An Unsupervised Cluster-wise Color Segmentation of Medical and Camera Images using Genetically improved Fuzzy-Markovian Decision Relational Model

Abstract

The traditional Fuzzy C-means (FCM) has been adopted worldwide to perform different kinds of image segmentation. However, owing to the fact that it is very susceptible to noise and other image artifacts, its usage is no longer a priority in the constantly changing real world application. The motivation of this paper is to propose a robust & unsupervised Image Segmentation framework known as GIFMRCM for enhancing the underlying delicate architectures of the human brain with ease. GIFMRCM introduces a new objective function by utilising a degree of mutual connectivity factor between pixels and the center. The manuscript can be broken up into two major constituents - Image Segmentation using GIFMRCM, and Cluster-wise color space representation of the GIFMRCM image using k-means hard clustering approach in a CIE L*a*b* color space. Experimentation on medical images shows that the proposed algorithm can improve the performance of image segmentation, and remove noise efficiently. The cluster-wise feature extraction procedure proposed in this paper is also able to extract delicate regions of human brain with ease.

Keywords

Image segmentation GIFMRCM mutual connectivity objective function CIE L*a*b* color space

1 Introduction

Image segmentation is used in many computer vision techniques, it can be described as a method in which a given image is partitioned into multiple, yet meaningful regions having homogenous features of the image components [1, 2]. As for instance, medical image segmentation, object based video coding and surveillance system requires their features to be extracted efficiently in order to enhanceperformance. Image segmentation has three broad divisions i.e. – pixel based, region- based and contour based segmentation [3, 4]. Many image segmentation techniques have been proposed in the past few decades, however the performance level in noisy images is not satisfactory enough. Metaheuristic algorithms such as Genetic evolution or swarm intelligence based algorithms are popular among researchers because clustering with them need no prior training samples, this factor reduces the computational time significantly [5, 6].

Clustering or grouping together can be described as a method of categorizing data with the motive of discovering similarities among data by virtue of their characteristics. The main objective is to identify and represent individual groupings which occur naturally in large set of data to paint a more clear picture of the system’s behaviour. It is of two main types: Soft and Hard clustering. Hard clustering is a technique in which each data point in a particular group of data can only belong to one cluster, the k-means algorithm is an example of hard clustering. While, soft clustering is an approach in which no constraint is place on the particles, i.e. the data points can belong to two or more clusters however the sum of the membership value of each data points from all the clusters must be a equal to 1. The membership value indicates the degree or level of belongingness to the clusters, the popular Fuzzy C-Means (FCM) algorithm is an example of such an approach [7 –10]. FCM is an unsupervised method which basically partition data based on location of data points, partitioning of the data points into several clusters is done by compacting data in the same clusters and separating the data in different ones. The membership values of each data points or every pixels in the image are assigned according to the distance of the features with the classes. A major disadvantage of it is that it does not take into consideration the local or spatial information of the neighbouring pixels in the image which makes it quite susceptible tonoise [11].

Image luminance amplitude is the most basic attribute for any monochrome image and a chief component for a color image. Color image segmentation increases the computational complexity of a classification problem. A total of 16 million different colors can be simulated in a simple 24 bit RGB computer monitor, thus it is very difficult to analyse all the colors in the image distinctly. Soft computing is one such way which can be used to approximately model and impart solutions to such problems where the classification or differentiation of the colors are inherently difficult. A color image consists of more features as compared to gray scale images, and for which reason it has received considerable attention over the recent years. Among the chief requirements of a good image segmentation procedure some properties worth mentioning are – the segmented image should not inherently incorporate in itself significantly varying colors for the region under consideration, and single connected region which is of the same color should not be of more than one label. Segmentation of color image requires higher computational cost than its gray scale counterpart, however with the advent of powerful processors and decreasing cost of color sensors the problem has become a thing of the past. As a matter of fact, there has been significant growth in the number of techniques for segmenting color images over the past few years[12, 13].

