Cortical Surface Shape Analysis Based on Alexandrov Polyhedra
Shape analysis has been playing an important role in early diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's diseases (AD). However, obtaining effective shape representations remains challenging. This paper proposes to use the Alexandrov polyhedra as surface-based shape signatures for cortical morphometry analysis. Given a closed genus-0 surface, its Alexandrov polyhedron is a convex representation that encodes its intrinsic geometry information. We propose to compute the polyhedra via a novel spherical optimal transport (OT) computation. In our experiments, we observe that the Alexandrov polyhedra of cortical surfaces between pathology-confirmed AD and cognitively unimpaired individuals are significantly different. Moreover, we propose a visualization method by comparing local geometry differences across cortical surfaces. We show that the proposed method is effective in pinpointing regional cortical structural changes impacted by AD.
Code (0)
등록된 구현이 없습니다.
Tasks
PrognosisSimilar Papers 제목 키워드 기반
Polyhedral Surface: Self-supervised Point Cloud Reconstruction Based on Polyhedral Surface
Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this probl…
Point cloud reconstructionWavelet based multi-scale shape features on arbitrary surfaces for cortical thickness discrimination
Hypothesis testing on signals defined on surfaces (such as the cortical surface) is a fundamental component of a variety of studies in Neuroscience. The goal here is to identify regions that exhibit changes as a function …
Two-sample testingHybrid-CSR: Coupling Explicit and Implicit Shape Representation for Cortical Surface Reconstruction
We present Hybrid-CSR, a geometric deep-learning model that combines explicit and implicit shape representations for cortical surface reconstruction. Specifically, Hybrid-CSR begins with explicit deformations of template…
Surface ReconstructionPolyhedronNet: Representation Learning for Polyhedra with Surface-attributed Graph
Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shap…
Representation LearningShape Analysis With Hyperbolic Wasserstein Distance
Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian …
ClassificationGeneral Classification