Neural Implementation of Shape-Invariant Touch Counter Based on Euler Calculus

One of the goals of neuromorphic engineering is to imitate the brain's ability to recognize and count the number of individual objects as entities based on the global consistency of the information from the population of activated tactile (or visual) sensory neurons whatever the objects' shapes are. To achieve this flexibility, it may be worth examining an unconventional algorithm such as topological methods. Here, we propose a fully parallelized algorithm for a shape-invariant touch counter for 2-D pixels. The number of touches is counted by the Euler integral, a generalized integral, in which a connected component counter (Betti number) for the binary image was used as elemental module. Through examples of touches, we demonstrate transparently how the proposed circuit architecture embodies the Euler integral in the form of recurrent neural networks for iterative vector operations. Our parallelization can lead the way to Field-Programmable Gate Array or Digital Signal Processor implementations of topological algorithms with scalability to high resolutions of pixels.