In this paper, the authors investigate data reduction techniques using cytological image data for the purpose of further classification applying modern approaches. Cytological images are widely used in diagnosing cancerous and precancerous conditions of the breast. Classification of the whole image is a rather time consuming process, so the authors apply an approach when quantitative characteristics of micro-objects (cell nuclei) are used for classification. The authors carried out a comparative analysis of the classification of the cytological images based on the quantitative characteristics of their nuclei using modern classifiers. The main criteria for describing micro-objects (cell nuclei) are the following ones: area, perimeter, circumference, maximum width and length, area and perimeter of the bounding box. The structure of the biomedical image classification system is developed, including image processing stages, calculations of quantitative characteristics of micro-objects, data reduction and classification. The principal component method is used as data reduction technique. To classify data the following methods are used: a single-layer perceptron, logistic regression, support vectors machine, and the k-nearest neighbor method. Testing was performed using BPCI2100 database of cytological images of cancerous and precancerous conditions of the breast.
1,2,3,4,5,6 Ternopil National Economic University, 46001, Ukraine
7 Lviv Polytechnic National University, 79000, Ukraine
Cytological and histological images are used to diagnose precancerous and cancerous
conditions of the breast. After a microscopic examination, a specialist can determine
the type of an image. To simplify the analysis process of cytological and histological
images, a number of automated microscopy systems (AMSs) with functions for image
processing were developed. The use of artificial intelligence, in particular artificial
neural networks, support vector machines, etc. show the current trends of
improvement in AMSs [
The main advantage of using quantitative characteristics for the purpose of microobject classification is the lack of a subjective human factor. Therefore, an urgent problem is evaluation of the quantitative characteristics of micro-objects, their reduction and data classification using modern classifiers to improve diagnostic accuracy. 2
Classification is an important part of the data analysis process, which can be
performed by different algorithms divided into different groups. These groups are based
on machine learning techniques [
The analysis of the above-mentioned publications has shown that scientists pay considerable attention to the problem of finding the ways of diagnosing precancerous and cancerous conditions of the breast on the basis of artificial intelligence systems. However, the complexity of the study and the large number of classifiers require additional research and comparative analysis, and a considerable amount of data needs to be reduced in size. 3
The purpose of this work is to analyze the existing means of artificial intelligence and their applications for the classification of cytological images based on the quantitative characteristics of micro-objects. To achieve this goal, the following tasks must be accomplished: 1. To reduce data using the principal component method. 2. To develop the structure of classification system of cytological images. 3. To conduct computer experiments in order to carry out a comparative analysis of the classifiers.
Formally, the formulation of the problem is as follows. Assume a set of features (1):
X xij , i 1, m , j 1, n , (1) where n – a number of features, m – a number of their implementations. In addition, a set of classes P is given.
To carry out the classification procedure we use a set of classifiers (2):
C C1 , C2 , ..., Ct , where t – a number of classifiers.
After applying the PCA, we obtain a set of components Y yi , where Vі 1, m . Each component is a linear combination of features (3):
y j w1 j x1 w2 j x2 ... wrj xr , when r m .
Thus, we get a set of components with their contributions yk , I k , k 1, s , where s – a number of principal components.
The classification accuracy 0 is specified. Then, it is necessary to find s value in such a way: s Y s min Y . (4)
Y s Y , 0 4
Input feature matrix X is given:
X
In columns there are features, they are indexed by j ( j 1, n ), and the lines are their implementations. They are indexed by i ( і 1, m ).
The PCA implementation can be presented by a number of steps. 1. Centering and rationing of the output data is performed according to the formula (6): xij xj , (6)
j where j – the number of the original variable, i – the implementation number of the j -th variable, and x j and j – the arithmetic mean and root mean square deviation of the x j feature. 2. Calculating the covariance (S) or correlation (R) matrix.
x21 covx2 ,x1 S cov xn ,x1 cov x1 ,x2 (7) (8) (9) (10) 3. Finding the eigenvalues 1 2 … p 0 of the matrix S (or R) using characteristic equation (10):
det S E 0 or det R E 0 , where E – a unitary matrix (a square matrix with ones on the diagonal and zeros elsewhere).
4. Finding the eigenvector for each eigenvalue j . The eigenvector is the solution to the system of equations (11): where w – eigenvector. 5. Finding linear combinations for principal components y j y j w1 j x1 w2 j x2 ... wpj xp . (11) (12) 6. Analysis of the contribution of each of the principal components and their ranking in ascending order.
The contribution of each component is evaluated by the formula (13): 1 2 ... p where j – a number of a component.
I j j , (13)
The lack of clear contours of cell nuclei leads to difficulties in cytological image
processing. Transmission of the digital image from the camera to the microscope and via
communication channels to the computer causes pulse noises, which can often be
classified by the software system as a part of the investigated object. Examples of
cytological images of precancerous and cancerous conditions of the breast are taken
from the BPCI2100 database [
During the study, the following quantitative characteristics of cell nuclei were determined: area, perimeter, length, width, circumference, coordinate Xc, coordinate Yc, length of the major axis, length of the minor axis, angle of inclination of the major axis to the OX axis, perimeter of a bounding box, coordinate Bx, coordinate By, bounding box width, bounding box length, bounding box area, aspect ratio.
The structure of cytological image classification module is shown in Figure 2. The classification process consists of the following steps:
1. Filtering the input image. This stage makes it possible to reduce noise. Gaussian and Median filtering is used to reduce Gaussian and pulse noise, respectively. Filtering can significantly improve image quality that will have positive impact on the next stages.
2. Segmentation. A segmentation stage is required to select particular areas in the
image (cell, background nuclei). For cytological images, the best results were shown
by watershed algorithms, k-means, and threshold segmentation. Based on these
algorithms, an algorithm for segmentation of cytological and histological images was
developed [
Cell nuclei are selected using the image contour selection algorithm developed by
the authors[
After converting the image into the type of “white background – black objects”, the quantitative characteristics of the particular micro-objects are evaluated. 3. Data reduction. The principal component method is used to reduce the data size. 4. Classification. Data in the form of an array of numbers is fed to the classification module. The classification module implements the support vector method, logistic regression, a single-layer perceptron and the k-nearest neighbor method. Classification results in an associative array that includes data on the parameters of the nuclei and their corresponding classes.
To analyze the classification results, ROC-curves were constructed and AUC coefficients were calculated. 6
The software module for testing the cytological image classification techniques is written in Java programming language and deeplearning4j library.
An example of the data reduction of the analysis of the cytological image cell nuclei is given in Figure 3.
The results of the classification of the cytological images by the support vector method are shown in Figure 4.
2 components (AUC = 0.75)
3 components (AUC = 0.6 5 components (AUC = 0.79) 8 components (AUC = 0.91)
Classification quality score using the support vector method on the basis of the AUC coefficient is shown in Figure 5. ig. 5. Classification quality score using the support vector method
The analysis of the results in Figure 5 shows that the highest classification accuracy can be achieved using 8 components. Classification results with the use of a singlelayer perceptron are shown in Figure 6.
2 components (AUC=0.27) 3 components (AUC=0.93) The AUC coefficient shows that the best classification quality is obtained with the use of 3 components.
The results of the classification of the cytological images based on multiclass logistic regression are shown in Figure 7.
Therefore, the best result is achieved with the use of 3 and 5 components and is 75%.
Conclusions 1. Using the basic algorithms of low, medium and high levels of computer vision, a classification structure of cytological images is developed. The developed structure includes the use of the principal component method to reduce the data size. 2. Applying the principal component method, the input indicators were reduced which showed that mainly three components are informative. 3. Computer experiments have shown that the best result of the classification of the quantitative characteristics of the cytological image nuclei is obtained using the 3 major components. The AUC is about 93%.