Edge Detection in Gray Level Images based on the Shannon Entropy

Abstract

Most of the classical mathematical methods for edge detection based on the derivative of the pixels of the original image are Gradient operators, Laplacian and Laplacian of Gaussian operators. Gradient based edge detection methods, such as Roberts, Sobel and Prewitts, have used two 2-D linear filters to process vertical edges and horizontal edges separately to approximate first-order derivative of pixel values of the image. The Laplacian edge detection method has used a 2-D linear filter to approximate second-order derivative of pixel values of the image. Major drawback of second-order derivative approach is that the response at and around the isolated pixel is much stronger. In this research study, a novel approach utilizing Shannon entropy other than the evaluation of derivates of the image in detecting edges in gray level images has been proposed. The proposed approach solves this problem at some extent. In the proposed method, we have used a suitable threshold value to segment the image and achieve the binary image. After this the proposed edge detector is introduced to detect and locate the edges in the image. A standard test image is used to compare the results of the proposed edge detector with the Laplacian of Gaussian edge detector operator. In order to validate the results, seven different kinds of test images are considered to examine the versatility of the proposed edge detector. It has been observed that the proposed edge detector works effectively for different gray scale digital images. The results of this study were quite promising

A generalized entropy-based two-phase threshold algorithm for noisy medical image edge detection

“…GLGM histogram employs Fibonacci quantized gradient magnitude to e ectively characterize spatial information by applying entropic image thresholding; Singh and Singh [26] proposed an algorithm based on Shannon entropy for edge detection in gray level images obtaining acceptable results; in [46], El-Khamy et al used the relationship of the probability partition and the fuzzy 2-partition of the image gradient to select the optimal gradient-threshold, then it selects the algorithm that assures that the entropy reaches a minimum value; in [47], El-Sayed, presented a new algorithm for edge detection using both Shannon entropy and Tsallis entropy and in [48], Elaraby et al proposed a new algorithm for edge detection of images based on hybrid types of entropy.…”

“…The results are usually examined either by visual inspection as a qualitative measure [1,26] or quantitatively by di erent indexes [27][28][29][30][31][32][33][34][35]. Some of these algorithms utilize a linking technique collecting pixels that belong to a set of edges [36][37][38].…”

“…Compared with other methods, the most important advantages of entropy-based approaches for edge detection are the ease of its implementation and the few number of operations [26]. Entropy-based approaches are very stable and e cient in noisy environments [26]. Their comparison with other edge-detection algorithms has shown that they have high capability and have been successfully applied to problems of edge detection in noisy image [26].…”

“…Entropy-based approaches are very stable and e cient in noisy environments [26]. Their comparison with other edge-detection algorithms has shown that they have high capability and have been successfully applied to problems of edge detection in noisy image [26].…”

“…Entropy is de ned in terms of the probabilistic behavior of a source of information. Compared with other methods, the most important advantages of entropy-based approaches for edge detection are the ease of its implementation and the few number of operations [26]. Entropy-based approaches are very stable and e cient in noisy environments [26].…”