A Homologically Persistent Skeleton is a fast and robust descriptor for a sparse cloud of interest points and saliency features in noisy 2D images

2D images often contain irregular salient features and interest points with non-integer coordinates. Our skeletonization problem for such a noisy sparse cloud is to summarize the topology of a given 2D cloud across all scales in the form of a graph, which can be used for combining local features into a more powerful object-wide descriptor. We extend a classical Minimum Spanning Tree of a cloud to a Homologically Persistent Skeleton, which is scale-and-rotation invariant and depends only on the cloud without extra parameters. This graph (1) is computable in time O(n logn) for any n points in the plane; (2) has the minimum total length among all graphs that span a 2D cloud at any scale and also have most persistent 1-dimensional cycles; (3) is geometrically stable for noisy samples around planar graphs.