Related papers: Geodesic Models with Convexity Shape Prior
We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of…
Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating…
Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based…
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…
We study the query complexity of geodesically convex (g-convex) optimization on a manifold. To isolate the effect of that manifold's curvature, we primarily focus on hyperbolic spaces. In a variety of settings (smooth or not; strongly…
We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…
Spatial perception aims to estimate camera motion and scene structure from visual observations, a problem traditionally addressed through geometric modeling and physical consistency constraints. Recent learning-based methods have…
It has been shown numerically that the performance of the Levenberg-Marquardt algorithm can be improved by including a second order correction known as the geodesic acceleration. In this paper we give the method a more sound theoretical…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and…
This paper introduces a differentiable representation for the optimization of boustrophedon path plans in convex polygons, explores an additional parameter of these path plans that can be optimized, discusses the properties of this…
This paper presents a two-stage prediction-based control scheme for embedding the environment's geometric properties into a collision-free Pythagorean Hodograph spline, and subsequently finding the optimal path within the parameterized free…
Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…
Convex Shapes (CS) are common priors for optic disc and cup segmentation in eye fundus images. It is important to design proper techniques to represent convex shapes. So far, it is still a problem to guarantee that the output objects from a…
Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the…
Mobile robots in dynamic environments require fast planning, especially when onboard computational resources are limited. While classic potential field based algorithms may suffice in simple scenarios, in most cases algorithms able to…
We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of $L$-smooth and geodesically convex (g-convex) or $\mu$-strongly g-convex…
This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…
Deep learning models have been widely applied across various domains and industries. However, many fields still face challenges due to limited and insufficient data. This paper proposes a Feature Augmentation on Adaptive Geodesic Curve…
Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image…
We propose an algorithmic framework for efficient anytime motion planning on large dense geometric roadmaps, in domains where collision checks and therefore edge evaluations are computationally expensive. A large dense roadmap (graph) can…