article

The Use of Size Functions for Comparison of Shapes Through Differential Invariants

Authors:

Françoise Dibos,

Patrizio Frosini,

Denis PasquignonAuthors Info & Claims

Journal of Mathematical Imaging and Vision, Volume 21, Issue 2

Pages 107 - 118

https://doi.org/10.1023/B:JMIV.0000035177.68567.3b

Published: 01 September 2004 Publication History

Abstract

For comparison of shapes under subgroups of the projective group, we can use a lot of invariants and especially differential invariants coming from multiscale analysis. But such invariants, as we have to compute curvature, are very sensitive to the noise induced by the dicretization grid. In order to resolve this problem we use size functions which can recognize the “qualitative similarity” between graphs of functions that should be theorically coinciding but, unfortunately, change their values due to the presence of noise. Moreover, we focus this study on a projective differential invariant which allows to decide if one shape can be considered as the deformation of another one by a rotation of the camera.

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Dahmani DLarabi SCheref M(2019)Efficient representation of size functions based on moments theoryMultimedia Tools and Applications10.1007/s11042-019-07859-978:19(27957-27982)Online publication date: 1-Oct-2019
https://dl.acm.org/doi/10.1007/s11042-019-07859-9
Ferri MTomba IVisotti AStanganelli I(2017)A Feasibility Study for a Persistent Homology-Based k-Nearest Neighbor Search Algorithm in Melanoma DetectionJournal of Mathematical Imaging and Vision10.1007/s10851-016-0680-657:3(324-339)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s10851-016-0680-6
Biasotti SCerri ABronstein ABronstein M(2016)Recent Trends, Applications, and Perspectives in 3D Shape Similarity AssessmentComputer Graphics Forum10.1111/cgf.1273435:6(87-119)Online publication date: 1-Sep-2016
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Index Terms

The Use of Size Functions for Comparison of Shapes Through Differential Invariants
1. Theory of computation

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cover image Journal of Mathematical Imaging and Vision

Journal of Mathematical Imaging and Vision Volume 21, Issue 2

September 2004

85 pages

ISSN:0924-9907

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Copyright © Copyright © 2004 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 September 2004

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Cited By

Dahmani DLarabi SCheref M(2019)Efficient representation of size functions based on moments theoryMultimedia Tools and Applications10.1007/s11042-019-07859-978:19(27957-27982)Online publication date: 1-Oct-2019
https://dl.acm.org/doi/10.1007/s11042-019-07859-9
Ferri MTomba IVisotti AStanganelli I(2017)A Feasibility Study for a Persistent Homology-Based k-Nearest Neighbor Search Algorithm in Melanoma DetectionJournal of Mathematical Imaging and Vision10.1007/s10851-016-0680-657:3(324-339)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s10851-016-0680-6
Biasotti SCerri ABronstein ABronstein M(2016)Recent Trends, Applications, and Perspectives in 3D Shape Similarity AssessmentComputer Graphics Forum10.1111/cgf.1273435:6(87-119)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1111/cgf.12734
Mrozek MŻElawski MGryglewski AHan SKrajniak A(2012)Homological methods for extraction and analysis of linear features in multidimensional imagesPattern Recognition10.1016/j.patcog.2011.04.02045:1(285-298)Online publication date: 1-Jan-2012
https://dl.acm.org/doi/10.1016/j.patcog.2011.04.020
Cagliari FFerri MGualandri LLandi C(2012)Persistence modules, shape description, and completenessProceedings of the 4th international conference on Computational Topology in Image Context10.1007/978-3-642-30238-1_16(148-156)Online publication date: 28-May-2012
https://dl.acm.org/doi/10.1007/978-3-642-30238-1_16
Cerri AFrosini PKropatsch WLandi C(2011)A global method for reducing multidimensional size graphsProceedings of the 8th international conference on Graph-based representations in pattern recognition10.5555/2009206.2009208(1-11)Online publication date: 18-May-2011
https://dl.acm.org/doi/10.5555/2009206.2009208
Su C(2009)Palm-print recognition by matrix discriminatorExpert Systems with Applications: An International Journal10.1016/j.eswa.2009.01.05236:7(10259-10265)Online publication date: 1-Sep-2009
https://dl.acm.org/doi/10.1016/j.eswa.2009.01.052
Biasotti SDe Floriani LFalcidieno BFrosini PGiorgi DLandi CPapaleo LSpagnuolo M(2008)Describing shapes by geometrical-topological properties of real functionsACM Computing Surveys10.1145/1391729.139173140:4(1-87)Online publication date: 15-Oct-2008
https://dl.acm.org/doi/10.1145/1391729.1391731
Biasotti SCerri AFrosini PGiorgi DLandi C(2008)Multidimensional Size Functions for Shape ComparisonJournal of Mathematical Imaging and Vision10.1007/s10851-008-0096-z32:2(161-179)Online publication date: 1-Oct-2008
https://dl.acm.org/doi/10.1007/s10851-008-0096-z
Cerri AFerri MGiorgi D(2006)Retrieval of trademark images by means of size functionsGraphical Models10.1016/j.gmod.2006.07.00168:5(451-471)Online publication date: 1-Sep-2006
https://dl.acm.org/doi/10.1016/j.gmod.2006.07.001

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