1.1 Related works

Image Segmentation & Segmentation A new FCM segmentation method called Symmetry Spatial Possibilistic FCM in which the symmetry information was integrated with SPFCM and calculated possibilistic values of fuzzy membership values in [1]. A method for clustering pixels in a non-iterative manner was proposed by using human perception-based color qunatisation scheme and peaks of bins from the 3D histogram for quantised color space [12]. A method for detecting defect for reflective and transparent surface based on fuzzy logic was proposed in [15], they were able to achieve a high sensitivity value of 83.5 %. A new algorithm for segmenting noisy images which used both local data as well as membership information called Local membership Relative Entropy based FCM (LMREFCM) was proposed. The local data information was incorporated by adding a weighted distance to the standard distance computed from the locally smoothed data which more likely resulted in assigning suitable membership values to the pixels in the immediate vicinity [16]. An improved fuzzy clustering algorithm known as FLICM was proposed, which introduced pixel relevance into the fuzzy factor and could efficiently estimate the damping extent accurately. Performance was improved because non-local context information was be utilized in the proposed algorithm [17]. A brain tumour segmentation method based on Convolution Neural Networks (CNN) was proposed by exploring small 3x3 kernels. The use of small kernels allowed designing a deeper architecture given the fewer number of weights in the network [18]. An unsupervised image segmentation algorithm known as Fuzzy-based Artificial Bee Colony was proposed, it had very fast convergence and low computational cost [19]. A novel segmentation fusion method was proposed which considered information from neighbouring pixels to boost image segmentation. Experimental results showed that it can achieve satisfactory segmentation results which provided clear gray gradation and satisfactory visual effects. Intensity consistency and edge information is maintained well in each segmented region [20]. A method for detecting brain tumour using MR Images using a modified k-means clustering technique and watershed algorithm for detecting brain tumour was proposed in [21]. A method known as Segmentation-Based Adaptive Image Enhancement (SAIE) was proposed in which the parameters were chosen based on the global properties or the local characteristics of different parts of each image [22]. A novel idea of combining SFCM and swarn intelligence based Artificial Bee Colony for medical image segmentation was proposed in [23]. An approach for detecting brain tumour accurately using K-means clustering technique integrated with Fuzzy C-Means algorithm was proposed in [24]. A novel method known as Attanassov Intuitionistic fuzzy set theory to segment blood vessels and blood cells in pathological images was proposed, it used Sugeno type intuitionistic fuzzy generator followed by thresholding technique [25]. A detailed survey about the applications of Genetic Algorithm fir segmenting medical images was presented in [26]. An automated technique for segmenting vascular retinal images was proposed by combining differential filters with morphological operators for filling vessel segments in [27]. Similar techniques for segmenting medical images have also been proposed in [7] and [28].

Color based Image Enhancement & Segmentation A method for efficiently combining texture and color features segmenting PolSAR images was proposed in [29]. A detailed literature review for night vision imaging techniques was carried out in [30]. Techniques such as contrast enhancement, color transfer based clustering, fast color contrast enhancement and pseudo colour fusion algorithm for self-adaptive enhancement system were among many areas studied. A method for segmenting medical images was proposed, where the minimization of the energy function were weighted according to their relative importance in detecting boundaries. The relative importance was computed based on local edge features collected from the adjacent region located inside and outside of the evolving contour [31]. A technique for segmenting sky or cloud images was proposed by systematically analyzing different color space components by considering partial least-square regression algorithm in [32]. A hybrid technique for segmenting color images was proposed in [33], wherein an input image which is initially converted into CIE L*a*b* color space is segmented using FCM and feed forward Neural Network. An appearance-based person re-identification method was proposed which used color as the feature for effectively processing color invariants in [34]. An adaptive image segmentation approach based on color clustering was proposed to divide pedestrian image adaptively into reasonable regions. A color image segmentation technique for both unsupervised and supervised segmentation of color images based on neural networks was proposed in [35].

1.2 Outline of our Contributions

The motivation of this paper is to propose a robust unsupervised Image Segmentation framework for Images captured for either medical purpose or any real camera image for robotic vision. The work is inspired by the behaviour of an agent which is consistently weighing its decision in a search space constrained by the Markov Decision Process (MDP) [36] and [37]. All the activities in an MDP are represented as a state-action pair, in order to receive the best reward the agent has to choose a suitable action from a transitional probability matrix [14 , 44]. Applying the concept of MDP, the FCM algorithm can be suitably varied to represent a “state - action” pair. The “action” being represented by the membership values of the data point, whereas the “state” being represented by the values of centroid determined by the previous iteration of the objective function. This model allows selection based on the degree of belongingness to one another.

The novel contribution of the present manuscript can be analysed over two prospects. Firstly, the introduction of noisy MRI Images and camera images to GIFMRCM technique results in more crisp membership value classification which is duly proven by the values of cluster validity coefficients tabulated in the following sections. Decrease of noise luminance level and differentiative contrast between different regions are also observed allowing better contour detection. Secondly, a hybrid color segmentation method is also being proposed in which the MRI input images which were segmented by the GIFMRCM algorithm is represented in CIE L*a*b* color space. The next step is further classification of cluster-wise information using hard k-means clustering, wherein regions belonging to different clusters are extracted into different images. Each of the different images which are extracted as a result of the hard k-means clustering algorithm are integral or constituent part of the originally color segmented images.

