Performing edge detection by Difference of Gaussians using q-Gaussian kernels

In image processing, edge detection is a valuable tool to perform the extraction of features from an image. This detection reduces the amount of information to be processed, since the redundant information (considered less relevant) can be disconsidered. The technique of edge detection consists of determining the points of a digital image whose intensity changes sharply. This changes are, for example, due to the discontinuities of the orientation on a surface. A well known method of edge detection is the Difference of Gaussians (DoG). The method consists of subtracting two Gaussians, where a kernel has a standard deviation smaller than the previous one. The convolution between the subtraction of kernels and the input image results in the edge detection of this image. This paper introduces a method of extracting edges using DoG with kernels based on the q-Gaussian probability distribution, derived from the qstatistic proposed by Constantino Tsallis. To demonstrate the method's potential, we compare the introduced method with the tradicional DoG using Gaussians kernels. The results showed that the proposed method can extract edges with more accurate details.