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.#R##N##R##N#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#R##N##R##N#(1) #R##N#is computable in time O(nlogn)  for any n points in the plane;#R##N##R##N#(2) #R##N#has the minimum total length among all graphs that span a 2D cloud at any scale and also have most persistent 1-dimensional cycles;#R##N##R##N#(3) #R##N#is geometrically stable for noisy samples around planar graphs.
['Vitaliy Kurlin']
A Homologically Persistent Skeleton is a Fast and Robust Descriptor of Interest Points in 2D Images