The paper is organized in the following order. Section 2 highlights a detailed discussion about the proposed unsupervised probabilistic segmentation framework. Section 3 proposes a new approach for converting gray scale images into color space representation and subsequently extracting cluster-wise information. An exhaustive analysis of the proposed image segmentation methodology by using MRI and real camera images is presented in section 4. Section 5 discusses the simulation results for the proposed cluster-wise color extraction, followed by cluster strength analysis and their implementation. Section 6 concludes the paper.

2 Proposed Image Segmentation Algorithm – “Genetically Improved Fuzzy-Markovian Relational Clustering Matrix (GIFMRCM)”

When considering whether a certain individual belongs to a cluster, the individual does not completely belong to just one cluster in the real world; sometimes one individual belongs to two or more clusters. The division situation is denoted by the degree of affiliation, however one disadvantage of Fuzzy C-means clustering is that it does not consider the degree of affinity between the membership value of each data point and the centroid of which cluster it is a part of, neither does it contain any method for incorporating spatial or local information in mage in image context. This increases the probability of inappropriately assigning membership values of data points to certain clusters in which that has less affinity value, which also makes it very sensitive to noise and other imaging artifacts. An MDP can be considered as a set M=(S,A,T,r,y), where S = s₁, …, s_N is a set of finite number of N states that collectively represents a constantly changing or dynamic environment. A = a₁, …, a_k is a set of k actions. is a transition probability function, or transition model, where stands for the state transition probability upon applying action a ∈ A in state s ∈ S leading to state in state [36 , 45].

Genetically Improved Fuzzy-Markovian Relational Clustering Matrix (GIFMRCM) is an improved version of Fuzzy C-Means clustering technique whose goal is to extract appropriate membership values of each data point and centroid values from a relational clustering matrix. The problem of clustering is implemented as a Markov Decision Process (MDP); wherein the current value of centroid is termed as, whereas the membership values of each data point is termed as. Assume that we have an n x m rectangular matrix R = (r_ij) among n data points and m centroid, where r_ij, i = 1, n, j = 1, m is the degree of mutual affinity. High value of r_ij means a high connectivity between the state and action. In such tasks, the goal is often mainly to find centroid clusters in conjunction with selecting their cluster-wise typical or suitable membership value of data points. The membership values are not intended to be exclusively assigned to clusters, indeed some common data points may have a larger typicality in multiple clusters. So, the typicality of each data point should be independently evaluated in each cluster.

GIFMRCM can be mathematically formulated as follows:

Encoding – Each chromosome represents a solution which is a sequence of cluster centers. For a space having K dimensions, each of the cluster centers are represented by K number of consecutive genes in the chromosomes. The intensity value of a pixel are represented by genes in the chromosome.

Population Initialisation – Setting chromosomes as vector containing centroids of the clusters. In our implementation, the population is set as 10, and the number of generations as 10. In traditional method, the accuracy of a solution is determined by letting the function run for many generations and then stopping when the minimum improvement is equal to or less than 0.0001. Our proposed method was tested more than 50 times by keeping the number of generation as 10 each time, and the number of clusters were varied. The values of cluster validity indices obtained during each run shows that out method have the capacity for obtaining better solutions in lesser time.

Evaluation of Fitness Function – The fitness function is set as the inverse of the value function or objective function proposed in (1).

Let an unlabelled data set X = (x₁, x₃, x_n) be the pixel intensities, where n is the number of image pixels to determine their membership. Also, let U = (u_ik) be a set of actions whose membership values are to be determined with respect to the states represented by V = (V₁,.., V_c), where i = 1 to c, j = 1 to n data points, and c is the number of clusters. The image pixels are partitioned into c clusters by iteratively minimizing an objective function, k is the number of pixels.

$J (U, V) = \sum_{i = 1}^{c} \sum_{k = 1}^{n} (u_{ik})^{m} d^{2} (x_{k}, v_{i}) R_{ik} + B$ (1) where, $B = \frac{α}{n_{c}} [\sum_{t = 0}^{α} γ^{t} (\sum_{i = 1}^{c} \sum_{k = 1}^{n} (u_{ik})^{m} R_{ik})]$ (2)

