluding cells with min_state and max_state values. A cell is treated as a noise free cell if its value is greater than min_state and less than max_state and its state is not changed in the CA algorithm. Let us define some notations for describing the CA algorithm. We denote the maximum value of a pixel by

T_max and the minimum value of the pixel by T_min. P_i,j, stands for the centre pixel in a 3x3 window. Herein an array of size 8 x1 is denoted by T. This array contains pixel values in a 3x3 window excluding the centre pixel in an ascending order. We denote three channels of colour image by I_R, I_G and I_B. Steps 2 through 5 are applied on all three channels of colour texture dataset images (I_R, I_G and I_B) and combined in step 6 to get a restored colour image.

2.2 Colour Block Matching 3D algorithm

Colour block matching 3D (C-BM3D) algorithm, deployed for restoring Prague and Brodatz texture dataset images deteriorated with Gaussian noise is discussed herein. Complete discussion of theoretical and analytical details of this restoration algorithm are available in [10, 11, 30]. This restoration algorithm is a two-stage algorithm and both stages are described here in brief. First of all, a colour RGB noisy image is converted in YUV colour space. In the first stage, a colour noisy YUV input image is divided into 2D blocks. Each 2D block is considered as a reference block. Blocks similar to a reference block are grouped to form sets of 3D block in an image. We denote these 3D blocks by${ z}_{Y}{,z}_{U}$and ${z}_{V}$.

Wavelet transform (db2, db4, db6) or discrete cosine transform (DCT) is applied on the 3D blocks, namely, ${z}_{Y}{,z}_{U}$ and${ z}_{V}$. Noise is filtered in the first stage by using hard-thresholding on the transform coefficients. The inverse 3D transform of these 3D blocks is then computed, and weighted averaging is applied on the overlapping 2D blocks to get the first estimate of the restored image.

Steps in first stage of C-BM3D algorithm:

1. Convert colour RGB input image to YUV colour space.

2. Divide each of three components of YUV image in 2D blocks.

3. Each of the total 2D blocks is treated as a reference block and set of 2D blocks similar to reference block are put together to get a 3D set of similar 2D blocks, namely,${ z}_{Y}{,z}_{U}$ and ${z}_{V}$.

4. Apply transform such as Wavelet (db2, db4, db6) or DCT on each of the 3D sets obtained in step-3.

5. Apply thresholding operation on transform coefficients to filter noise.

6. Compute inverse 3D transform of 3D blocks obtained in step-5.

7. Apply weighted averaging on overlapping 2D blocks to get first restored estimate of the YUV image.

In the second stage, six 3D sets are produced. Three 3D sets are obtained in these six sets by applying a 2D block matching process on the original noisy image. The remaining three 3D sets are obtained by applying a 2D block matching process on the first restored estimate of the noisy input image. A Wiener filter is used to filter noise in the second stage instead of hard-thresholding. The rest of the restoration process is similar to the first stage.

In this section, first we discuss formulation of the segmentation problem followed by a description of the novel algorithm developed for segmentation of colour textures using MRF and custom Median filter.

3.1 Formulation of Segmentation Problem

The MRF model-based segmentation task is formulated as an energy function using Gibbs distribution and Bayesian frame work [13, 28, 46]. In the MRF model-based energy function, the total energy expression consists of two energy terms viz. label energy and feature energy. Here we denote total energy by$U\left(x\right)$. Total energy is the sum of feature energy ${U}_{f}$ and label energy ${U}_{l}$ as given in (1). Total feature energy ${U}_{f}$contains two terms viz. ${U}_{f1}$, ${U}_{f2}$. Mathematical expression for ${U}_{f1}$is provided in (2) and for${ U}_{f2 }$it is provided in (3). The label energy term is denoted by ${U}_{l}$ and its expression is given in (4).

