Efficient classification using the Euler characteristic

•A topological object descriptor using Euler characteristics of subsets is proposed.•The EC-Graph descriptor encodes useful information about the spatial distribution.•An efficient method for calculating a series of EC values is proposed.•An efficient method for calculating the EC in a sliding window is proposed.•EC-Graph achieves state of the art classification results on images and 3D objects.

This paper introduces an object descriptor for classification based on the Euler characteristic of subsets created by thresholding a function at multiple levels (sub-level filtration). We demonstrate the effectiveness of this basic topological invariant of sets, the Euler characteristic, and use it to compute descriptors in two different domains – images and 3D mesh surfaces. The descriptors used as input to linear SVMs achieve state of the art classification results on various public data sets. Moreover, these descriptors are extremely fast to compute. We present linear time methods to calculate the Euler characteristic for multiple threshold values and to compute the Euler characteristic in a sliding window.