Pathology Detection and Analysis in Atherosclerosis Images

through Color Clustering Approach

R.Ravindraiah,

Assistant professor, ECE Dept., MITS,

Madanapalle-517325,AP, India, ravindra.ranga@gmail.com

Abstract: Image enhancement and segmentation plays a key role in pathology detection and analysis of medical

images. In this paper we discuss on a most threatening complication of heart patients usually called as Cardio

Vascular Disease (CVD) or Atherosclerosis (also known as arteriosclerotic vascular disease or ASVD). This is a

condition in which an artery wall thickens as a result of the accumulation of fatty materials such as cholesterol

which leads to luminal narrowing and cause Ischemic injury

In this paper we discuss a color clustering algorithm based on hierarchical binary tree region growing approach. Image display devices may allow only a limited number of colors to be simultaneously displayed. This set of

available colors, called a color palette, may be selected by a user from a wide variety of available colors. Such

device limitations make it difficult to represent high definition images which must then be quantized by a palette

with limited size. This color quantization problem is considered in two parts: the selection of an optimal color

palette and the optimal mapping of each pixel of the image to a color from the palette.

Tree structured color palettes greatly reduce the computational requirements of the palette design and pixel mapping

tasks, while allowing colors to be properly allocated to densely populated areas of the color space and hence useful

to cluster different regions in electron micrograph images easily and make the analysis of the pathology easier to a cardiologist.

Keywords: Atherosclerosis disease, Color quantization

I. INTRODUCTION:

Cardiovascular disease is responsible for 80%of deaths among diabetic patients much of which has been

attributed to CAD (coronary artery disease). However, there is an increasing recognition that diabetic patients suffer

from an additional cardiac insult termed „diabetic Cardiomyopathy‟ [1]. The underlying problem in most of the diabetic patients with

CVD is Atherosclerosis leading to narrowing of blood vessels supplying the heart; there by causing heart failure

[2][3]. Atherosclerosis (also known as arteriosclerotic vascular disease or ASVD) is a condition in which an artery

wall thickens as the result of a build-up of fatty materials such as cholesterol. Epidemiological and Clinical trial data

have confirmed the greater incidence and prevalence of heart failure in diabetes [4].

The biological vision system is one of the most important means of exploration of the world to humans,

performing complex tasks with great ease such as analysis, interpretation, recognition and pattern

classification[5].The ultimate aim in a large number of image processing applications is to extract important features from the image data, from which a description, interpretation, or understanding of the scene can be obtained for

human viewers, or to provide `better' input for other automated image processing techniques[6]. Segmentation of

atherosclerosis images (Electron micrograph Images) subdivides into its constituent regions or objects. The level of

detail to which the sub division is carried depends on the problem being solved. Considerable care should be taken

to improve the probability of accurate segmentation. Segmentation algorithms for monochrome images generally are

based on one of two basic categories dealing with properties of intensity values: discontinuity and similarity. In the

first category, the assumption is that boundaries of regions are sufficiently different from each other and from the

background to allow boundary detection based on local discontinuities in intensity. Edge-based segmentation is the principal approach used in this category. Region-based segmentation approaches in the second category are based on

partitioning an image into regions that are similar according to predefined criteria [7].

II. HIERARCHICAL BINARY TREE COLOR CLUSTERING ALGORITHM:

A.COLOR PALETTE DESIGN

The image is assumed to be on a rectangular grid of N pixels. The set of all grid points is denoted by S, and its

members s Є S may be explicitly written as s = (i, j ) where i is the row index and j is the column index. The color

value of the pixel at grid point s is denoted x, = [r,, g,, b,]' where the components are the red, green, and blue tri

stimulus values for the pixel [8] and superscript t means transpose. For a typical monitor, there is a nonlinear

relationship between the input value of the primary and its displayed intensity. For a particular primary such as red,

this relationship may be approximated by

Ir=r

γ

where Z, is the intensity, r is the input to the display, and ϒ= 2.3. More accurate models for this relationship

generally include constant, linear, and logarithmic terms [4]. In order to compensate for this nonlinear relationship

between input and luminance, it is common for video cameras and other image capture devices to pre distort their

output by the inverse relationship:

r= Ir(1/γ)

We shall refer to the pre distorted primary color values as the gamma corrected colors. In effect, this is the

coordinate system being used if one manipulates color image data and directly displays it without correction. It is

important to emphasize that the gamma corrected colors are not linear in intensity, and that the gamma correction,

and therefore the resulting coordinate system, varies with changes in a display's parameters. However, the gamma

corrected colors have the advantage that they may be directly displayed without transformation, and that they are

less susceptible to noise than the corresponding linear primary intensities [ 8].

