Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A faster strongly polynomial minimum cost flow algorithm
Operations Research
Matching shapes with a reference point
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
A Pseudo-Metric for Weighted Point Sets
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Matching Convex Shapes with Respect to the Symmetric Difference
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Finding color and shape patterns in images
Finding color and shape patterns in images
Matching point sets with respect to the earth mover’s distance
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A near linear time constant factor approximation for Euclidean bichromatic matching (cost)
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On Minimizing the Maximum Sensor Movement for Barrier Coverage of a Line Segment
ADHOC-NOW '09 Proceedings of the 8th International Conference on Ad-Hoc, Mobile and Wireless Networks
On minimizing the sum ofensor movements for barrier coverage of a line segment
ADHOC-NOW'10 Proceedings of the 9th international conference on Ad-hoc, mobile and wireless networks
| Hi-index | 0.00 |
The Earth Mover's Distance (EMD) on weighted point sets is a distance measure with many applications. Since there are no known exact algorithms to compute the minimum EMD under transformations, it is useful to estimate the minimum EMD under various classes of transformations. For weighted point sets in the plane, we will show a 2-approximation algorithm for translations, a 4-approximation algorithm for rigid motions and an 8-approximation algorithm for similarity transformations. The runtime for translations is O(TEMD(n,m)), the runtime of the latter two algorithms is O(nmTEMD(n,m)), where TEMD(n,m) is the time to compute the EMD between two fixed weighted point sets with n and m points, respectively. All these algorithms are based on a more general structure, namely on reference points. This leads to elegant generalizations to higher dimensions. We give a comprehensive discussion of reference points for weighted point sets with respect to the EMD.