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Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions.
Foundations of algebraic topology
S. Eilenberg and N. Steenrod · 1952
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Introduction to piecewise-linear topology
C. P. Rourke and B. J. Sanderson · 1972
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Algebraic topology: a first course
M. J. Greenberg and J. R. Harper · 1981
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On the use of size functions for shape analysis
A. Verri, C. Uras, P. Frosini, and M. Ferri · 1993
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Size theory as a topological tool for computer vision
P. Frosini and C. Landi · 1999
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Size homotopy groups for computation of natural size distances
P. Frosini and M. Mulazzani · 1999
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Towards computing homology from finite approximations
V. Robins · 1999
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Computational topology at multiple resolutions
V. Robins · 2000
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Size functions and formal series
P. Frosini and C. Landi · 2001
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Aspetti computazionali delle funzioni di taglia (Italian)
M. d’Amico · 2002
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Topological persistence and simplification
H. Edelsbrunner, D. Letscher, and A. Zomorodian · 2002
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Computational Homology
T. Kaczynski, K. Mischaikow, and M. Mrozek · 2004
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Persistence barcodes for shapes
G. Carlsson, A. Zomorodian, A. Collins, and L. J. Guibas · 2005
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A. J. Zomorodian · 2005
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Retrieval of trademark images by means of size functions
A. Cerri, M. Ferri, and D. Giorgi · 2006
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Multidimensional size functions for shape comparison
S. Biasotti, A. Cerri, P. Frosini, D. Giorgi, and C. Landi · 2008
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Describing shapes by geometrical-topological properties of real functions
S. Biasotti, L. De Floriani, B. Falcidieno, P. Frosini, D. Giorgi, C. Landi, L. Papaleo, and M. Spagnuolo · 2008
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Persistent homology—a survey
H. Edelsbrunner and J. Harer · 2008
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Barcodes: the persistent topology of data
R. Ghrist · 2008
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Multi-scale representation and persistency for shape description
D. Moroni, M. Salvetti, and O. Salvetti · 2008
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Topology and data
G. Carlsson · 2009
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One-dimensional reduction of multidimensional persistent homology, 2007
F. Cagliari, B. Di Fabio, and M. Ferri · 2007
Cited alongside, same era.
Stability of persistence diagrams
D. Cohen-Steiner, H. Edelsbrunner, and J. Harer · 2007
Cited alongside, same era.
Coverage in sensor networks via persistent homology
V. de Silva and R. Ghrist · 2007
Cited alongside, same era.
Natural pseudo-distance and optimal matching between reduced size functions
M. d’Amico, P. Frosini, and C. Landi
Cited in the paper.
Čech type approach to computing homology of maps
M. Mrozek
Cited in the paper.
The theory of multidimensional persistence
G. Carlsson and A. Zomorodian · 2009
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Proximity of persistence modules and their diagrams
F. Chazal, D. Cohen-Steiner, M. Glisse, L. J. Guibas, and S. Y. Oudot · 2009
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