Two linear-time algorithms for computing the minimum length polygon of a digital contour

Abstract
The Minimum Length Polygon (MLP) is an interesting first order approximation of a digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity of the shape, its perimeter is a good estimate of the perimeter of the digitized shape. We present here two novel equivalent definitions of MLP, one arithmetic, one combinatorial, and both definitions lead to two different linear time algorithms to compute them. This paper extends the work presented in Provençal and Lachaud (2009), by detailing the algorithms and providing full proofs. It includes also a comparative experimental evaluation of both algorithms showing that the combinatorial algorithm is about 5 times faster than the other. We also checked the multigrid convergence of the length estimator based on the MLP.
Type
Publication
Discrete Applied Mathematics, 159(18): 2229-2250, 2011
Digital Geometry
Minimum Length Polygon
Minimum Perimeter Polygon
Digital Straightness
Christoffel Word
Length Estimator
Word Combinatorics
2D
Computational Complexity

Authors
Professor of Computer Science
My research interests include digital geometry, geometry processing, image analysis, variational models and discrete calculus.