Content-Based Image Retrieval at the End of the Early Years
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multidimensional binary search trees used for associative searching
Communications of the ACM
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Summed-area tables for texture mapping
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Retrieval of trademark images by means of size functions
Graphical Models - Special issue on the vision, video and graphics conference 2005
Stability of Persistence Diagrams
Discrete & Computational Geometry
Size functions for comparing 3D models
Pattern Recognition
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
Extending Persistence Using Poincaré and Lefschetz Duality
Foundations of Computational Mathematics
Recognition of Occluded Shapes Using Size Functions
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
Size functions for the morphological analysis of melanocytic lesions
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
A new algorithm for computing the 2-dimensional matching distance between size functions
Pattern Recognition Letters
Shape recognition via an a contrario model for size functions
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part II
Persistent homology and partial similarity of shapes
Pattern Recognition Letters
Multi-scale approximation of the matching distance for shape retrieval
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
SHREC'12 track: stability on abstract shapes
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval
Pattern Recognition Letters
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Two of the main ingredients of topological persistence for shape comparison are persistence diagrams and the matching distance. Persistence diagrams are signatures capturing meaningful properties of shapes, while the matching distance can be used to stably compare them. From the application viewpoint, one drawback of these tools is the computational cost for evaluating the matching distance. In this paper we introduce a new framework for the matching distance estimation: It preserves the reliability of the entire approach in comparing shapes, extremely reducing the computational cost. Theoretical results are supported by experiments on 3D-models.