Related papers: Deep neural networks on diffeomorphism groups for …

Establishing point-to-point correspondences across multiple 3D shapes is a fundamental problem in computer vision and graphics. In this paper, we introduce DcMatch, a novel unsupervised learning framework for non-rigid multi-shape matching.…

The problem of finding a time-dependent vector field which warps an initial set of points to a target set is common in shape analysis. It is an example of a problem in the diffeomorphic shape matching regime, and can be thought of as a…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…

Meshes are widely used in 3D computer vision and graphics, but their irregular topology poses challenges in applying them to existing neural network architectures. Recent advances in mesh neural networks turn to remeshing and push the…

We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the…

In this work, we used deep neural networks (DNNs) to solve a fundamental problem in differential geometry. One can find many closed-form expressions for calculating curvature, length, and other geometric properties in the literature. As we…

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…

Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high…

X-ray Ptychography is an advanced computational microscopy technique which is delivering exceptionally detailed quantitative imaging of biological and nanotechnology specimens. However coarse parametrisation in propagation distance,…

We present a new deep learning approach for matching deformable shapes by introducing {\it Shape Deformation Networks} which jointly encode 3D shapes and correspondences. This is achieved by factoring the surface representation into (i) a…

Learning methods for relative camera pose estimation have been developed largely in isolation from classical geometric approaches. The question of how to integrate predictions from deep neural networks (DNNs) and solutions from geometric…

We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…

Curvilinear structures, which include line-like continuous objects, are fundamental geometrical elements in image-based applications. Reconstructing these structures from images constitutes a pivotal research area in computer vision.…

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

In this paper we present a new two-level iterative algorithm for tomographic image reconstruction. The algorithm uses a regularization technique, which we call edge-preserving Laplacian, that preserves sharp edges between objects while…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

Registration, which aims to find an optimal one-to-one correspondence between different data, is an important problem in various fields. This problem is especially challenging when large deformations occur. In this paper, we present a novel…