$$U\left(x\right)= {U}_{f}+ {U}_{l}$$

$${U}_{f1}= \sum _{s \in S}\left\{\text{ln}\left(\sqrt{{\left(2\pi \right)}^{K}\left|{{\Sigma }}_{m}\right|}\right)\right\}$$

$${U}_{f2}= \sum _{s \in S}\left[\frac{1}{2}\left({y}_{s}^{k}- {u}_{m}^{k}\right){\sum }_{m}^{-1}{\left({y}_{s}^{k}- {u}_{m}^{k}\right)}^{T}\right]$$

$${U}_{l}= \left[\beta \sum _{t \in {N}_{s}}\delta \left({x}_{s}, {x}_{t}\right)\right]$$

Where,

$\delta \left({x}_{s}, {x}_{t}\right)=1$ if ${x}_{s} \ne {x}_{t}$

$\delta \left({x}_{s}, {x}_{t}\right)= -1$ if ${x}_{s}= {x}_{t}$

Here K denotes the feature vector length and taken as 3 for three LUV colour space as features in our work.$\delta$ is the delta Kronecker function. A mean vector of class m is denoted by${ u}_{m}^{k}$, with k = 1, 2, …, K. ${{\Sigma }}_{m}$ denotes covariance of class m.${ y}_{s}^{k}$ denotes a feature vector for pixel s in the image matrix S. ${x}_{s}$ and ${x}_{t}$ denote labels of a pixel at s and t in an image lattice. The neighbourhood of pixel s in image matrix S is denoted by${ N}_{s}$. Simulated annealing is used to minimize the total energy to obtain a segmentation solution. MRF parameters covariance and mean are computed by chopping a small section of every texture segment.

3.2 MRF Based Segmentation Algorithm

Eighty multi-class benchmark texture images in Prague texture dataset [33] and two benchmark images from Brodatz texture dataset [27] are used to carry out experimentation in this study. A two-stage novel MRF segmentation algorithm using the custom Median filter is developed and used for segmentation of these texture images. In the initial part of the first stage, conversion of the RGB input texture image to CIE Luv colour space is performed, and Luv colour space is used as features of the input texture image. Simulated annealing is used as the optimization algorithm to minimize energy in the first stage of this algorithm to get the first estimate of the segmentation result.

In Fig. 1, the first row and third column show the crude segmentation result obtained in the first step of this algorithm on a multi-class benchmark texture image in the Prague dataset. Boundaries in crude segmentation results are good, but there are dots and small islands in the image. The second stage of this algorithm removes these dots and islands using the custom Median filter. Figure 1 shows the progressive refinement of crude segmentation results according to an increase in the window size of the custom Median filter. The quantitative metrics used to determine the window size of custom Median filter in this algorithm are SSIM, MSE and PSNR. These metrics are used here to determine closeness of segmented result to ground truth. SSIM takes into account structural information in segmented image and ground truth image including boundaries. It eliminates the limitations of PSNR and MSE as per [50]. Therefore, segmentation results associated with the value of SSIM close to 1 is the best among the three segmentation results associated with these three metrics. As indicated in Fig. 1, a maximum accuracy of 98.79% is obtained for the window with dimensions of 29 x 29 with a maximum value of SSIM = 0.9733 and boundaries are nicely preserved for this window size. The correct segmentation (CS) metric suggested by Hoover et al., [22] is used to calculate the accuracy of the segmentation.

Here dimensions of the custom Median filter window are enlarged to 29 x 29 to get optimum segmentation results with a maximum value of SSIM equal to 0.9733. In this algorithm, the custom Median filter has replaced the Gabor filter. Elimination of the Gabor filter reduces feature space dimensions, which effectively reduces computations.

Table 1 shows quantitative segmentation results with respect to the increase in the window size and values of quantitative segmentation performance parameters MSE, PSNR and SSIM on a restored benchmark image deteriorated with salt pepper noise of 20% density. As stated earlier, SSIM is the best parameter among these three parameters. As shown in table 1 the maximum accuracy of 98.79% is achieved for the window size of 29 x 29 for SSIM = 0.9733. For the PSNR parameter, a maximum accuracy of 98.68% is achieved for PSNR = 29.43 dB with the Median filter window size of 25 x 25. The MSE parameter has a minimum value of 0.0314 for the Median filter window with size 23 x 23. But, as discussed earlier, the segmentation result associated with the maximum value of SSIM is best and it is 98.79% for this image.

