On piecewise linear approximation of planar Jordan curves
Journal of Computational and Applied Mathematics
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
On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
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)
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
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
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Fast guaranteed polygonal approximations of closed digital curves
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
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This paper presents a formal framework for representing all reversible polygonalizations of a digital contour (i.e. the boundary of a digital object). Within these polygonal approximations, a set of local operations is defined with given properties, e.g., decreasing the total length of the polygon or diminishing the number of quadrant changes. We show that, whatever the starting reversible polygonal approximation, iterating these operations leads to a specific polygon: the Minimum Length Polygon. This object is thus the natural representative for the whole class of reversible polygonal approximations of a digital contour. Since all presented operations are local, we obtain the first dynamic algorithm for computing the MLP. This gives us a sublinear time algorithm for computing the MLP of a contour, when the MLP of a slightly different contour is known.