Alternatively, standard coordinate systems have been defined for the representation of colors. Two such coordinate

systems are the L*a*b* and the L*u*v* color spaces [ 9]. These coordinate systems are nonlinearly related to the

primary intensities, and are chosen so that a fixed Euclidean distance represents a fixed perceptual distance

independent of position in the space. Gentile et al. have studied the application of the L*u*v* coordinate system to

the problems of image quantization [10], halftoning [11], and gamut mismatch [12]. This work indicates that these

coordinate systems can substantially improve quantized image quality relative to standard coordinate systems which

are linearly related to primary luminances. Therefore, it is reasonable to expect that perceptually based coordinate systems such as L*u*v* could improve the quality of displayed images relative to gamma corrected coordinates.

However, it will be assumed throughout this paper that the original image is specified in terms of gamma corrected

coordinates, since this avoids the computational requirements of coordinate transformation methods. All the

techniques developed can, of course, be applied using perceptually based color spaces.

B. BINARY TREE PLATELETE DESIGN

The objective of the palette design algorithm is to partition S into M disjoint sets or clusters where M is the

predetermined palette size determined by hardware constraints. The algorithm proposed here constrains the partitioning of S to have the structure of a binary tree. Each node of the tree represents a subset of S, and the

children of any node partition the members of the parent node into two sets. The set of image pixels corresponding

to node n is denoted Cn. For purposes of illustrating the operations of the algorithm, we will number the nodes so

that the root is 1 and the children of node n are 2n and 2n +1

Since the leaves of the tree form a partition of S, the pixels in S may be coded by representing all pixels in each leaf

node with a single color in the palette. Only the members of the tree's leaf nodes need be stored when the algorithm

is implemented. Each of the leaf node sets can be stored as a linked list. When a node is split, the linked list may be

reorganized into two lists without relocating any of the image color data. The method for generating the binary tree is specified by the number of leaves, M, the method of splitting a node into its two children, and the order in which

the nodes are split. The methods used for splitting nodes and determining which nodes to split both attempt to

minimize the total squared difference between the actual and quantized image.

The TSE is defined by

where qn is the quantization value used to represent the colors in the set Cn. In order to restrict the complexity of the

algorithm, second-order statistical properties will be used to determine the order and manner in which nodes will be

split. The three required cluster statistics are

……(1)

where Rn is a 3 X 3 matrix, and m, is a 3 component vector. Since the mean value of a cluster is the point from

which there is minimum squared deviation, the quantization value of a cluster q, is assumed equal to the cluster mean:

We also define the cluster covariance as

The splitting of a node into two nodes is equivalent to choosing two new quantization levels, q2, q2n+1 and

associating each member of the cluster with the closer quantization level. This, in turn, is equivalent to selecting a

plane which best splits the cluster's colors. In the proposed algorithm, we determine the direction in which the

cluster variation is greatest, and then split the cluster with a plane which is perpendicular to that direction and passes

through the cluster mean. For a large cluster with Gaussian distribution it can be shown that this strategy is optimal.

