Shape analysis via inconsistent surface registration

Abstract

In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with prominent feature landmarks, it is more desirable to have a method that automatically detects the most relevant parts of the two surfaces and finds the optimal landmark-matching alignment between those parts, without assuming any global 1-1 correspondence between the two surfaces. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory. It further enables us to quantify the dissimilarity of two shapes using quasi-conformal distortion and differences in mean and Gaussian curvatures, thereby providing a natural way for shape classification. Experiments on Platyrrhine molars demonstrate the effectiveness of our method and shed light on the interplay between function and shape in nature.

References in corpus (13)

• Boundary First Flattening
• Algorithms to automatically quantify the geometric similarity of anatomical surfaces
• TEMPO: Feature-Endowed Teichmüller Extremal Mappings of Point Clouds
• Fast Disk Conformal Parameterization of Simply-connected Open Surfaces
• Parallelizable global conformal parameterization of simply-connected surfaces via partial welding
• Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing
• Tooth morphometry using quasi-conformal theory
• A Linear Formulation for Disk Conformal Parameterization of Simply-Connected Open Surfaces
• Density-equalizing maps for simply-connected open surfaces
• Area-preserving mapping of 3D ultrasound carotid artery images using density-equalizing reference map
• Efficient Feature-based Image Registration by Mapping Sparsified Surfaces
• Fast Spherical Quasiconformal Parameterization of Genus-0 Closed Surfaces with Application to Adaptive Remeshing
• Inconsistent Surface Registration via Optimization of Mapping Distortions

Cited by in corpus (4)

• Free-boundary conformal parameterization of point clouds
• Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory
• Quasiconformal model with CNN features for large deformation image registration
• Data-driven quasiconformal morphodynamic flows