The performance of the proposed segmentation algorithm with the three parameters SSIM, MSE and PSNR against segmentation accuracy is shown graphically in Fig. 2, Fig. 3 and Fig. 4 respectively.

Prague and Brodatz texture dataset are used herein for experimentation. Texture segments in Prague dataset are cropped pieces of texture regions from 114 textures containing 10 different varieties of textures [33]. The maximum number of texture segments in a texture image is 12, whereas, the minimum number is 3 in this dataset. This texture dataset is developed for quantitative performance evaluation of supervised and unsupervised segmentation algorithms on its benchmark images. Benchmark images of color Brodatz textures are also used for experimentation and performance of proposed approach on these images is compared with recent deep learning-based texture segmentation algorithm using U-net [27].

Figure 5 and Fig. 6 show the restoration performance of the C-BM3D algorithm on the two Brodatz texture benchmark images based on mean values of SSIM and PSNR metrics. All these images are noise contaminated with zero mean Gaussian noise with variance values viz. 10, 20, 30, 40 and 50. Figure 5 shows a graph of the mean values of SSIM against

five different variance values. All SSIM values are close to ideal value of 1. Figure 6 shows a graph of mean values of PSNR against five different values of variance. PSNR values are significantly high. For example, for Gaussian noise with high variance value of 50, PSNR is 28.84 dB. A novel MRF approach with the custom Median filter is developed and used herein for segmentation of the restored texture benchmark images.

Table 2 shows quantitative segmentation results obtained on 16-class Brodatz texture benchmark image tainted with salt pepper noise and Gaussian noise using proposed approach and deep learning approach using U-net [27] evaluated on noise free 16 class Brodatz texture benchmark image. Segmentation accuracy obtained using deep learning approach on noise free image is 82.50% whereas accuracy achieved on restored image is 98.54% for 70% density of salt pepper noise and the accuracy for restored image is 97.60% for Gaussian noise with variance 50. This proves robustness and effectiveness of proposed approach for noisy textures.

Table 3 shows quantitative performance of proposed approach and deep learning-based approach on 5 class Brodatz color texture benchmark image. Segmentation accuracy obtained on noise free image using deep learning approach is 97.40% whereas accuracy achieved on restored image is 98.65% for 70% density of salt pepper noise and the accuracy for restored image is 97.80% for Gaussian noise with variance 50. This proves robustness and effectiveness of proposed approach for noisy textures.

Table 4 shows restoration performance of the CA algorithm for all 80-texture benchmark images tainted with salt-pepper noise. The mean value of SSIM for all 80 images is 0.9859 for 20% noise density and it is 0.9043 for 70% noise density. The mean of PSNR values for 20% salt pepper noise density is 35.48 dB and it is 27.19 dB for 70% noise density.

Figure 9 and Fig. 10 show the restoration performance of the C-BM3D algorithm on the 80 Prague texture benchmark images based on SSIM and PSNR metrics. All these images are noise contaminated with zero mean Gaussian noise with variance values viz. 10, 20, 30, 40 and 50. Figure 9 shows a graph of the mean values of SSIM against five different variance values. All SSIM values are close to ideal value of 1.

Figure 10 shows a graph of mean values of PSNR against five different values of variance. PSNR values are significantly high. For example, for Gaussian noise with high variance value of 50, PSNR is 27.63 dB. A novel MRF approach custom Median filter is developed and used herein for segmentation of the restored texture benchmark images.

