Visibility of disjoint polygons
Algorithmica
Visibility graph recognition
Efficiently Computing and Representing Aspect Graphs of Polyhedral Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
An output-sensitive algorithm for computing visibility
SIAM Journal on Computing
The Robot Localization Problem
SIAM Journal on Computing
Visibility Queries in Simple Polygons and Applications
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Measuring Resemblance of Complex Patterns
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Efficient visibility queries in simple polygons
Computational Geometry: Theory and Applications
Proximity and reachability in the plane.
Proximity and reachability in the plane.
Shape Matching by Random Sampling
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Study on the matching similarity measure method for image target recognition
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part II
Shape matching by random sampling
Theoretical Computer Science
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Visibility partitions play an important role in computer vision and pattern matching. This paper studies a new type of visibility, reflection-visibility, with applications in affine pattern matching: it is used in the definition of the reflection metric between two patterns consisting of line segments. This metric is affine invariant, and robust against noise, deformation, blurring, and cracks. We present algorithms that compute the reflection visibility partition in O((n+k) log(n)+v) randomised time, where k is the number of visibility edges (at most O(n2)), and v is the number of vertices in the partition (at most O(n2+k2)). We use this partition to compute the reflection metric in O(r(nA + nB)) randomised time, for two line segment unions, with nA and nB line segments, separately, where r is the complexity of the overlay of two reflection-visibility partitions (at most O(nA4 + nB4)).