| description, image segmentation, image enhancement, image compression and pattern recognition etc. is one of the most important fundamental feature of an image. It is not so much that we argue the importance of the edge of image. There is a plethora of papers in the subject and are so many scientists who work on this problem and derive a lot of edge detection filters and algorithms that are various degrees of success of different image. Conjoint pixels, whose gray-level change greatly are considered image edge. In mathematics, this distributing change is often depicted by gradient. In this paper, we research several traditional and new types of algorithms, some of which are based on differential equations, and analyze their merit and disadvantage. Various kinds of traditional and modern edge detection methods are compared and their algorithms are presented in this paper. Which one is best depends on different application. But there do exist some common requirements. Canny developed three continuous criteria to compare the performance of different filters: good detection, good localization and low-responses. He also provided the respective expressions. Using these expressions, optimal linear filter of certain edge can be acquired and a comparison of different operators can be made. But Canny criteria is continuous and the optimal filter acquired is also a continuous function. However, the factual image data is discrete and the filter should also be discrete. Demigny solved this problem by introducing discrete criteria and the correspondent optimal linear smooth filter. The optimal linear filter and its smooth operators are presented in this paper under the combined criteria. They are integrated with edge detection techniques to perform edge detection and by using it, multiple edge images are detected. By small scale filtering image containing rich detail information and good localization ability...
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