Related papers: Learning from landmarks, curves, surfaces, and sha…

We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively…

This work addresses the challenge of analyzing geometric structures using Kendall's 3D Shape Space. While Riemannian geometry provides a robust framework for shape analysis (independent of scale, position, and orientation) the transition…

We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We…

We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…

One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised…

Shape affects both the physical and chemical properties of a material. Characterizing the roughness, convexity, and general geometry of a material can yield information on its catalytic efficiency, solubility, elasticity, porosity, and…

This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…

This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the…

Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Geometric morphometrics (GMM) is widely used to quantify shape variation, more recently serving as input for machine learning (ML) analyses. Standard practice aligns all specimens via Generalized Procrustes Analysis (GPA) prior to splitting…

Statistical shape modeling is an essential tool for the quantitative analysis of anatomical populations. Point distribution models (PDMs) represent the anatomical surface via a dense set of correspondences, an intuitive and easy-to-use…

Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…

In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…

Template 3D shapes are useful for many tasks in graphics and vision, including fitting observation data, analyzing shape collections, and transferring shape attributes. Because of the variety of geometry and topology of real-world shapes,…

The projective shape of a configuration of k points or "landmarks" in RP(d) consists of the information that is invariant under projective transformations and hence is reconstructable from uncalibrated camera views. Mathematically, the…

Statistical shape modeling is the computational process of discovering significant shape parameters from segmented anatomies captured by medical images (such as MRI and CT scans), which can fully describe subject-specific anatomy in the…

Deep Learning architectures, albeit successful in most computer vision tasks, were designed for data with an underlying Euclidean structure, which is not usually fulfilled since pre-processed data may lie on a non-linear space. In this…