Speeding up the K\"ohler's method of contrast thresholding

TL;DR

This paper introduces a new parallelized algorithm for K{"o}hler's contrast thresholding method, significantly reducing computational complexity and enabling real-time image and video processing.

Contribution

A novel O(N M) algorithm for K{"o}hler's method that leverages parallel processing and vectorization for practical, high-speed image analysis.

Findings

Achieves a 405-fold speedup on large images.

Enables real-time video processing.

Reduces computational complexity from quadratic to linearithmic.

Abstract

K{\"o}hler's method is a useful multi-thresholding technique based on boundary contrast. However, the direct algorithm has a too high complexity-O(N 2) 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 K{\"o}hler's method is introduced with a complexity in O(N M), 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).