Similarity and Symmetry Measures for Convex Shapes Using Minkowski Addition
IEEE Transactions on Pattern Analysis and Machine Intelligence
State of the art in shape matching
Principles of visual information retrieval
Region-Based Tracking in an Image Sequence
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Maximizing the overlap of two planar convex sets under rigid motions
Computational Geometry: Theory and Applications
Finding a Guard that Sees Most and a Shop that Sells Most
Discrete & Computational Geometry
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Maximum overlap and minimum convex hull of two convex polyhedra under translations
Computational Geometry: Theory and Applications
Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
Computational Geometry: Theory and Applications
Geometric optimization and sums of algebraic functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Maximum overlap of convex polytopes under translation
Computational Geometry: Theory and Applications
Shape matching under rigid motion
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
We present an algorithm to compute a rigid motion that approximately maximizes the volume of the intersection of two convex polytopes P"1 and P"2 in R^3. For all @e@?(0,1/2] and for all n=1/@e, our algorithm runs in O(@e^-^3nlog^3^.^5n) time with probability 1-n^-^O^(^1^). The volume of the intersection guaranteed by the output rigid motion is a (1-@e)-approximation of the optimum, provided that the optimum is at least @l@?max{|P"1|,|P"2|} for some given constant @l@?(0,1].