Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment

The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similar...

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Bibliographic Details
Published in:Computer graphics forum Vol. 35; no. 6; pp. 87 - 119
Main Authors: Biasotti, S., Cerri, A., Bronstein, A., Bronstein, M.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.09.2016
Subjects:
3-D graphics
3D shape distances
3D shape matching
Analysis
Assessments
Classification
Deformation
I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling
I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling; I.3.6 [Computer Graphics]: Methodology and Techniques
I.3.6 [Computer Graphics]: Methodology and Techniques
Image processing systems
map-based correspondence
Mathematical analysis
Mathematical models
Segmentation
Shape recognition
Similarity
Studies
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map‐based methods also define (dense) shape correspondences. After presenting in detail the theoretical foundations underlying these approaches, we classify them by looking at their most salient features, including the kind of structure and invariance properties they capture, as well as the distances and the output modalities according to which the similarity between shapes is assessed and returned. We also review the usage of these methods in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Finally, the most promising directions for future research developments are discussed. The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map‐based methods also define (dense) shape correspondences.
Bibliography:istex:5165ECAABE2E84B1DE17B05BBBBCACC32D885DA2
ArticleID:CGF12734
ark:/67375/WNG-9CMWQRBH-X
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12734