Table 5 shows that the highest mean segmentation accuracy of 77.73% is obtained using the most recent approach

by Kiechle et al. [29] based on the CS metric on noise free images. This metric computes the percentage of the correctly labelled pixels in the segmented image using ground truth [22]. Table 5 shows the segmentation results of the benchmark images in the Prague texture dataset deteriorated with both salt pepper and Gaussian noise. The mean segmentation accuracy obtained is 82.20% for texture images tainted with salt pepper noise with 70% noise density and it is 85.99% for the case of Gaussian noise with variance of 50. These accuracy values are higher than the recent approach by [29] and a deep learning-based approach using FCNT [2] for noise free texture images. The mean segmentation accuracy obtained using the novel MRF approach on non-degraded texture images is 87.55%. SSIM is used herein to measure the structural similarity including boundaries between ground truth and the segmented results. The mean values of SSIM for all types of noise values are close to the ideal value of 1 as shown in table 5.

4.1 Result Analysis and Discussion

The cutting-edge performance of the restoration algorithms and novel MRF approach is obvious in terms of higher segmentation accuracy, when compared with most recent deep learning-based texture segmentation algorithm using U-net [27] and another recent deep learning approach in [2] and a one reported in [29]. As per visual observation of color Prague and Brodatz texture benchmark images most of the classes in color texture benchmark images have different colors with small variation in color content and hence the classes can be perfectly discriminated using color as features. The MRF approach using a custom Median filter achieves higher segmentation accuracy because the CIE Luv colour space used in this algorithm is uniform Euclidean colour space [45]. This makes estimation of colour distance precise to separate out texture segments in the image during the segmentation process, and to use this colour space as features with custom Median filter yields higher segmentation accuracy than the most recent approaches on restored texture images. Reducing the value of SSIM means there is a loss of structural information in the restored image, including boundaries, and reduction in PSNR also indicates loss of details in the restored image. Loss of the information in the input image degrades the performance of segmentation. Therefore, the mean segmentation accuracy reduces for the restored texture images relative to non-degraded images in both Prague and Brodatz texture datasets.

Qualitative segmentation results for six Prague texture images are shown in Fig. 11. The novel MRF approach proposed for segmentation uses colour as texture features. Therefore, the segmentation performance degrades if the same colour exists in neighbouring texture segments. For example, the green colour segments located in the right upper and bottom part of a texture image tm12-2-12 in Fig. 11 get merged and it degraded the segmentation performance. The same justification is applicable for all other images.

The mean segmentation accuracy achieved on the benchmark images in Prague and Brodatz texture dataset, using the novel MRF approach is higher than all three most recently reported algorithms for both, noise-free and noise-degraded texture images. This high segmentation accuracy for highly noisy textures is achieved due to the cutting-edge performance of the novel MRF segmentation approach and the CA and C-BM3D restoration algorithms. The additional quantitative metric used for the evaluation of the segmentation performance is SSIM. Outperforming results are achieved in terms of SSIM for segmentation. It is inferred that, as the SSIM metric degrades, a declining trend is observed for segmentation accuracy also. The proposed approach has applications in satellite image analysis, noisy texture analysis and noisy texture retrieval, for medical image analysis, industrial applications, remote sensing etc. Texture images can be degraded with other types of noise such as Poisson noise or a combination thereof, including salt pepper, Gaussian and speckle noise as future scope.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Conflict of interest

None.

Contributors

Sanjaykumar Kinge: Identification of research gap through literature survey. Development of texture segmentation algorithm, implementation of restoration algorithms and article drafting.

B. Sheela Rani: Validation of results and refinement of article.

Mukul Sutaone: Validation of results and refinement of article.

Data Availability

Prague texture dataset link: https://mosaic.utia.cas.cz/

Brodatz texture dataset link: https://multibandtexture.recherche.usherbrooke.ca/colored%20_brodatz_more.html

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Segmentation of Restored Colour Texture Images Using MRF with Cellular Automata and Colour Block Matching 3D Algorithms

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Abstract

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1. Introduction

2. Restoration Algorithms

2.1 Cellular Automata Restoration Algorithm

2.2 Colour Block Matching 3D algorithm

3. Texture Segmentation Algorithm

3.1 Formulation of Segmentation Problem

3.2 MRF Based Segmentation Algorithm

4. Experimentation And Results

4.1 Result Analysis and Discussion

5. Conclusion

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References

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