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Shape from point features

We present a nonparametric and efficient method for shape localization that improves on the traditional sub-window search in capturing the fine geometry of an object from a small number of feature points. Our method implies that the discrete set of features capture more appearance and shape information than is commonly exploited. We use the a-complex by Edelsbrunner et al. to build a filtration of simplicial complexes from a user-provided set of features. The optimal value of a is determined automatically by a search for the densest complex connected component, resulting in a parameter-free algorithm. Given K features, localization occurs in O(K log K) time. For VGA-resolution images, computation takes typically less than 10 milliseconds. We use our method for interactive object cut, with promising results.