Sublinear Time Directional Chamfer Matching

We study object localization problem in images, given a single hand-drawn example or a gallery of shapes as the object model. Although many shape matching algorithms have been proposed over the decades, chamfer matching remains to be among the fastest and most robust approaches in the presence of clutter. In this paper, we significantly improve the accuracy of chamfer matching while reducing the computational time from linear to sublinear. Specifically, we incorporate edge orientation information to matching framework such that the resulting cost function is piecewise smooth and the cost variation is tightly bounded. Moreover, we present a sublinear time algorithm for exact computation of the directional chamfer matching score using techniques from 3D distance transforms and directional integral images. In addition, the smooth cost function allows to bound the cost distribution of large neighborhoods and skip the bad hypotheses within. The experiments show that the presented approach improves the speed of the original chamfer matching upto an order of 45x, and it is magnitudes of order faster than other state of art techniques while the accuracy is comparable.