Finding the Optimal Bit-Quad Patterns for Computing the Euler Number of 2D Binary Images Using Simulated Annealing

Abstract

This paper presents an automatic method for obtaining formulas to calculate the Euler number in 2D binary images. This problem is addressed as a combinatorial optimization problem, where specific bit-quad patterns are optimally combined. An algorithm based on simulated annealing is devised to find optimal expressions to compute the Euler number, considering 4- and 8-connectivity. The proposed approach found the complete family of expressions using three bit-quad patterns that correctly estimate the Euler number. Besides, another 58 new expressions are found that use more than three bit-quads. Hence, the proposed method can obtain automatically explainable formulas of the Euler number, and it can be potentially extended to other image representations.KeywordsEuler numberBit-quad patternsCombinatorial optimizationSimulated annealingExplainability