Where, c is the number of clusters, u is the membership value of the actions, while v representing the states. In (1), the update amount is divided by the total number of states n_c to make sure that the value function J greater than the amount of updates in GIFMRCM. α & γ indicates the learning rate and discount rate respectively. d² (x_k, v_i) represents the square of the Euclidean distance between the pixel intensity value x_k and the centroid value v_i along with constraint $\sum_{i = 1}^{c} u_{ik} = 1$ , and the degree of fuzzification m ≥ 1. R_ik is a relational matrix between U and V such that: $R_{ik} = u_{ik} . V$ (3) A data point x_k belongs to a specific cluster v_i that is given by the membership value u_ik of the data point to that cluster.. J_m (U, V) is an objective function which is minimized iteratively by constantly adjusting the values of u_ik and v_i. The value of v_i is calculated as well as optimised using crossover and mutation. $U_{ik} = \sum_{j = 1}^{c} (\frac{d^{2} (x_{k}, v_{i})}{d^{2} (x_{k}, v_{j})})^{\frac{- 1}{m - a}}$ (4) Similar to the popular MDP model, a discounted reward term has been added in (1) so that the fit chromosomes are selected after giving due weightage to the data points which have greater value ofR_ij. During each generation, based on the membership values or and centroid values, the objective function is being updated constantly.

Crossover – The crossover step recombines the bits (genes) of the two selected strings or chromosomes. Single point crossover operator is used in the current paper. The previous best centers of each iteration are used as genes for crossover during each iteration.

Mutation – The next operation mutation is performed in a bit-by-bit basis. If p_m = 0.01, i.e. we expect on an average 1% bit mutation, then there exist 10 chromosomes * 5bits/chromosomes = 50 bits in the whole population. 1% bit mutation thus means 50 * 0.01 = 0.5 bit mutation. Since every bit has an equal chance of mutation, we generate a random number in [0, 1] and if the generated number is p_m < 0.01, we select the chromosomes formulation. Thus for each chromosomes, we test the feasibility of the chromosome for mutation. To identify the bit position of mutation, we generate a random number in [0, n - 1], where n is the word- length of the chromosomes. If random number generated is p, the p^th bit of the selected chromosomes will be mutated. Mutation ensures that the algorithm converges to the global minima instead of getting stuck in localminima.

3 Proposed hybrid color segmentation model using integrated GIFMRCM and k-means clustering

An efficient image segmentation approach was proposed using k-means clustering integrated with Fuzzy C-means algorithm. It was followed by thresholding and level set segmentation for accurately detecting brain tumours. It is also mentioned herein that K-means can detect a brain tumour faster, whereas FCM could detect features more accurately [24].

Similarly in the current section of this paper, the main goal of the authors is to develop a new technique for classifying a GIFMRCM segmented colored MR Images into multiple cluster-wise images with each image being a constituent part of the original GIFMRCM segmented colored MR Image. The framework of the proposed algorithm is summarized below:

Step 1: Reading the original Image

Step 2: Pre-processing the original Image to reduce noise and increase contrast

Step 3: GIFMRCM Segmentation is performed

Step 4: Converting Image from RGB Color space to CIE L*A*B* color space

The CIELAB color space is one of the approximately uniform color spaces recommended for device-independent color representation in electronic color image systems. The axes of lightness L* and chromaticities a* and b* have to be suitably quantized. The values of L* run from 0 (black) to 100 (white). The horizontal axes are represented by a* and b* which are at right angles to each other and cross each other in the centre (which is neutral, i.e. grey, black or white). It is based on the principle that a color cannot be both red and green, or blue and yellow. The a* axis is green at one extremity (represented by -a), and red at the other (+a). The b* axis blue at one end (-b), yellow (+b) at the other end and at centre of each axis is 0. The advantages of CIE L*a*b* color space as mentioned in [12 , 35] are asfollows:

It is designed to approximate human vision

The CIE L*a*b* color space includes all perceivable colors.

It is device independent.

It is used in many industries apart from printing and photography.

It provides exact color specifications for paint.

Step 5: Classifying the Colors in “L*a*b*” space using K-Means Hard clustering – The k-means clustering assumes each data points as having a location in space; it tends to find partitions in such a way that the data points are as close as possible to each other, and as far from other data points belonging to other clusters. In this way the resulting image is as close as possible to the colored image which was already segmented using GIFMRCM algorithm.

Step 6: Labelling every pixel in the Image using the results from Step 5 – The k-means segmentation returns multiple sets of indices corresponding to the information carried by each clusters.

Step 7: Creating Images that segment the input MR Images by color – Using ‘Reshape’ function with the indices gathered in step 6 will result in number of images equalling to the number of clusters which were defined originally.

