A Variational Model Dedicated to Joint Segmentation, Registration, and Atlas Generation for Shape Analysis Article Swipe
Noémie Debroux
,
John A. D. Aston
,
Fabien Bonardi
,
Alistair Forbes
,
Carole Le Guyader
,
Marina Romanchikova
,
Carola‐Bibiane Schönlieb
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1137/19m1271907
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1137/19m1271907
In medical image analysis, constructing an atlas, i.e. a mean representative of an ensemble of images, is a critical task for practitioners to estimate variability of shapes inside a population, and to characterise and understand how structural shape changes have an impact on health.This involves identifying significant shape constituents of a set of images, a process called segmentation, and mapping this group of images to an unknown mean image, a task called registration, making a statistical analysis of the image population possible.To achieve this goal, we propose treating these operations jointly to leverage their positive mutual influence, in a hyperelasticity setting, by viewing the shapes to be matched as Ogden materials.The approach is complemented by novel hard constraints on the L ∞ norm of both the Jacobian and its inverse, ensuring that the deformation is a bi-Lipschitz homeomorphism.Segmentation is based on the Potts model, which allows for a partition into more than two regions, i.e. more than one shape.The connection to the registration problem is ensured by the dissimilarity measure that aims to align the segmented shapes.A representation of the deformation field in a linear space equipped with a scalar product is then computed in order to perform a geometry-driven Principal Component Analysis (PCA) and to extract the main modes of variations inside the image population.Theoretical results emphasizing the mathematical soundness of the model are provided, among which existence of minimisers, analysis of a numerical method, asymptotic results and a PCA analysis, as well as numerical simulations demonstrating the ability of the model to produce an atlas exhibiting sharp edges, high contrast and a consistent shape.
Related Topics
Concepts
Population
Shape analysis (program analysis)
Atlas (anatomy)
Artificial intelligence
Segmentation
Image registration
Jacobian matrix and determinant
Computer science
Mathematics
Pattern recognition (psychology)
Computer vision
Image (mathematics)
Applied mathematics
Biology
Sociology
Static analysis
Paleontology
Demography
Programming language
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1137/19m1271907
- OA Status
- green
- References
- 58
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2955894367
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2955894367Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1137/19m1271907Digital Object Identifier
- Title
-
A Variational Model Dedicated to Joint Segmentation, Registration, and Atlas Generation for Shape AnalysisWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2020Year of publication
- Publication date
-
2020-01-01Full publication date if available
- Authors
-
Noémie Debroux, John A. D. Aston, Fabien Bonardi, Alistair Forbes, Carole Le Guyader, Marina Romanchikova, Carola‐Bibiane SchönliebList of authors in order
- Landing page
-
https://doi.org/10.1137/19m1271907Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1907.01840Direct OA link when available
- Concepts
-
Population, Shape analysis (program analysis), Atlas (anatomy), Artificial intelligence, Segmentation, Image registration, Jacobian matrix and determinant, Computer science, Mathematics, Pattern recognition (psychology), Computer vision, Image (mathematics), Applied mathematics, Biology, Sociology, Static analysis, Paleontology, Demography, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
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58Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.materials.The | 110 |
| abstract_inverted_index.practitioners | 21 |
| abstract_inverted_index.registration, | 72 |
| abstract_inverted_index.segmentation, | 57 |
| abstract_inverted_index.representation | 177 |
| abstract_inverted_index.representative | 10 |
| abstract_inverted_index.geometry-driven | 199 |
| abstract_inverted_index.hyperelasticity | 99 |
| abstract_inverted_index.population.Theoretical | 215 |
| abstract_inverted_index.homeomorphism.Segmentation | 137 |
| cited_by_percentile_year | |
| countries_distinct_count | 2 |
| institutions_distinct_count | 7 |
| citation_normalized_percentile.value | 0.00424564 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |