On the Detection of Dominant Points on Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
CVGIP: Image Understanding
On a metric distance between fuzzy sets
Pattern Recognition Letters
On Hausdorff-like metrics for fuzzy sets (poster session)
Pattern Recognition Letters
SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
Note on Hausdorff-like metrics for fuzzy sets
Pattern Recognition Letters
Image Processing: The Fundamentals
Image Processing: The Fundamentals
The Earth Mover's Distance under Transformation Sets
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
A Geometric Approach to 3D Object Comparison
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Perceptual metrics for image database navigation
Perceptual metrics for image database navigation
Finding color and shape patterns in images
Finding color and shape patterns in images
An Improved Method of Angle Detection on Digital Curves
IEEE Transactions on Computers
Representation and geometric computation using the extended Gaussian image
Pattern Recognition Letters
Searching notated polyphonic music using transportation distances
Proceedings of the 12th annual ACM international conference on Multimedia
Proceedings of the 15th international conference on World Wide Web
Music retrieval: a tutorial and review
Foundations and Trends in Information Retrieval
Matching point sets with respect to the Earth Mover's Distance
Computational Geometry: Theory and Applications
A survey of content based 3D shape retrieval methods
Multimedia Tools and Applications
Multimedia Retrieval Algorithmics
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
The Representation and Matching of Images Using Top Points
Journal of Mathematical Imaging and Vision
Computational geometric aspects of rhythm, melody, and voice-leading
Computational Geometry: Theory and Applications
Perceptually relevant and piecewise linear matching of silhouettes
Pattern Recognition
Content based image retrieval using multiscale top points a feasibility study
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
On nonmetric similarity search problems in complex domains
ACM Computing Surveys (CSUR)
Selecting vantage objects for similarity indexing
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)
IWDM'06 Proceedings of the 8th international conference on Digital Mammography
Matching point sets with respect to the earth mover’s distance
ESA'05 Proceedings of the 13th annual European conference on Algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Approximation algorithms for computing the earth mover's distance under transformations
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Stability of top-points in scale space
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Using proportional transportation distances for measuring document similarity
ECIR'06 Proceedings of the 28th European conference on Advances in Information Retrieval
Non-crossing matchings of points with geometric objects
Computational Geometry: Theory and Applications
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We derive a pseudo-metric for weighted point sets. There are numerous situations, for example in the shape description domain, where the individual points in a feature point set have an associated attribute, a weight. A distance function that incorporates this extra information apart from the points' position can be very useful for matching and retrieval purposes. There are two main approaches to do this. One approach is to interpret the point sets as fuzzy sets. However, a distance measure for fuzzy sets that is a metric, invariant under rigid motion and respects scaling of the underlying ground distance, does not exist. In addition, a Hausdorff-like pseudo-metric fails to differentiate between fuzzy sets with arbitrarily different maximum memebership values. The other approach is the Earth Mover's Distance. However, for sets of unequal total weights, it gives zero distance for arbitrarily different sets, and does not obey the triangle inequality. In this paper we derive a distance measure, based on weight transportation, that is invariant under rigid motion, respects scaling, and obeys the triangle inequality, so that it can be used in efficient database searching. Moreover, our pseudo-metric identifies only weight-scaled versions of the same set. We demonstrate its potential use by testing it on two different collections, one of company logos and another one of fish contours.