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Landmark-free geometric methods in biological shape analysis.

ABSTRACT: In this paper, we propose a new approach for computing a distance between two shapes embedded in three-dimensional space. We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces. The conformal map is chosen to minimize a symmetric deformation energy Esd(f) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence. We show that the energy of the minimizing map gives a well-behaved metric on the space of genus zero surfaces. In contrast to most methods in this field, our approach does not rely on any assignment of landmarks on the two surfaces. We illustrate applications of our approach to geometric morphometrics using three datasets representing the bones and teeth of primates. Experiments on these datasets show that our approach performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.

SUBMITTER: Koehl P

PROVIDER: S-EPMC4707851 | biostudies-literature | 2015 Dec

REPOSITORIES: biostudies-literature

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Landmark-free geometric methods in biological shape analysis.

Koehl Patrice P Hass Joel J

Journal of the Royal Society, Interface 20151201 113

In this paper, we propose a new approach for computing a distance between two shapes embedded in three-dimensional space. We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces. The conformal map is chosen to minimize a symmetric deformation energy Esd(f) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence ...[more]

PMID: 26631331

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Project description:Geometric morphometrics (GM) enable the quantification of morphological variation on various scales. Recent technical advances allow analyzing complex three-dimensional shapes also in cases where landmark-based approaches are not appropriate. Pelvic girdle bones (basipterygia) of Sulawesi ricefishes are 3D structures that challenge traditional morphometrics. We hypothesize that the pelvic girdle of ricefishes experienced sex-biased selection pressures in species where females provide brood care by carrying fertilized eggs supported by elongated pelvic fins ("pelvic brooding"). We test this by comparing pelvic bone shapes of both sexes in species exhibiting pelvic brooding and the more common reproductive strategy "transfer brooding," by using landmark-free 2D and 3D GM, as well as qualitative shape descriptions. Both landmark-free approaches revealed significant interspecific pelvic bone variation in the lateral process, medial facing side of the pelvic bone, and overall external and internal wing shape. Within pelvic brooders, the three analyzed species are clearly distinct, while pelvic bones of the genus Adrianichthys are more similar to transfer brooding Oryzias. Female pelvic brooding Oryzias exhibit prominent, medially pointing tips extending from the internal wing and basipterygial plate that are reduced or absent in conspecific males, Adrianichthys and transfer brooding Oryzias, supporting our hypothesis that selection pressures affecting pelvic girdle shape are sex-biased in Sulawesi ricefishes. Furthermore, both sexes of pelvic brooding Oryzias have overall larger pelvic bones than other investigated ricefishes. Based on these differences, we characterized two reproductive strategy- and sex-dependent pelvic girdle types for Sulawesi ricefishes. Morphological differences between the investigated pelvic brooding genera Adrianichthys and Oryzias provide additional evidence for two independent origins of pelvic brooding. Overall, our findings add to a better understanding on traits related to pelvic brooding in ricefishes and provide a basis for upcoming studies on pelvic girdle function and morphology.

Dataset Information

Landmark-free geometric methods in biological shape analysis.

Publications

Landmark-free geometric methods in biological shape analysis.

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