Shape 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 metric for the Wasserstein space. It intrinsically measures the similarities between shapes and is robust to image noise. Thus it has the potential for the 3D shape indexing and classification research. While the algorithms for computing Wasserstein distance have been extensively studied, most of them only work for genus-0 surfaces. This paper proposes a novel framework to compute Wasserstein distance between general topological surfaces with hyperbolic metric. The computational algorithms are based on Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram and the method is general and robust. We apply our method to study human facial expression, longitudinal brain cortical morphometry with normal aging, and cortical shape classification in Alzheimer's disease (AD). Experimental results demonstrate that our method may be used as an effective shape index, which outperforms some other standard shape measures in our AD versus healthy control classification study.
Code (0)
등록된 구현이 없습니다.
Tasks
ClassificationGeneral ClassificationSimilar Papers 제목 키워드 기반
Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but o…
image-classificationImage ClassificationImproving Hyperbolic Representations via Gromov-Wasserstein Regularization
Hyperbolic representations have shown remarkable efficacy in modeling inherent hierarchies and complexities within data structures. Hyperbolic neural networks have been commonly applied for learning such representations …
Few-Shot Image Classificationimage-classificationImage ClassificationLink Prediction+1Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchy
Finding meaningful distances between high-dimensional data samples is an important scientific task. To this end, we propose a new tree-Wasserstein distance (TWD) for high-dimensional data with two key aspects. First, our…
Wasserstein-Aligned Hyperbolic Multi-View Clustering
Multi-view clustering (MVC) aims to uncover the latent structure of multi-view data by learning view-common and view-specific information. Although recent studies have explored hyperbolic representations for better tackl…
Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds
While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. T…