The decomposition of deformation: new metrics to enhance shape analysis in medical imaging
In landmarks-based Shape Analysis size is measured, in most cases, with Centroid Size. Changes in shape are decomposed in affine and non affine components. Furthermore the non affine component can be in turn decomposed in a series of local deformations (partial warps). If the extent of deformation b...
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| Format: | Article |
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/51435/ |
| _version_ | 1848798494970609664 |
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| author | Varano, Valerio Piras, Paolo Gabriele, Stefano Teresi, Luciano Nardinocchi, Paola Dryden, Ian L. Torromeo, Concetta Puddu, Paolo E. |
| author_facet | Varano, Valerio Piras, Paolo Gabriele, Stefano Teresi, Luciano Nardinocchi, Paola Dryden, Ian L. Torromeo, Concetta Puddu, Paolo E. |
| author_sort | Varano, Valerio |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In landmarks-based Shape Analysis size is measured, in most cases, with Centroid Size. Changes in shape are decomposed in affine and non affine components. Furthermore the non affine component can be in turn decomposed in a series of local deformations (partial warps). If the extent of deformation between two shapes is small, the difference between centroid size and m-Volume increment is barely appreciable. In medical imaging applied to soft tissues bodies can undergo very large deformations, involving large changes in size. The cardiac example, analyzed in the present paper, shows changes in m-Volume that can reach the 60%. We show here that standard Geometric Morphometrics tools (landmarks, Thin Plate Spline, and related decomposition of the deformation) can be generalized to better describe the very large deformations of biological tissues, without losing a synthetic description. In particular, the classical decomposition of the space tangent to the shape space in affine and non affine components is enriched to include also the change in size, in order to give a complete description of the tangent space to the size-and-shape space. The proposed generalization is formulated by means of a new Riemannian metric describing the change in size as change in m-Volume rather than change in Centroid Size. This leads to a redefinition of some aspects of the Kendall’s size-and-shape space without losing Kendall’s original formulation. This new formulation is discussed by means of simulated examples using 2D and 3D platonic shapes as well as a real example from clinical 3D echocardiographic data. We demonstrate that our decomposition based approaches discriminate very effectively healthy subjects from patients affected by Hypertrophic Cardiomyopathy. |
| first_indexed | 2025-11-14T20:20:40Z |
| format | Article |
| id | nottingham-51435 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:20:40Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-514352020-05-04T19:33:34Z https://eprints.nottingham.ac.uk/51435/ The decomposition of deformation: new metrics to enhance shape analysis in medical imaging Varano, Valerio Piras, Paolo Gabriele, Stefano Teresi, Luciano Nardinocchi, Paola Dryden, Ian L. Torromeo, Concetta Puddu, Paolo E. In landmarks-based Shape Analysis size is measured, in most cases, with Centroid Size. Changes in shape are decomposed in affine and non affine components. Furthermore the non affine component can be in turn decomposed in a series of local deformations (partial warps). If the extent of deformation between two shapes is small, the difference between centroid size and m-Volume increment is barely appreciable. In medical imaging applied to soft tissues bodies can undergo very large deformations, involving large changes in size. The cardiac example, analyzed in the present paper, shows changes in m-Volume that can reach the 60%. We show here that standard Geometric Morphometrics tools (landmarks, Thin Plate Spline, and related decomposition of the deformation) can be generalized to better describe the very large deformations of biological tissues, without losing a synthetic description. In particular, the classical decomposition of the space tangent to the shape space in affine and non affine components is enriched to include also the change in size, in order to give a complete description of the tangent space to the size-and-shape space. The proposed generalization is formulated by means of a new Riemannian metric describing the change in size as change in m-Volume rather than change in Centroid Size. This leads to a redefinition of some aspects of the Kendall’s size-and-shape space without losing Kendall’s original formulation. This new formulation is discussed by means of simulated examples using 2D and 3D platonic shapes as well as a real example from clinical 3D echocardiographic data. We demonstrate that our decomposition based approaches discriminate very effectively healthy subjects from patients affected by Hypertrophic Cardiomyopathy. Elsevier 2018-02-21 Article PeerReviewed Varano, Valerio, Piras, Paolo, Gabriele, Stefano, Teresi, Luciano, Nardinocchi, Paola, Dryden, Ian L., Torromeo, Concetta and Puddu, Paolo E. (2018) The decomposition of deformation: new metrics to enhance shape analysis in medical imaging. Medical Image Analysis, 46 . pp. 35-56. ISSN 1361-8423 Geometric Morphometrics Decomposition of Deformation Riemannian Metrics Size and Shape Left Ventricle Deformation https://www.sciencedirect.com/science/article/pii/S136184151830029X doi:10.1016/j.media.2018.02.005 doi:10.1016/j.media.2018.02.005 |
| spellingShingle | Geometric Morphometrics Decomposition of Deformation Riemannian Metrics Size and Shape Left Ventricle Deformation Varano, Valerio Piras, Paolo Gabriele, Stefano Teresi, Luciano Nardinocchi, Paola Dryden, Ian L. Torromeo, Concetta Puddu, Paolo E. The decomposition of deformation: new metrics to enhance shape analysis in medical imaging |
| title | The decomposition of deformation: new metrics to enhance shape analysis in medical imaging |
| title_full | The decomposition of deformation: new metrics to enhance shape analysis in medical imaging |
| title_fullStr | The decomposition of deformation: new metrics to enhance shape analysis in medical imaging |
| title_full_unstemmed | The decomposition of deformation: new metrics to enhance shape analysis in medical imaging |
| title_short | The decomposition of deformation: new metrics to enhance shape analysis in medical imaging |
| title_sort | decomposition of deformation: new metrics to enhance shape analysis in medical imaging |
| topic | Geometric Morphometrics Decomposition of Deformation Riemannian Metrics Size and Shape Left Ventricle Deformation |
| url | https://eprints.nottingham.ac.uk/51435/ https://eprints.nottingham.ac.uk/51435/ https://eprints.nottingham.ac.uk/51435/ |