Edge detection using logarithm function

Edge detection is a commonly performed operation in image processing. In this paper, we propose a new method for edge detection using the logarithm function. The pixel values within a mask are normalized so that they can be regarded as probabilities. A positive constant is added to the probabilities to avoid zero values. Then, the sum of the logarithms of the adjusted probabilities is calculated. A threshold is chosen for generating the black and white edge image. Morphological operation is applied as post processing for refining the edges. Simulation results show that the proposed method has consistent performance on various sample images, which is competitive with the Sobel and Canny operators for edge detection. It is shown that the proposed method has almost identical performance as the entropy method. This phenomenon is well explained by using the theory of quasientropy.