Selected Image Segmentation Techniques

Blast cells segmentation can be typically performed using various segmentation methods. This section discusses the segmentation techniques applied in this research for the purpose of blast cells segmentation.

3.2.3.1.1 Otsu Threshold

Otsu method is one of the most significant techniques for pixels-based threshold invented in 1979 by Nobuyuki Otsu (Otsu, 1979). It assumes that the image has two classes , of pixels, namely, foreground and background then select the global optimal threshold by maximizing the between-class variance. Let be an image represented with gray levels 0,1,2, … , 1 . The number of pixels at gray level denoted by and the total number of pixels is represented by  . The probability of gray level is denoted by (Otsu, 1979):

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, 0 , 1 (3.1)

Figure 3.6 depicts a typical histogram of a bi-level image, where the image has two classes with gray level 0,1, … , and with gray level 1, 2, … , 1 .

Figure 3.6: Typical histogram of a bi-level image

The gray level probability distributions of and  can be obtain by equation 3.2 and 3.3 respectively

Pr _(3.2)

Pr (3.3)

Then the means of the two classes can be calculated by equation 3.4 and 3.5 respectively

/ _(3.4)

/ _(3.5)

The total mean of the gray level is denoted by

(3.6) The class variances are

/ _(3.7)

/ _(3.8)

The within-class variance is

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The between class variance is

(3.10) The total variance of gray level is

(3.11)

Otsu method (Otsu, 1979) chooses the optimal threshold by maximizing the between- class variance, which is equivalent to minimizing the within-class variance, since the total variance (the sum of the within-class variance and the between-class variance) is constant for different partitions (Otsu, 1979).

max min (3.12)

3.2.3.1.2 Seeded Region Growing (SRG)

In 1994 Adams and Bischof introduced segmentation algorithm which is robust, rapid and free of tuning parameters known as Seeded Region Growing (SRG) (Adams & Bischof, 1994).

The essential idea behind SRG is that, the observation of the pixels belonging to one element of the object can possess similar properties, such as, the gray level value. Therefore if the considered pixel has gray level value that is near the common gray value of the region, this pixel can be associated into this region.

SRG is an iterative process initiated in a pixel from the set of seeds   , , … , . Pixels at the seed's border are subsequently labeled whether or not they are part of the same region as the seeds (Hirschmugl et al., 2007). The seeds are either chosen automatically based on some feature presented in the image or interactively according to the user opinion.

The SRG process develops inductively from the choice of seeds selected, known as, the initial state of the sets    , , … , .

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In SRG, each step of the process performs addition of one pixel to any on the above sets. Then considering the state of the set   after steps, let be the set of all unallocated pixels (none labeled), bordering at least one of the regions   such that (Adams & Bischof, 1994):

  |   (3.13)

  Where  is the second-order neighborhood of the pixel of interest as shown in Figure 3.7

1, 1) , 1) 1, 1)

1, ) , ) 1, )

1, 1) , 1) 1, 1)

Figure 3.7: The second-order neighborhood , of current testing pixel at , If for, we have that meet just one of the  , then we can define

1,2, … , to be that index such that ,       and is a measure of how is different from the region it joins. The simplest definition of is (Adams & Bischof, 1994):

  (3.14)

Where is the gray level intensity of the image pixel  . If meets two or more of the  , is taken to be the value of such that meets   and is also minimized. In these circumstances, it is desirable to classify the pixel as the boundary pixel and append it to set  , which is a set of already-found boundary pixels.

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We then take such that (Adams & Bischof, 1994):

(3.15) And append to  . This process completes step  1. This entire process is iteratively repeated until all pixels are allocated. In SRG, the process starts with each    being one of the seed sets. Thus, the definition of in equation (3.13) and (3.14) ensures that the final segmentation is as homogenous as possible.

Practically, the criteria to choose the seed depends on the nature of the problem. For instance, if the targeted region needs to be detected using infrared images, the brightest pixels are chosen. The pixels homogeneity can be traced based on any characteristic of the ROI in the image such as texture, color, average intensity, etc.

