Bipartite graph matching for points on a line or a circle
Journal of Algorithms
A faster strongly polynomial minimum cost flow algorithm
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The Kantorovich metric for probability measures on the circle
Journal of Computational and Applied Mathematics
Silhouette-based occluded object recognition through curvature scale space
Machine Vision and Applications
A linear time algorithm for a matching problem on the circle
Information Processing Letters
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Edge, Junction, and Corner Detection Using Color Distributions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Accurate 3D image colour histogram transformation
Pattern Recognition Letters - Special issue: Colour image processing and analysis
Region Correspondence for Image Matching via EMD Flow
CBAIVL '00 Proceedings of the IEEE Workshop on Content-based Access of Image and Video Libraries (CBAIVL'00)
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 4 - Volume 4
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Optimal Mass Transport for Registration and Warping
International Journal of Computer Vision
Image similarity search with compact data structures
Proceedings of the thirteenth ACM international conference on Information and knowledge management
Region-Based Image Retrieval with High-Level Semantic Color Names
MMM '05 Proceedings of the 11th International Multimedia Modelling Conference
Effective and efficient object-based image retrieval using visual phrases
MULTIMEDIA '06 Proceedings of the 14th annual ACM international conference on Multimedia
An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automated colour grading using colour distribution transfer
Computer Vision and Image Understanding
Adaptive image retrieval based on the spatial organization of colors
Computer Vision and Image Understanding
A Linear Time Histogram Metric for Improved SIFT Matching
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Assignment Problems
A Statistical Approach to the Matching of Local Features
SIAM Journal on Imaging Sciences
Geodesic shape retrieval via optimal mass transport
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Shape representation and recognition through morphological curvature scale spaces
IEEE Transactions on Image Processing
An Image Morphing Technique Based on Optimal Mass Preserving Mapping
IEEE Transactions on Image Processing
Space-Efficient approximation scheme for circular earth mover distance
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets
Journal of Mathematical Imaging and Vision
Hi-index | 0.00 |
This paper is devoted to the study of the Monge-Kantorovich theory of optimal mass transport, in the special case of one-dimensional and circular distributions. More precisely, we study the Monge-Kantorovich problem between discrete distributions on the unit circle S 1, in the case where the ground distance between two points x and y is defined as h(d(x,y)), where d is the geodesic distance on the circle and h a convex and increasing function. This study complements previous results in the literature, holding only for a ground distance equal to the geodesic distance d. We first prove that computing a Monge-Kantorovich distance between two given sets of pairwise different points boils down to cut the circle at a well chosen point and to compute the same distance on the real line. This result is then used to obtain a dissimilarity measure between 1-D and circular discrete histograms. In a last part, a study is conducted to compare the advantages and drawbacks of transportation distances relying on convex or concave cost functions, and of the classical L 1 distance. Simple retrieval experiments based on the hue component of color images are shown to illustrate the interest of circular distances. The framework is eventually applied to the problem of color transfer between images.