Persistent homology and partial similarity of shapes

Pattern Recognition Letters

Volumn 33, Issue 11, 2012, Pages 1445-1450

  Di Fabio, Barbara ^a   Landi, Claudia ^a,b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

Author keywords

Extended persistence; Hausdorff distance; Mayer Vietoris formula

Indexed keywords

3D DATA SETS; DESCRIPTORS; EXTENDED PERSISTENCE; HAUSDORFF DISTANCE; MAYER-VIETORIS FORMULA; PARTIAL HAUSDORFF DISTANCE; PERSISTENT HOMOLOGY; SHAPE COMPARISON;

PATTERN RECOGNITION; SOFTWARE ENGINEERING;

GEOMETRY;

EID: 84862203262     PISSN: 01678655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patrec.2011.11.003     Document Type: Conference Paper

References (13)

1. Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B., 2006a. Size functions for 3D shape retrieval, in: SGP'06: Proc. of the fourth Eurographics Symposium on Geometry Processing, pp. 239-242.
2. S. Biasotti, S. Marini, M. Spagnuolo, and B. Falcidieno Sub-part correspondence by structural descriptors of 3D shapes Computer-Aided Design 38 2006 1002 1019 (Pubitemid 44331200)
3. A. Bronstein, M. Bronstein, and R. Kimmel Numerical Geometry of Non-Rigid Shapes 2008 Springer Publishing Company Incorporated
4. A.M. Bronstein, M.M. Bronstein, A.M. Bruckstein, and R. Kimmel Analysis of two-dimensional non-rigid shapes Internat. J. Comput. Vision 78 2008 67 88 (Pubitemid 351354425)
5. G. Carlsson, A. Zomorodian, A. Collins, and L. Guibas Persistence barcodes for shapes Internat. J. Shape Model. 11 2005 149 187 (Pubitemid 43269360)
6. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer Stability of persistence diagrams Discrete Comput. Geom. 37 2007 103 120
7. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer Extending persistence using Poincaré and Lefschetz duality Found. Comput. Math. 9 2009 79 103
8. B. Di Fabio, and C. Landi A Mayer-Vietoris formula for persistent homology with an application to shape recognition in the presence of occlusions Found. Comput. Math. 11 2011 499 527
9. S. Eilenberg, and N. Steenrod Foundations of Algebraic Topology 1952 Princeton University Press Princeton, New Jersey
10. Frosini, P., 1992. Measuring shapes by size functions. In: D.P. Casasent (Ed.), Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 1607, pp. 122-133.
11. Frosini, P., Landi, C., 1997. New pseudo-distances for the size function space. In: Melter, R.A., Wu, A.Y., Latecki, L.J. (Eds.), Proc. SPIE, Vision Geometry VI, vol. 3168, pp. 52-60.
12. D.P. Huttenlocher, G.A. Klanderman, and W. Rucklidge Comparing images using the Hausdorff distance IEEE Trans. Pattern Anal. Machine Intell. 15 1993 850 863 (Pubitemid 23703609)
13. A. Verri, C. Uras, P. Frosini, and M. Ferri On the use of size functions for shape analysis Biol. Cybernet. 70 1993 99 107