# Cancer Affected White Blood Cells Biology Essay

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The cancer cells are multiplicative in nature. Doctors face difficulties in counting the white blood cells at a particular stage due to crowding of cells. This project proposes the robust segmentation algorithm that can reliably separate touching cells. Segmentation is the main important step in medical image processing. Precisely locating the area of interest in an image, in the presence of inherent uncertainty and ambiguity, is a challenging problem in medical imaging. Here one is often faced with a situation that demands proper segmentation. The algorithm is composed of two steps. It begins with a detecting and finding the cells in the region that utilizes level set algorithm. Next, the contour of big cell is obtained using level set active contour based on a Heaviside function. Finally, the proposed algorithm is compared with several images which aids in applications such as locating the tumors and other pathologies etc.,

Cancer prevalence in India is estimated to be around 2.5 million, with over 8,00,000 new cases and 5,50,000 deaths occurring each year due to this disease.Â More than 70% of the cases report for diagnostic and treatment services in the advanced stages of the disease, which has lead to a poor survival and high mortality rate. The impact of cancer is far greater than mere numbers. Its diagnosis causes immense emotional trauma and its treatment, a major economical burden, especially in a developing country like India [1].

Segmenting individual cells in blood cancer is usually the first step that is required in automatic image analysis. Segmentation is a challenging problem due to the complex nature of the cells. Image segmentation is the process of building a partition of the image into connected regions, such that pixels of the region are homogenous according to some criterion (gray value, motion, etc).Segmentation plays an important role in image processing.

Recently an automatically identify and the multiple cells by exploiting the shape and intensity characteristics of the cells was proposed in [2]. An energy functional dependent upon the gradient magnitude along the cell boundary, the region homogeneity within the cell boundary and spatial overlap of the detected cells is minimized. [3] proposed a complete segmentation procedure that solves the cluster-separation problem using moving interface models and a model-based combinatorial optimization scheme. They were segmented for clustering images not for overlapping regions.

Each of these segmentation methods produced good results on regions exhibiting little or no cell crowding; however, they often failed to separate touching cells accurately. The watershed family of algorithms has become one of the most commonly used segmentation methods to address the challenge of touching cells. However, the primary limitation of the watershed approaches is that they often result in over segmentation. Some algorithms such as marker controlled watershed [4], Otsu method [5], rule based strategies [6-8] were developed to address this problem. When the intensity of overlapping regions is brighter (or darker) than the non overlapping regions within individual cells, a set of false seeds will be created in the overlapping regions [9]. This is not surprising because the voting schema in [9] is biased toward the boundary of the object. The edges of overlapping regions contribute to the creation of false seeds within the overlapping regions. The significant improvement of the new algorithm that applies a shifted Gaussian kernel [10] and mean shift onto single-pass voting to generate more accurate and quicker seed detection was proposed later.

The rest of the paper is organized as follows. The importance, needs of image segmentation and the methods used in this project is described in section 2. In section 3, we formulated the derivation of level set. The modified level set algorithm is described in section 4. In section 5, we validate our method by various experiments on cancer and normal microscopic blood smear images.

Image Segmentation

In image processing and computer vision, segmentation is the process of partitioning a digital image into multiple segments (sets of pixels, also known as super pixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and boundaries in images.

More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain visual characteristics. This reduces the pixel data to region based information. Segmentation of an image which classifies voxels/pixels into objects or groups.

2.1 Need For Segmentation

In image processing it can be number of pixels with the same intensity in general. Segmentation is to separate the homogeneous area. The analysis of blood slides is a powerful tool in determining the health status of an individual and could detect several diseases. The count and shape, lineage and maturity level of white and red blood cells (RBC) could aid in the diagnosis of diseases that range from inflammatory to leukemia. Many automated techniques were proposed to overcome the tedious and time consuming task of human experts in counting and classifying white blood cells. Various techniques were used for the segmentation stage including mean shift algorithm, histogram equalization, thresholding, watershed algorithm.

2.2 Mean Shift Based Seed Detection

Mean shift is a non-parametric feature-space analysis technique, a so-called mode seeking algorithm. Application domains include clustering in computer vision and image processing. Mean shift is a procedure for locating the maxima of a density function given discrete data sampled from that function. It is useful for detecting the modes of this density and it is an iterative method.

2.3 Level Set Method

The level set method (LSM) is a numerical technique for tracking interfaces and shapes. The advantage of the level set method is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects. Also, the level set method makes it very easy to follow shapes that change topology, for example when a shape splits in two, develops holes, or the reverse of these operations. All these make the level set method a great tool for modeling time-varying objects, like inflation of an airbag, or a drop of oil floating in water. The advantage of level set methods are implicit, parameter free method and provides a direct way to estimate the geometric properties of evolving structure and the applications include edge extraction, code tracking and contour tracking.

Consider the most general case the following form of curve propagation is

C (p,t) = F(k) * N where C is a closed curve propagation

F(k) is a force and N is normal to curve/surface

The level set method represents the curve in the form of an implicit surface is

The level set method accounts to representing a closed curve using an auxiliary function called the level set function. This is derived from the initial contour according to the following condition:

C (p, 0) = {(x,y) : }

and the level set method manipulates C implicitly, through the function . is assumed to take positive values inside the region and negative values outside the region which is determined by the curve propagation C.

The level set flow can be re-written in the following form

where H is a Hamiltonian.

2.4 Active Contour

Active contour model [11], also called snakes, is a framework for delineating an object outline from a possibly noisy 2D image. This framework attempts to minimize an energy associated to the current contour as a sum of an internal and external energy.

Internal energy is defined within the contour itself to maintain the contour smooth and external energy is computed from the image data to move the contour toward an object boundary. When the external and internal energy becomes equal, the energy attains equilibrium and contour stabilizes.

The active contour or snakes model is popular in computer vision, and led to several developments in 2D and 3D. In two dimensions, the active shape model represents a discrete version of this approach, taking advantage of the point distribution model to restrict the shape range to an explicit domain learned from a training set. The advantages over classical techniques are snakes are autonomous and self-adapting in their search for a minimal energy state. They can be easily manipulated using external image forces. They can be made sensitive to image scale by incorporating Gaussian smoothing in the image energy function. They can be used to track dynamic objects in temporal as well as the spatial dimensions. [11]

Cell Segmentation

Consider the image I that has N cells. Assume that the image uo is formed by two regions of approximatively piecewise-constant intensities, of distinct values uoi and uoo. Assume further that the object to be detected is represented by the region with the value uoi. Let denote its boundary by Co. Then uo â‰ˆ uoi we have inside the object [or inside (Co)], and uo â‰ˆ uoo outside the object [or outside (Co)]. Now let us consider the following "fitting" term or level set energy functional term:

F1(C) + F2(C) = +

Where c1 and c2 are constants depend on C are the averages of uo inside C and respectively outside C. The energy term can be written as the sum of two fitting terms. In this simple case, it is obvious that, the boundary of the object, is the minimizer of the fitting term

â‰ˆ0â‰ˆF1 (Co) + F2(Co)

The constants c1 and c2 can be denoted as

C1 =

C2 =

Where H(x,y) is Heaviside function which will be discussed in next section and K(x,y) is defined as 2D Gaussian kernel function:

K =

Ïƒ is standard deviation.

For instance, if the curve C is outside the object, then F1(C) > 0 and F2(C) â‰ˆ 0. If the curve is inside the object, then F1(C) â‰ˆ 0 but F1(C) > 0. If the curve is both inside and outside the object, then F1(C) > 0 and F2(C) > 0. Finally, the fitting energy is minimized if C=Co, i.e., if the curve is on the boundary of the object. These basic remarks are illustrated in Fig. 1.

F1(C)>0, F2(C) â‰ˆ 0,Fitting>0 F1(C)â‰ˆ0,F2(C)>0,Fitting>0

F1(C)>0,F2(C)>0,Fitting>0 F1(C)â‰ˆ0,F2(C)â‰ˆ0,Fitting=0

Figure 1. Boundary condition

In active contour model we will minimize the above fitting term and we will add some regularizing terms, like the length of the curve C, and or the area of the region inside C proposed by [12] which is based on the Mumford-Shah model [13]. Therefore, we introduce the energy functional F (c1, c2, C), defined by

F (c1, c2, C) = Âµ*length(C) + v*Area (inside(C)) + Î»1

Âµ â‰¥ 0, v â‰¥ 0, Î»1, Î»2 > 0 are fixed parameters. In numerical calculations, Î»1 = Î»2 = 1 and v = 0. If this value is small enough, then it segments smaller objects otherwise it segments larger objects in the cell region.

Therefore, consider the minimization problem is

In the isoperimetric inequality the length is comparable with area is given by

Area (inside(C)) â‰¤ c* length (C)

where c is a constant.

