Related papers: Aggregated Pairwise Classification of Statistical …
We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…
A fundamental question in learning to classify 3D shapes is how to treat the data in a way that would allow us to construct efficient and accurate geometric processing and analysis procedures. Here, we restrict ourselves to networks that…
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…
Statistical shape modeling (SSM) is an enabling quantitative tool to study anatomical shapes in various medical applications. However, directly using 3D images in these applications still has a long way to go. Recent deep learning methods…
Categorical data does not have an intrinsic definition of distance or order, and therefore, established visualization techniques for categorical data only allow for a set-based or frequency-based analysis, e.g., through Euler diagrams or…
Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. Biased by Euclidean thinking, circles are commonly considered as the simplest. However, their constructions as digital images are only approximations to the…
The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…
A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across…
Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…
In this paper, we focus on the two tasks of 3D shape abstraction and semantic analysis. This is in contrast to current methods, which focus solely on either 3D shape abstraction or semantic analysis. In addition, previous methods have had…
Large intra-class variation is the result of changes in multiple object characteristics. Images, however, only show the superposition of different variable factors such as appearance or shape. Therefore, learning to disentangle and…
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced…
In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We…
The gauge invariant elastic metric on the shape space of surfaces involves the mean curvature and the normal deformation, i.e. the sum and the difference of the principal curvatures $\kappa_1,\kappa_2$. The proposed gauge invariant elastic…
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
The recent advances in 3-D imaging technologies give rise to databases of human shapes, from which statistical shape models can be built. These statistical models represent prior knowledge of the human shape and enable us to solve shape…