Precise edge detection: representation by Boolean functions, implementation on the CNN

An edge detection problem is considered in the paper. It is proposed to reduce the edge detection problem on binary images to evaluation of the Boolean functions. A separate processing of the binary planes with their further integration into resulting image is used for edge detection on the gray-scale images. The different Boolean functions for detection of edges corresponding to the upward and downward brightness overleaps, to the narrow directions (south-north, south-east-north-west, etc.) are considered. All the processing functions are non-threshold Boolean functions of nine variables (such a number of variables corresponds to the processing within a 3×3 local window around the each pixel). Since all the functions are not threshold, CNN with universal binary neurons are proposed to be used for their implementation. The weighting templates for all functions are obtained by learning. The software simulation results are also presented