More specifically, we determine that unit vector e which maximizes the expression

Since Ŕ is symmetric, the solution is the eigenvector e, corresponding to the largest or principal eigenvector λn, of

8. The total squared variation in the direction e, is therefore

……………..(2)

Once the principal eigenvector has been determined, points in C, can be sorted into two sets C2n, and C2n+I in the

following way:

……………….(3)

Finally, the new statistics for each node may be calculated by first calculating R2n, m2n,, and N2n, for node 2n, and

then applying the relations

………….(4)

The order in which nodes are split is chosen with the objective of producing the greatest reduction in TSE at each

stage of the algorithm. Because this strategy does not look ahead to the results of further splits, it is not necessarily

optimal; however, one would expect it to perform well in most practical situations. When a node is split its variance

is mainly reduced along the direction of the principal eigenvector. Therefore, it is reasonable to assume that the reduction in TSE should be proportional to the total squared variation along the direction of the principal

eigenvector e, of R,. For this reason, the principal eigen value X, is used as a measure of the expected reduction in

TSE if node n is split. Given this approximation, the best allocation of a single quantization level is to split the leaf

with the largest principal eigenvector.

The basic binary quantization algorithm may now be described.

1) Set C1 = S.

2) Calculate R 1 , m1, and N1.

3) Do the following M - 1 times: 3.1) Find the leaf n such that X, is largest.

3.2) Use (3) to form the new nodes 2n and 2n+1

3.3) Calculate R, m, and N for new nodes using (4)

RESULTS:

In pathology, an atheroma (“tumor full gruel-like matter”) is an accumulation and swelling in artery walls that is

made up of (mostly) macrophage cells, or debris, that contain lipids (cholesterol and fatty acids), calcium and a variable amount of fibrous connective tissue. Atheroma occurs in atherosclerosis, which is one of the three subtypes

of arteriosclerosis; atherosclerosis, Monckeberg's arteriosclerosis and arteriolosclerosis.

In the context of heart or artery matters, atheromata are commonly referred to as atheromatous plaques. It is an

unhealthy condition, but is found in most humans.

The accumulation (swelling) is always between the endothelium lining and the smooth muscle wall central region

(media) of the arterial tube. While the early stages, based on gross appearance, have traditionally been termed fatty

streaks by pathologists, they are not composed of fat cells, i.e. adipose cells, but of accumulations of white blood

cells, especially macrophages that have taken up oxidized low-density lipoprotein (LDL). After they accumulate large amounts of cytoplasmic membranes (with associated high cholesterol content) they are called foam cells.

When foam cells die, their contents are released, which attracts more macrophages and creates an extracellular lipid

core near the center to inner surface of each atherosclerotic plaque. Conversely, the outer, older portions of the

plaque become more calcific, less metabolically active and more physically stiff over time.

Fig a1: Typical micrograph image of atherosclerosis

Fig a2: the lumen remained is observed

Fig a3: the rupture on the occluded intima is seen

The thick red- thrombus is detected

Variation between Media and plaque is observed

Atherosclerosis plaque [Lipid core]is detected

Fig: a4

The plaque occluded is detected

Fig: a5

The percentage of lumen left is observed here

The gap between media and occluded intima is observed

Calcium content is detected

Fig b1: Histological features of atherosclerosis in humans. A Masson's trichrome stained, coronal section of the left

anterior descending artery of a thrombotically occluded atherosclerotic lesion which led to a fatal myocardial

infarction. Blue stain indicates collagen-rich regions, pale red indicates normal cellular regions, and deep red

indicates the mural thrombus in the lumen of the artery.

Fig b2: clustered image 1

Thrombus is clearly visible

Cholesterol rich core is segmented

Lumen spited and the spread of fibrous cap, thrombus and variation in media and fibrous cap is seen

Ruptured lesion that supports the flow of blood into the plaque is observed

Fig b3:

The accumulated cholesterol rich region is seen.

The extreme borders of the lumen [before and after occlusion] left is detected

We can calculate the area of original lumen and the occluded lumen.

Swelling of the media is observed

Restonic lesion is detected

Fig b4:

The remaining lumen left is detected

Fig b5:

Thrombus is completely detected

Ruptures are seen clearly

Media is detected

Fig b6:

Thick blue- fibrous cap is detected and the ruptures are observed

Gap between the actual and occluded lumen is observed

Percentage of lumen left is observed

The accumulated cholesterol is detected

The swelling in the media is observed

CONCLUSION

Thus the results attained through this method are quite optimun for the analysis of Cardiovascular complications

easily not only for a Cardiologist but even for a novice.

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