Related papers: Geodesic Models with Convexity Shape Prior

This paper introduces the geodesics of triangulated image object shapes. Both rectilinear and curvilinear triangulations of shapes are considered. The triangulation of image object shapes leads to collections of what are known as nerve…

The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…

Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized,…

We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…

A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…

This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

We introduce a data-driven version of the plus Cartan connection on the homogeneous space $\mathbb{M}_2$ of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and…

This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with…

This paper presents a method for local motion planning in unstructured environments with static and moving obstacles, such as humans. Given a reference path and speed, our optimization-based receding-horizon approach computes a local…

Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…

The motion planning problem involves finding a collision-free path from a robot's starting to its target configuration. Recently, self-supervised learning methods have emerged to tackle motion planning problems without requiring expensive…

Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…

For bone segmentation, the classical geodesic active contour model is usually limited by its indiscriminate feature extraction, and then struggles to handle the phenomena of edge obstruction, edge leakage and bone fracture. Thus, we propose…

Motion Planning (MP) is a critical challenge in robotics, especially pertinent with the burgeoning interest in embodied artificial intelligence. Traditional MP methods often struggle with high-dimensional complexities. Recently neural…

Computing an array of all pairs of geodesic distances between the pixels of an image is time consuming. In the sequel, we introduce new methods exploiting the redundancy of geodesic propagations and compare them to an existing one. We show…

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary…

The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of…

We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…