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Excerpt from On the Detection of Robust Curves Given m points in the plane and a threshold t. a curve is defined to be robust if at least t points lie on it. Efficient algorithms for detecting robust curves are given; the key contribution is to use randomized sampling. In addition, an approximate version of the problem is introduced. A geometric solution to this problem is given; it too can be enhanced by randomization. These algorithms are readily generalized to solve the problem of robust curve detection in a scene of curve fragments: given a set of curve segments, a curve is defined to be robust if curve segments of total length at least l lie on . Again, both an exact and an approximate version of the problem are considered. The problems and solutions are closely related to the well-investigated Hough Transform technique. A recent survey paper by Illingworth and Kittler [IK88] refers to the Hough Transform, HT, as .. . a technique of almost unique promise for shape and motion analysis in images containing noisy, missing, and extraneous data but its adoption has been slow due to its computational and storage complexity..., and cites 144 papers written on it by 1988. On the skeptical side, a few papers (e.g., [Br83] and [Gh90]) offer criticism of the HT technique. Most criticism is directed towards the sensitivity of the HT and suggests not to use it blithely. While the present paper is inspired by HT, it applies a notion of robust curves to overcome the sensitivity related criticism, while maintaining the power of HT. We hope that our algorithms will contribute ideas to designers of software systems for scene analysis. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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