First and second order full-differential in the edge detection of images

In this paper, concepts of the first- and second-order differentials of images are presented to deal with the changes of pixels. They are the basic ideas in mathematics. We propose and reformulate them with a uniform definition framework. Based on our observation and analysis of the difference, we propose an algorithm to detect the edge from an image. Experiments on Corel 5K and PASCAL VOC2007 are carried out to show the difference between the first- and the second-order differentials. After a comparison with Canny operator and the proposed first-order differential, the main result shows that the second-order differential has a better performance on analyzing context changes of an image.