Content-Based Image Retrieval at the End of the Early Years
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability of Persistence Diagrams
Discrete & Computational Geometry
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
The Theory of Multidimensional Persistence
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
Image segmentation using topological persistence
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Topology noise removal for curve and surface evolution
MCV'10 Proceedings of the 2010 international MICCAI conference on Medical computer vision: recognition techniques and applications in medical imaging
Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications
Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detailed reconstruction of 3D plant root shape
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
The Adaptive Topology of a Digital Image
ISVD '12 Proceedings of the 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering
SHREC'12 track: stability on abstract shapes
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
PHOG: photometric and geometric functions for textured shape retrieval
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Multidimensional persistent modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense. Furthermore, it is presented a method to visualize topological features of a shape via persistence spaces. Finally, it is shown that this method is resistant to perturbations of the input data.