Machine Learning-based Formulas for Computing the Euler Characteristic of Binary Images.

The computer vision community has proposed numerous formulations for object description based on human perceptivity and vast knowledge of the problem domain. In order to reduce human intervention, deep learning techniques are widely used to learn features automatically. However, they lack the property of explainability; that is, a human being understands the meaning of all the parts that make up the calculation of a feature. In this paper, we empirically show how Artificial Intelligence can automatically discover explainable formulations of a topological feature for binary images called the Euler characteristic. The training images are represented by bit-quad patterns, and a single-layer artificial neural network automatically learns the optimal combination of bit-quads to provide valid formulations to correctly calculate the Euler characteristic. We report the results on binary images of different complexities and sizes and compare them with state-of-the-art machine learning algorithms. Finally, we present 14 new equations to calculate the Euler number never reported in literature.