On-line construction of the convex hull of a simple polyline
Information Processing Letters
Optimal shortest path queries in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
On piecewise linear approximation of planar Jordan curves
Journal of Computational and Applied Mathematics
Some combinatorial properties of Sturmian words
Theoretical Computer Science
Sturmian words, Lyndon words and trees
Theoretical Computer Science
Polygonal approximations that minimize the number of inflections
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
A note on minimal length polygonal approximation to a digitized contour
Communications of the ACM
Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
On approximation of Jordan surfaces in 3D
Digital and image geometry
A Comparative Evaluation of Length Estimators of Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Lyndon + Christoffel = digitally convex
Pattern Recognition
Minimum-Perimeter Polygons of Digitized Silhouettes
IEEE Transactions on Computers
What Does Digital Straightness Tell about Digital Convexity?
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Two linear-time algorithms for computing the minimum length polygon of a digital contour
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Digital deformable model simulating active contours
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Convex shapes and convergence speed of discrete tangent estimators
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
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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 Provencal and Lachaud (2009) [26], 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.