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 $\alpha$-complex by Edelsbrunner et al. to build a filtration of simplicial complexes from a user-provided set of features. The optimal value of alpha 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.
We use the idea of alpha complexes to bound the shape of discrete feature points in the 2D image domain. Here are the MATLAB/C++ [code] and the [paper].
