Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Computer Vision and Image Understanding
On finding lowest common ancestors in trees
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Assigning footprints to dot sets: an analytical survey
COSIT'09 Proceedings of the 9th international conference on Spatial information theory
Automatic recognition of 2D shapes from a set of points
ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part I
What is the region occupied by a set of points?
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Shape reconstruction from unorganized set of points
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
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We introduce a method that identifies the boundary of a nonconvex shape of a set of points in the plane. The boundary of the shape is explored through finding empty regions recursively within a shell that encapsulates all of the points. Our algorithm is output sensitive and runs in linear O(@?n) time determined by the output parameter @?, which is proportional to the length of the nonconvex boundary measured by a threshold unit distance. The recursive nature of our algorithm allows a tree structure that characterizes the empty regions, and by complementarity, the nonconvex shape itself. We use a distance measure based on lowest common ancestor of a pair of nodes in this tree and define the complexity of a shape as the average of the distances between all pairs. We present computational results on data size, threshold, shape complexity and noise on a set of different nonconvex shapes.