On-line construction of the convex hull of a simple polyline
Information Processing Letters
Fitting polygonal functions to a set of points in the plane
CVGIP: Graphical Models and Image Processing
On approximating polygonal curves in two and three dimensions
CVGIP: Graphical Models and Image Processing
A protocol for performance evaluation of line detection algorithms
Machine Vision and Applications - Special issue on performance evaluation
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Cartographic Line Simplification and Polygon CSG Formulae and in O(n log* n) Time
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
New Results on Path Approximation
Algorithmica
Polygonal chain approximation: a query based approach
Computational Geometry: Theory and Applications
Robust and Accurate Vectorization of Line Drawings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Farthest-point queries with geometric and combinatorial constraints
Computational Geometry: Theory and Applications
Digital line recognition, convex hull, thickness, a unified and logarithmic technique
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Tentative Prune-And-Search For Computing Fixed-Points With Applications To Geometric Computation
Fundamenta Informaticae
A near-linear time guaranteed algorithm for digital curve simplification under the Fréchet distance
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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For a given polygonal chain, we study the min-# problem, which consists of finding an approximate and ordered subchain with a minimum number of vertices under a given approximation criterion. We propose the first near-linear time algorithm for the min-# problem that ensures optimality in the number of vertices and that retains the shape of the input polygonal chain at the same time. Previous algorithms with near-linear time performance produced geometrical inconsistencies and former methods used to preserve the features of the original chain required a quadratic time complexity. When we set the approximation error equal to the pixel pitch, our simplification criterion guarantees that the rendering of the simplification lies at most half a pixel away from the original chain, contrary to other methods that do not offer a direct control over the rendering. Thus, we avoid producing visible topological inconsistencies. Moreover, our method is based on basic data structures, which leads to a simple and efficient implementation.