This paper describes the underlying ideas and algorithmic details of a computer program that performs at a human level of competence for a significant subset of the curve partitioning task. It extends and rounds out the technique and philosophical approach originally presented by Fischler and Bolles (1986). In particular, it provides a unified strategy for selecting and dealing with interactions between salient points, even when these points are salient at different scales of resolution. Experimental results are presented involving on the order of 1000 real and synthetically generated images. >