Fuzzy Logic Approaches in the Task of Object Edge Detection

Abstract

The task of reducing the computational complexity of contour detection in images is considered in the article. The solution to the task is achieved by modifying the Canny detector and reducing the number of passes through the original image. In the first case, two passes are excluded when determining the adjacency of the central pixel with eight adjacent ones in a frame of size 3х3. In the second case, three passes are excluded, two as in the first case and the third one necessary to determine the angle of gradient direction. This passage is provided by a combination of fuzzy rules. The goal of the work is to increase the performance of computational operations in the process of detecting the edges of objects by reducing the number of passes through the original image. The process of edge detection is carried out by some computational operations of the Canny detector with the replacement of the most complex procedures. In the proposed methods, fuzzification of eight input variables is carried out after determining the gradient and the angle of its direction. The input variables are the gradient difference between the central and adjacent cells in a frame of size 3х3. Then a base of fuzzy rules is built. In the first method, four fuzzy rules and one pass are excluded depending on the angle of gradient direction. In the second method, sixteen fuzzy rules themselves set the angle of the gradient direction, while eliminating two passes along the image. The gradient difference between the central cell and adjacent cells makes it possible to take into account the shape of the gradient distribution. Then, based on the center of gravity method, the resulting variable is defuzzified. Further use of fuzzy a-cut makes it possible to binarize the resulting image with the selection of object edges on it. The presented experimental results showed that the noise level depends on the value of the a-cut and the parameters of the labels of the trapezoidal membership functions. The software was developed to evaluate fuzzy edge detection methods. The limitation of the two methods is the use of piecewise-linear membership functions. Experimental studies of the performance of the proposed edge detection approaches have shown that the time of the first fuzzy method is 18% faster compared to the Canny detector and 2% faster than the second fuzzy method. However, during the visual assessment, it was found that the second fuzzy method better determines the edges of objects.