4 Simulation results for the proposed Image segmentation procedure

4.1 Cluster Validity Indices

– To evaluate the performance of the fuzzy clustering system, three cluster validity functions have been used viz. the fuzzy partition coefficient (V_pc), the fuzzy partition entropy (V_pe) and the validity function (V_xb) given respectively, by

$V_{pc} = \frac{1}{N} \sum_{i = 1}^{c} \sum_{j = 1}^{N} u_{ij}^{2}$ (5) $V_{pe} = - \frac{1}{N} \sum_{i = 1}^{c} \sum_{j = 1}^{N} u_{ij} \log u_{ij}$ (6)

$V_{xb} = \frac{\sum_{i = 1}^{c} \sum_{j = 1}^{N} | | x_{j} - x_{i} | |^{2}}{N * (\min_{i \neq k} (| | v_{k} - v_{i} | |^{2}))}$ (7) The fuzzy partition validity functions V_pc and V_pe indicates the level of fuzziness for better performance. The best clustering result is achieved when V_pc = 1 (or maximal) or V_pe = 0 (or minimal). The validity function V_xb gives the connection between fuzzy partition and feature property of the image, this property makes V_xb more important than V_pc and V_pe. A good clustering result is obtained when V_xb is minimum [3, 43].

4.2 Experiments & Results on Medical images

In this subsection, four Magnetic Resonance (MR) images are acquired from a reputed diagnostic library upon request. It is well known that MR images are usually contaminated by Rician noise [48], resulting in the existence of partial volume effect (PVE) and intensity homogeneity (IH)[9 , 17].

The original MRI images Figs. 1(a), 3(a) and 4(a) are 512x512 pixels, while 2(a) is 383x500 pixels. Figs. 1(b), 2(b), 3(b), and 4(b) are the results of performing Adaptive Histogram Equalisation on the input images. It can be that this method results in noise in almost every part of the image. Figs. 1(d), 2(d), 3(d), and 4(d) are the GIFMRCM segmented images, it can be observed that the fine details of the original image is preserved in the segmentation results. The GIFMRCM segmented images also shows better contrast between the different regions of the human brain in comparison to original images and FCM segmented images.

Fig.1

Segmentation of 1^st Image (MRI) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

Fig.2

Segmentation of 2^nd Image (MRI) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

Fig.3

Segmentation of 3^rd Image (MRI) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

Fig.4

Segmentation of 4^th Image (MRI) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

Table 1 highlights the comparison of the segmentation accuracy of the proposed algorithm on ordinary MR Images, however the level of noise is also increased as a result of performing Adaptive Histogram Equalization. The comparison is between four different MR Images acquired upon request from laboratory, i.e. Image 1, Image 2, Image 3 and Image 4. The experiment has been computed for varying number of clusters i.e. three clusters, four clusters and five clusters, the results of which is tabulated in table III, IV and V. However, the results presented in Figs. 1, 2, 3 and 4 are obtained using three clusters because of the highest value of cluster validity function associated with it. The number of generations and the chromosomes is set to 10 for reducing computational time. To compare the algorithms quantitatively, V_pc, V_pe, and V_xb are adopted to measure the algorithm, and corresponding values on the four medical images are tabulated. It is quite evident that in all the three experiments, GIFMRCM outperforms FCM in terms of V_pc, V_pe, and V_xb, meaning that the membership values in the proposed algorithm is more crisp. It can thus be understood that the proposed algorithm can segment corresponding areasefficiently.

Table 1

Computed clustering validation Indices of FCM and GIFMRCM

Image	Algorithm	Modality	Vpc	Vpe	Vxb
Image 1	FCM	MRI	0.677	0.272	2.218
Image 1	GIFMRCM	MRI	0.845	0.128	0.0175
Image 2	FCM	MRI	0.775	0.204	1.5312
Image 2	GIFMRCM	MRI	0.805	0.15	0.0112
Image 3	FCM	MRI	0.742	0.211	1.8723
Image 3	GIFMRCM	MRI	0.857	0.112	0.0087
Image 4	FCM	MRI	0.77	0.201	1.3212
Image 4	GIFMRCM	MRI	0.851	0.127	0.0221

4.3 Experiments & Results on Real Camera images

Table 2 highlights the comparison of the segmentation accuracy of the proposed algorithm on real camera Images, however the level of noise is also increased as a result of performing Adaptive Histogram Equalization. The comparison is between four different camera images, i.e. Image 5, Image 6, Image 7 and Image 8. The experiment has been computed for varying number of clusters i.e. three clusters, four clusters and five clusters, the results of which is tabulated in Tables 3, 4 and 5. However, the results presented in Figs. 5, 6, 7 and 8 are obtained using three clusters because of the highest value of cluster validity function associated with it. The number of generations and the chromosomes is set to 10 for reducing computational time. To compare the algorithms quantitatively, V_pc, V_pe, and V_xb are adopted to measure the algorithm, and corresponding values on the four medical images are tabulated. It is quite evident that in all the three experiments, GIFMRCM outperforms FCM in terms of V_pc, V_pe, and V_xb, meaning that the membership values in the proposed algorithm is more crisp. It can thus be understood that the proposed algorithm can segment corresponding areas efficiently.

