# br Image segmentation br Image

2.2. Image segmentation

Image segmentation is an operation that separates an image into non-overlapping fragments. The Otsu’s global thresholding is one of the most straightforward and practical approaches to segment an image into foreground and background objects [31]. In this type of segmentation, input gray level or colored im-age is transformed into a binary image, where the region of interest (foreground) in the input image is separated or distin-guished from non-region of interest or background. The thresh-old value t is selected for the segmentation of foreground from the background by reducing the variance of intra-class between foreground and background.
The approach in [31] provides an optimal threshold by reduc-ing the intra-class variance (the variation within the class), which is presented as a weighted sum of variances of the two MK2206 as given by the following equation:
ση2(t) = η0(t)σ02(t) + η1(t)σ12(t)
(1)
where η0 and η1 represent the weights, which correspond to the probabilities of the two classes, t is the threshold value and σ0 and σ1 represent the two-class variances.

Fig. 2. Data flow diagram of the proposed approach.

Once converted to a binary image, there exist some unwanted non-cell objects, which need to be removed. Therefore, the mor-phological closing operation is applied to the input image I by a structuring element M to remove unwanted objects, as given by the following equation:

I • M = (I ⊕ M) ⊖ M,
(2)
where the operator ⊕ corresponds to the morphological dila-tion and ⊖ corresponds to the morphological erosion. However, further improvement in removing noise is achieved by the use of area-based thresholding [32], which eliminates most of the unwanted objects in the image.

2.3. Feature computation

When cell objects are properly segmented, the extraction of relevant features takes place from the regions of interest for bet-ter predictions. Cellular level features are mostly focusing on the characteristics of isolated cells. For isolated objects with limited information and unknown distribution, the task of classification is achieved by extracting features based on the shape morphol-ogy and texture along with other features, such as histogram of oriented gradients and wavelet-based features [33]. In the pro-posed approach, important shape-based along with texture-based features are extracted for the detection and classification.

2.3.1. Shape based morphological features

The nucleus shape is described with the help of morpholog-ical features for different types of cell differentiation. Due to the variety in morphologies of the nucleus, various morpholog-ical features are extracted such as area, perimeters, aspect ratio, solidity, eccentricity, shape signature, perimeter, compactness, extent, major-axis length, and minor-axis length. The detailed explanation is given below:

• Nucleus Area: The area of an object in a 2D image is deter-mined by computing the nucleus pixel region. Mathemati-cally, it can be given by:

where A represents the nucleus area, and S is the seg-mented image or region of interest (ROI) with m rows and

n columns.

• Perimeter: The perimeter is the distance of connecting each neighboring pair of pixels around the boundary of the nu-cleus. The simplest way to measure the perimeter of the nucleus is by counting the total number of edge pixels related to the object. It can be shown by the following mathematical formula:
∑
Pi = S (m, n) (4)
m,nϵBi

where Pi is the perimeter, S is the segmented image or region of interest (ROI) with m rows and n columns, and Bi represents the boundary pixels.

• Aspect Ratio: This feature is the best feature for differen-tiating the circular and non-circular objects or needle-like shapes. The range of Aspect Ratio value is between 0 and 1. The value closer to 1 will be more elongated (like malignant cells in our case), whereas, the value closer to 0 shows benign cells.
• Solidity: Solidity is the ratio of the area A of ROI to its convex hull. It is also an essential feature, which is computed as follows:

Area

Solidity =

ConvexHull

• Compactness: Compactness can be computed by the ratio of area and perimeter square. It is calculated using the following equation:

A

where the variables A and P represent the area and perime-ter, respectively.
• Circularity: It is the measure of circularity of the malignant cell nuclei, i.e., how much the nucleus of the cell is circular. mathematically, it is represented as follows:

Circularity =

2.3.2. Statistical based texture features
In texture based features, statistical methods using local fea-tures can be applied to analyze the spatial distribution of gray values of the nucleus at every pixel in the image [34]. These texture based features are used to understand the gray level pixel in the breast cytology microscopic image [35]. In the proposed approach, first-order statistical derivatives are used for the classi-fication. Some important texture features and their mathematical representations are given below: