An Efficient PAC Algorithm for Reconstructing a Mixture of Lines

Authors:
Sanjoy Dasgupta;Elan Pavlov;Yoram Singer
Affiliations:
-;-;-
Venue:
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
Year:
2002

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Abstract

In this paper we study the learnability of a mixture of lines model which is of great importance in machine vision, computer graphics, and computer aided design applications. The mixture of lines is a partially-probabilistic model for an image composed of line-segments. Observations are generated by choosing one of the lines at random and picking a point at random from the chosen line. Each point is contaminated with some noise whose distribution is unknown, but which is bounded in magnitude. Our goal is to discover efficiently and rather accurately the line-segments that generated the noisy observations. We describe and analyze an efficient probably approximately correct (PAC) algorithm for solving the problem. Our algorithm combines techniques from planar geometry with simple large deviation tools and is simple to implement.