Table 2
Computed clustering validation Indices of FCM and GIFMRCM

Image Algorithm Modality Vpc Vpe Vxb

Image 5 FCM Cam. Img. 0.471 0.464 2.4712

Image 5 GIFMRCM Cam.Img. 0.762 0.187 0.0274

Image 6 FCM Cam. Img. 0.529 0.392 2.0393

Image 6 GIFMRCM Cam. Img. 0.741 0.199 0.0128

Image 7 FCM Cam. Img. 0.653 0.293 1.0097

Image 7 GIFMRCM Cam. Img. 0.746 0.198 0.0287

Image 8 FCM Cam. Img. 0.684 0.26 0.7124

Image 8 GIFMRCM Cam. Img. 0.793 0.159 0.0119

Image	Algorithm	Modality	Vpc	Vpe	Vxb
Image 5	FCM	Cam. Img.	0.471	0.464	2.4712
Image 5	GIFMRCM	Cam.Img.	0.762	0.187	0.0274
Image 6	FCM	Cam. Img.	0.529	0.392	2.0393
Image 6	GIFMRCM	Cam. Img.	0.741	0.199	0.0128
Image 7	FCM	Cam. Img.	0.653	0.293	1.0097
Image 7	GIFMRCM	Cam. Img.	0.746	0.198	0.0287
Image 8	FCM	Cam. Img.	0.684	0.26	0.7124
Image 8	GIFMRCM	Cam. Img.	0.793	0.159	0.0119

Table 3

Cluster Validity function analysis for three clusters for the MR Images under consideration

Images	Algorithm	Clusters	Vpc	Vpe	Vxb
Image 1	GIFMRCM	3	0.845	0.128	0.0175
Image 2	GIFMRCM	3	0.805	0.15	0.0112
Image 3	GIFMRCM	3	0.857	0.112	0.0087
Image 4	GIFMRCM	3	0.851	0.127	0.0221

Table 4

Cluster Validity function analysis for four clusters for the MR Images under consideration

Images	Algorithm	Clusters	Vpc	Vpe	Vxb
Image 1	GIFMRCM	4	0.734	0.235	0.2401
Image 2	GIFMRCM	4	0.746	0.217	0.0172
Image 3	GIFMRCM	4	0.692	0.242	0.0135
Image 4	GIFMRCM	4	0.741	0.227	0.1536

Table 5

Cluster Validity function analysis for five clusters for the MR Images under consideration

Images	Algorithm	Clusters	Vpc	Vpe	Vxb
Image 1	GIFMRCM	5	0.437	0.466	1.6415
Image 2	GIFMRCM	5	0.396	0.517	2.5372
Image 3	GIFMRCM	5	0.543	0.383	0.2703
Image 4	GIFMRCM	5	0.57	0.309	0.0117

Fig.5

Segmentation of 5^th Image (Real Camera Image) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

Fig.6

Segmentation of 6^th Image (Real Camera Image) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

Fig.7

Segmentation of 7^th Image (Real Camera Image) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

Fig.8

Segmentation of 8^th Image (Real Camera Image) a. Original Image b. Adaptive Histogram Equalisation increases the contrast level of the desired regions as well as noise activity. c. FCM result d. GIFMRCM result.

GIFMRCM segmentation is also performed on four camera images for a possible implementation in robotic vision as future work. Figs. 5(a), 6(a) which has 642x362 pixels are a standard 24 bit color image having both vertical and horizontal resolution equal to 96 dpi. Figs. 7(a), 8(a) which has 1024x729 pixels are a standard 24 bit image having both vertical and horizontal resolution equal to 72 dpi. Figs. 5(b), 6(b), 7(b) and 8(b) are the results of performing Adaptive Histogram Equalisation on the input image with the objectives for increasing contrast level for more differentiation between neighbouring pixels. Figs. 5(d), 6(d),7(d) and 8(d) are the GIFMRCM segmented images, it can be observed that the fine details of the original image is preserved in the segmentation results. However, in the FCM segmented results shown in Figs. 5(c), 6(c), 7(c) and 8(c) most of the edges/features which were present in the original images are missing, meaning that these results cannot be accepted.

5 Simulation results for the proposed cluster-wise color extraction

5.1 Implementation on GIFMRCM segmented MR images

The GIFMRCM segmented images which were obtained in Figs. 1(d), 2(d), 3(d) and 4(d) are converted into RGB color space by using ‘Jet’ type colormap with intensity level 7. Figs. 9(c), 10(c), 11(c) and 12(c) are the GIFMRCM segmented images represented in RGB color space. It can be seen that these colored images are the actual interpretation of the regions underlying within each clusters in the gray scale segmented images. The proposed system is implemented in our medical images with three clusters because usage of either 4 or 5 clusters will results in less efficient classification of the membership values of the pixels or data points in the image. Using either one or two clusters is not acceptable in our current analysis because a color is made up of three primary colors. Detailed analysis is being carried out under ‘Cluster strength analysis’ heading of this section.

Fig.9

Cluster-wise color feature extraction of image 1 a. Original Image b. GIFMRCM segmented image. c. Color representation of the segmented gray scale image d. Extraction of 1^st cluster from 10(c) e. Extraction of 2^nd cluster from 10(c) f. Extraction of 3^rd cluster from 10(c).

Fig.10

Cluster-wise color feature extraction of image 2 a. Original Image b. GIFMRCM segmented image. c. Color representation of the segmented gray scale image d. Extraction of 1^st cluster from 11(c) e. Extraction of 2^nd cluster from 11(c) f. Extraction of 3^rd cluster from 11(c).

Fig.11

Cluster-wise color feature extraction of image 3 a. Original Image b. GIFMRCM segmented image. c. Color representation of the segmented gray scale image d. Extraction of 1^st cluster from 12(c) e. Extraction of 2^nd cluster from 12(c) f. Extraction of 3^rd cluster from 12(c).

Fig.12

Cluster-wise color feature extraction of image 4 a. Original Image b. GIFMRCM segmented image. c. Color representation of the segmented gray scale image d. Extraction of 1^st cluster from 13(c) e. Extraction of 2^nd cluster from 13(c) f. Extraction of 3^rd cluster from 13(c).

Fig. 9 (c), which is the colored GIFMRCM segmented image, is further decomposed into Fig. 9(d), 9(e) and 9(f). It can be seen that Fig. 9(d), 9(e) and 9(f) represents the bluish, reddish and yellowish regions of the original color segmented image fig. 9(c) respectively. It can be seen herein, that areas of brain which have been already grouped under different clusters can be extracted most smoothly using our approach with each color images so obtained being a distinct constituent entity of the segmented colorimage.

Fig. 10(c), which is the colored GIFMRCM segmented image, is further decomposed into Fig. 10(d), 10(e) and 10(f). It can be seen that Fig. 10(d), 10(e) and 10(f) represents the yellowish, bluish and reddish regions of the original color segmented image fig. 10(c). It can be seen herein, that areas of brain which have been already grouped under different clusters can be extracted most smoothly using our approach with each color images so obtained being a distinct constituent entity of the segmented colorimage.

Fig. 11(c), which is the colored GIFMRCM segmented image, is further decomposed into Fig. 11(d), 11(e) and 11(f). It can be seen that Figs. 11(d), 11(e) and 1(f) represents the yellowish, bluish and reddish regions of the original color segmented image fig. 11(c) respectively. It can be seen herein, that areas of brain which have been already grouped under different clusters can be extracted most smoothly using our approach with each color images so obtained being a distinct constituent entity of the segmented color image.

Fig. 12(c), which is the colored GIFMRCM segmented image, is further decomposed into Fig. 12(d), 12(e) and 12(f). It can be seen that Fig. 12(d), 12(e) and 12(f) represents the bluish (region belonging to 1st cluster), yellowish (region belonging to 2nd cluster) and reddish (region belonging to 3rd cluster) regions of the original color segmented image fig. 12(c) respectively. It can be seen herein, that areas of brain which have been already grouped under different clusters can be extracted most smoothly using our approach with each color images so obtained being a distinct constituent entity of the segmented color image.

5.2 Cluster Strength Analysis

The clustering strength of the proposed technique is analysed in detail by using the four MR Images previously considered in Section V by varying number of clusters.

Table 3 shows the results of the simulation work performed on the four MR Images when three clusters are considered. It can be seen that best result is obtained in the segmentation result of Image no. 3, i.e. V_pc = 0.857, V_pe = 0.112 and V_xb = 0.0087.

Similarly, Table 4 shows the simulation results performed on the four MR Images when four clusters are considered. It can also be seen that best result is obtained in the segmentation result of Image no. 2, i.e. V_pc = 0.746, V_pe = 0.217 and V_xb = 0.0172.

Similarly, Table 5 shows the simulation results performed on the four MR Images when five clusters are considered. It can also be seen that best result is obtained in the segmentation result of Image no. 4, i.e. V_pc = 0.570, V_pe = 0.309 and V_xb = 0.0117.

In Table 6, the optimal values from Tables 3, 4 and 5 are extracted and accommodated together, so that a multiple function graph can be plotted for observing the trend in change of cluster validity function values as the number of cluster in each experiment increases. It be seen that the V_pc deteriorates from 0.857 to 0.570 for number of clusters equal to three onwards. Whereas, the value of V_pe increases from 0.112 to 0.309 for number of clusters equal to three onwards, it may be noted that the highest grade partition entropy is zero (0). The computed value of Xie-Beni’s Validity function (V_xb) also degrades as the number of clusters are increased from three onwards.

Table 6
Comparison of optimal values of cluster validity functions selected from tables III, IV & V.

Images Algorithm Clusters Vpc Vpe Vxb

I3(Table3) GIFMRCM 3 0.857 0.112 0.0087

I2(Table 4) GIFMRCM 4 0.746 0.217 0.0172

I4(Table 5) GIFMRCM 5 0.57 0.309 0.117

Images	Algorithm	Clusters	Vpc	Vpe	Vxb
I3(Table3)	GIFMRCM	3	0.857	0.112	0.0087
I2(Table 4)	GIFMRCM	4	0.746	0.217	0.0172
I4(Table 5)	GIFMRCM	5	0.57	0.309	0.117

Consequently, the graph shown in fig. 13 is indicative in itself that for the current MRI images under observation, the quality of the clustering coefficients viz. Partition Coefficient (V_pc), Partition Entropy (V_pe) and Xie-Beni’s Validity function (V_xb) degrades gradually as the number of partitions are increases from three onwards. Thus, for the MR Images considered in the current cluster-wise color image segmentation work, optimal values are obtained by using three clusters. It may also be noted that in our current analysis using either one or two colors is not acceptable due to the basic fact that three primary colors are required for constructing an image.

Fig.13

Multiple function plot showing variations of V_pc, V_pe and V_xb against varying number of clusters.

6 Conclusion

In this paper, a novel image segmentation algorithm named GIFMRCM is proposed, which is being developed with inspiration from popular algorithms viz. Fuzzy C Means, Genetic algorithms and Markov Decision Process (MDP). In the proposed algorithm, the traditional FCM constraint of minimising an objective function based only on the spatial distance between the center and data has been solved by considering a “state-action pair” approach. The new objective function thus proposed is indicative of the fact that a relational factor (Rij) is being added so that the mutual connectivity between the membership value and centroid is being considered resulting in a more crisp clustering of pixels. Experimentation on medical and camera images shows that the proposed algorithm can improve the performance of image segmentation, and remove noise efficiently. The cluster-wise feature extraction procedure proposed in this paper is also able to extract delicate regions of human brain with ease. The proposed GIFMRCM was able to obtain an optimal value of Vxb equal to 0.0087, Vpc equal to 0.857, and Vpe equal to 0.112 in comparison with FCM.

In addition, the dynamic cluster-wise color segmentation procedure followed in this paper also creates an opportunity for more in-depth analysis of Robotic vision based image and video segmentation application for autonomous vehicles.

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An Unsupervised Cluster-wise Color Segmentation of Medical and Camera Images using Genetically improved Fuzzy-Markovian Decision Relational Model

Abstract

Keywords

1 Introduction

1.1 Related works

1.2 Outline of our Contributions

2 Proposed Image Segmentation Algorithm – “Genetically Improved Fuzzy-Markovian Relational Clustering Matrix (GIFMRCM)”

4 Simulation results for the proposed Image segmentation procedure

4.1 Cluster Validity Indices

5.1 Implementation on GIFMRCM segmented MR images

Table 6 Comparison of optimal values of cluster validity functions selected from tables III, IV & V. Images Algorithm Clusters Vpc Vpe Vxb I3(Table3) GIFMRCM 3 0.857 0.112 0.0087 I2(Table 4) GIFMRCM 4 0.746 0.217 0.0172 I4(Table 5) GIFMRCM 5 0.57 0.309 0.117

References

Table 6
Comparison of optimal values of cluster validity functions selected from tables III, IV & V.

Images Algorithm Clusters Vpc Vpe Vxb

I3(Table3) GIFMRCM 3 0.857 0.112 0.0087

I2(Table 4) GIFMRCM 4 0.746 0.217 0.0172

I4(Table 5) GIFMRCM 5 0.57 0.309 0.117