Relation With The Mumford-Shah Function

The Mumford-Shah functional [13] for segmentation is

= Âµ*length(C) + dxdy + dxdy

where Âµ and Î» are positive parameters. A reduced form of this problem is simply the restriction of FMS to piecewise constant functions u, i.e., u = constant ci on each connected component of. Therefore, as it was pointed out by D. Mumford and J. Shah, ci = average (uo) on each connected component. The reduced case is called the minimal partition problem.

The active contour model with v=0 and Î»1= Î»2= Î» is a particular case of the minimal partition problem, in which we look for the best approximation u of uo, as a function taking only two values, namely

u=

and with one edge C, represented by the snake or the active contour.

Level Set Formulation

In the level set method [14-15], the closed curve C, inside(C) and outside(C) which is represented by the zero level set of a Lipschitz function

C= = { (x,y) Ð„ â„¦ : (x,y) = 0}

inside(C) = = {(x,y) Ð„ â„¦ : (x,y) > 0}

outside(C) = â„¦ / = {(x,y) Ð„ â„¦ : (x,y) < 0}

For the level set formulation of our variational active contour model, we replace the unknown variable C by the unknown variable.

Using the Heaviside function H, and the one-dimensional Dirac measure, and defined, respectively, by

H (z) =

Differentiate Heaviside function with respect to z, we get

where is the slope of the closed curve. H should be a flat line in regions, therefore slope becomes zero. Then is zero for z> and z<.

If z=, z_= -a/2, z+= +a/2, then slope gives

The delta function, =

The energy function can be minimized by iteratively employing the gradient descent method.

= -

By this method, all the edges are detected. But some of the smaller cells are detected. To detect those smaller areas, Euler Lagrange equation is employed. This equation acts locally to separate smaller objects. Finally, all the edges are detected by level set formulation.

IV Modified Level Set Algorithm

This model is used to segment white blood cell areas by embedding the local image information. The energy functional area is given by

Where Î»1 and Î»2 > 0 are fixed parameters, KÏƒ is Gaussian kernel with standard deviation Ïƒ, f1 and f2 are two smooth functions that approximate the local image intensities inside and outside of contour C respectively.

f1(x) =

f2(x) =

The standard deviation Ïƒ plays an important role in practical applications and this value varies for several images.

In the above equation, the regularized parameter of Heaviside function H and dirac function âˆ‚ are as follows:

The flow of level set using ACM is as follows:

STEP 1: Initialize the parameters.

STEP 2: Find distance between the center and radius.

STEP 3: Apply Heaviside function and Delta function.

STEP 4: Apply piecewise smooth function to energy functional terms.

STEP 5: Iteration

STEP 6: Obtain the convolution of distance and K-Phi.

STEP 7: Update the iteration value inorder to segment the interested region.

V Results and discussion

Microscopic blood smear images and the cancer affected blood images were taken to validate the algorithm. Normal blood cells and cancer affected blood cells were segmented individually using modified level set algorithm and the parameters were calculated and listed in Table.

Anormal1.jpg B normal2.jpg

CD:\PROJECT\cell images\normal3.jpg DD:\PROJECT\cell images\cancer1edit.jpg

Figure 2. Input images

Image A&D is affected by cancer, remaining cells normal blood cells. The segmented result is as follows:

Aseg3300,r-20 edit.png Bsegedit.png

C DC:\Users\DELL\Desktop\KU SEG FIGURES\INPUT2\normal1\seg 50k,r-45edit.png

Figure 3. Segmented Result

The parameters will vary for different images. The parameter plays an important role in segmentation and it must be tuned very properly.

A B

C D

Figure 4. 3Dimensional Plot

This figure shows the corresponding 3Dimensional plot for various blood cells. Red color line shows the initial contour level set algorithm.

Table1. Values for various blood smear images

MEASURE

IMAGE A

IMAGE B

IMAGE C

IMAGE D

ITERATION

3300

2400

4500

4000

MEAN

35.2128

29.1133

30.6189

1.6395

VARIANCE

241.3513

193.9551

191.04

8.3557

PHI (OUTPUT)

57.5403

51.1224

49.7286

10.5306

HPHI

0.9724

0.9938

0.9936

0.8589

VI Conclusion

Thus the level set using active contour algorithm was evaluated and tested for various blood cells. This algorithm gives the segmentation result of white blood cells. This algorithm begins with detecting the cells in the region. By using those regions, white blood cells alone segmented.