The TPS Direct Transport: A New Method for Transporting Deformations in the Size-and-Shape Space

Modern shape analysis allows the fine comparison of shape changes occurring between different objects. Very often the classic machineries of generalized Procrustes analysis and principal component analysis are used in order to contrast the shape change occurring among configurations represented by h...

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Bibliographic Details
Published in:International journal of computer vision 2017-09, Vol.124 (3), p.384-408
Main Authors: Varano, Valerio, Gabriele, Stefano, Teresi, Luciano, Dryden, Ian L., Puddu, Paolo E., Torromeo, Concetta, Piras, Paolo
Format: Article
Language:English
Subjects:
Analysis
Artificial Intelligence
Computer Imaging
Computer Science
Data centers
Deformation
Homology
Image Processing and Computer Vision
Image processing systems
Methods
Pattern Recognition
Pattern Recognition and Graphics
Principal components analysis
Trajectories
Transport
Vision
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Summary:Modern shape analysis allows the fine comparison of shape changes occurring between different objects. Very often the classic machineries of generalized Procrustes analysis and principal component analysis are used in order to contrast the shape change occurring among configurations represented by homologous landmarks. However, if size and shape data are structured in different groups thus constituting different morphological trajectories, a data centering is needed if one wants to compare solely the deformation representing the trajectories. To do that, inter-individual variation must be filtered out. This maneuver is rarely applied in studies using simulated or real data. A geometrical procedure named parallel transport, that can be based on various connection types, is necessary to perform such kind of data centering. Usually, the Levi Civita connection is used for interpolation of curves in a Riemannian space. It can also be used to transport a deformation. We demonstrate that this procedure does not preserve some important characters of the deformation, even in the affine case. We propose a novel procedure called ‘TPS Direct Transport’ which is able to perfectly transport deformation in the affine case and to better approximate non affine deformation in comparison to existing tools. We recommend to center shape data using the methods described here when the differences in deformation rather than in shape are under study.
ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-017-1031-9