Content-Based Image Retrieval at the End of the Early Years
IEEE Transactions on Pattern Analysis and Machine Intelligence
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
A survey of content based 3D shape retrieval methods
Multimedia Tools and Applications
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Recognition of Occluded Shapes Using Size Functions
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
A new algorithm for computing the 2-dimensional matching distance between size functions
Pattern Recognition Letters
Comparing shapes through multi-scale approximations of the matching distance
Computer Vision and Image Understanding
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This paper deals with the concepts of persistence diagrams and matching distance. They are two of the main ingredients of Topological Persistence, which has proven to be a promising framework for shape comparison. Persistence diagrams are descriptors providing a signature of the shapes under study, while the matching distance is a metric to compare them. One drawback in the application of these tools is the computational costs for the evaluation of the matching distance. The aim of the present paper is to introduce a new framework for the approximation of the matching distance, which does not affect the reliability of the entire approach in comparing shapes, and extremely reduces computational costs. This is shown through experiments on 3D-models.