Speeding up the köhler's method of contrast thresholding

Köhler’s method is a useful multi-thresholding technique based on boundary contrast. However, the direct algorithm has a too high complexity O(N) i.e. quadratic with the pixel numbers N to process images at a sufficient speed for practical applications. In this paper, a new algorithm to speed up Köhler’s method is introduced with a complexity in O(NM), M is the number of grey levels. The proposed algorithm is designed for parallelisation and vector processing, which are available in current processors, using OpenMP (Open Multi-Processing) and SIMD instructions (Single Instruction on Multiple Data). A fast implementation allows a gain factor of 405 in an image of 18 million pixels and a video processing in real time (gain factor of 96).