ON NAVIGATING BETWEEN FRIENDS AND FOES

A problem of determining the optimal straight path between a planar set of points is considered. Each point contributes to the cost of a path a value that depends on the distance between the path and the point. The cost function, quantifying this dependence, can be arbitrary and may be different for different points. An algorithm to solve this problem, via an extension of the Hough transform, is described. The range of applications includes straight-line fitting to a set of points in the presence of outliers, navigation, and path planning. The suggested extended Hough transform can be tuned to be equivalent to well-known robust least squares techniques, and allows, in particular, to efficiently carry out approximate M-estimation.