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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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/44007/ |
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| author | Varano, Valerio Gabriele, Stefano Teresi, Luciano Dryden, Ian L. Puddu, Paolo E. Torromeo, Concetta Piras, Paolo |
| author_facet | Varano, Valerio Gabriele, Stefano Teresi, Luciano Dryden, Ian L. Puddu, Paolo E. Torromeo, Concetta Piras, Paolo |
| author_sort | Varano, Valerio |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:53:59Z |
| format | Article |
| id | nottingham-44007 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:53:59Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-440072020-05-04T18:52:58Z https://eprints.nottingham.ac.uk/44007/ The TPS Direct Transport: a new method for transporting deformations in the Size-and-shape Space Varano, Valerio Gabriele, Stefano Teresi, Luciano Dryden, Ian L. Puddu, Paolo E. Torromeo, Concetta Piras, Paolo 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. Springer 2017-07-01 Article PeerReviewed Varano, Valerio, Gabriele, Stefano, Teresi, Luciano, Dryden, Ian L., Puddu, Paolo E., Torromeo, Concetta and Piras, Paolo (2017) The TPS Direct Transport: a new method for transporting deformations in the Size-and-shape Space. International Journal of Computer Vision . ISSN 1573-1405 Geometric Morphometrics Shape analysis Inter-individual difference Riemannian manifold Deformation cycle Parallel transport Trajectory analysis Thin plate spline. https://link.springer.com/article/10.1007%2Fs11263-017-1031-9 doi:10.1007/s11263-017-1031-9 doi:10.1007/s11263-017-1031-9 |
| spellingShingle | Geometric Morphometrics Shape analysis Inter-individual difference Riemannian manifold Deformation cycle Parallel transport Trajectory analysis Thin plate spline. Varano, Valerio Gabriele, Stefano Teresi, Luciano Dryden, Ian L. Puddu, Paolo E. Torromeo, Concetta Piras, Paolo The TPS Direct Transport: a new method for transporting deformations in the Size-and-shape Space |
| title | The TPS Direct Transport: a new method for transporting
deformations in the Size-and-shape Space |
| title_full | The TPS Direct Transport: a new method for transporting
deformations in the Size-and-shape Space |
| title_fullStr | The TPS Direct Transport: a new method for transporting
deformations in the Size-and-shape Space |
| title_full_unstemmed | The TPS Direct Transport: a new method for transporting
deformations in the Size-and-shape Space |
| title_short | The TPS Direct Transport: a new method for transporting
deformations in the Size-and-shape Space |
| title_sort | tps direct transport: a new method for transporting
deformations in the size-and-shape space |
| topic | Geometric Morphometrics Shape analysis Inter-individual difference Riemannian manifold Deformation cycle Parallel transport Trajectory analysis Thin plate spline. |
| url | https://eprints.nottingham.ac.uk/44007/ https://eprints.nottingham.ac.uk/44007/ https://eprints.nottingham.ac.uk/44007/ |