3.2.3.1.3 Mathematical Morphology

Mathematical morphology is a non-linear process, which is considered as the basic foundation for many image processing algorithms. It can be used to investigate the geometrical structure in image by manipulating the original image with another image known as Structuring Element (SE) (Serra, 1982; Shih et al., 1995).

It has been proven that this technique is very useful for the analysis of biological and medical images (Wu et al., 1995). This processing technique has also proves to be a powerful tool for many computer-vision tasks in binary and gray scale images, such as image enhancement, noise suppression, edge detection, skeletonization, etc. (Ortiz et al.,

2002). 

Mathematical Morphology is based on simple mathematical concepts from set theory. Morphological operators are originally developed for binary images. However, it can also be used for gray level images.

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It views binary images as assets of its foreground (1-valued) pixels, and set operations such as set union and intersection can be applied directly to sets of binary image (Gonzalez et al., 2004). The two fundamental mathematical morphology operators are Dilation and Erosion.

Dilation is used to grow or thicken regions in a binary image, while in the gray level image; Dilation is used to brighten small dark areas, and to remove small dark "holes". According

to (Gonzalez et al., 2004), Dilation on an image by a structure element is denoted by and it is represented by the following Equation:

|   (3.16)

Where is the reflection of   . It means that dilation of by is done by reflecting and then shifting over by  . On the other hand, erosion is used to shrink or thins region in binary image, while in a gray level image, erosion darkens small bright areas, and remove very small bright areas like noise spikes or small spurs. Erosion is represented by the following Equation (Gonzalez et al., 2004):

| _(3.17)

The two basic morphological processes can be combined together to produce two more interesting operators, namely, Opening and Closing. The morphological opening (equation 3.18) is simply an erosion of by followed by dilation of the result by  (Gonzalez et al., 2004).

(3.18) Morphological opening is generally used to smooth region boundaries, break thin connection, and remove thin protrusions in images. On the other hand, morphological closing (equation 3.19) is performed by dilating by and then eroding the result by  (Gonzalez et al., 2004).

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Unlike opening, morphological closing tends to join narrow breaks, fill long thin gulfs, and fill holes smaller than  (Gonzalez & Woods, 2002; Gonzalez et al., 2004).

3.2.3.1.4 Watershed Segmentation

One of the most challenging problems in microbiological image processing is separating touching cells (Wilkinson & Schut, 1998). There are a number of factors that can lead to this type of problem during the process of PB smear preparation such as (i) the size of the drop of blood, (ii) the angle of the spreader slide and (iii) the speed at which the smear is made (Estridge & Reynolds, 2011).

The method that is usually preferred for separating touching, but mostly convex, features in an image is known as the watershed segmentation (Beucher & Lantejoul, 1979; Lantejoul & Beucher, 1981; Sun & Luo, 2009).

The watershed transform can be classified as a region-based segmentation approach. The intuitive idea underlying this method comes from geography: it is that of a landscape or topographic relief which is flooded by water, watersheds being the dividing lines of the domains of attraction of rain falling over the region. An alternative approach is to imagine the landscape being immersed in a lake, with holes pierced in local minima. Basins (also called `catchment basins') will fill up with water starting at these local minima, and, at points where water coming from different basins would meet, dams are built. When the water level has reached the highest peak in the landscape, the process is stopped. As a result, the landscape is partitioned into regions or basins separated by dams, called watershed lines or simply watersheds. A simulation of the watershed transform is shown is Figure 3.8.

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Figure 3.8 Simulation of the watershed transform. (a) Input image. (b) Punched holes at minima and initial flooding. (c) A dam is built when waters from different minima are about to merge. (d) Final flooding, with three watershed lines and four catchment basins.

(Wu et at., 2010)

Advantages of the watershed transform include the fact that it is a fast, simple and intuitive method. More importantly, it is able to produce a complete division of the image in separated regions even if the contrast is poor, thus there is no need to carry out any post- processing work, such as contour joining, thus the watershed segmentation technique has been widely used in medical image segmentation (Ng et al., 2008), such as the segmentation of blood cell images (Nemane & Chakkarwar, 2012; Sharif et al., 2012) , MRI brain images (Ng et al., 2006), Pap smear images (Plissiti et al., 2010; Orozco- Monteagudo et al, 2013), Colonoscopy images (Hwang et al., 2007) and many others.