Topology and Local Optima in Computer Vision

We present an application of persistent homology to the image correspondence problem, also known as image registration, which is used to produce 3D reconstructions of scenery from two or more cameras. We present a novel filtered complex in the sense of persistent homology, and show that nontrivial homology groups in its persistence diagrams correspond to recognizable anomalies in images pairs, such as repeated patterns, which contribute to non-convexity of the relevant cost function. We present examples with actual image pairs, and prove a basic result that the corresponding homology classes are invariant under certain continuous deformations.