Related papers: Deep neural networks on diffeomorphism groups for …
In deformable registration, the geometric framework - large deformation diffeomorphic metric mapping or LDDMM, in short - has inspired numerous techniques for comparing, deforming, averaging and analyzing shapes or images. Grounded in…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…
We investigate the dependence of the approximation capacity of deep residual networks on its depth in a continuous dynamical systems setting. This can be formulated as the general problem of quantifying the minimal time-horizon required to…
We propose PyTorchGeoNodes, a differentiable module for reconstructing 3D objects and their parameters from images using interpretable shape programs. Unlike traditional CAD model retrieval, shape programs allow reasoning about semantic…
We introduce in this paper a learning paradigm in which the training data is transformed by a diffeomorphic transformation before prediction. The learning algorithm minimizes a cost function evaluating the prediction error on the training…
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…
We design and implement a Python library to help the non-expert using all these powerful tools in a way that is efficient, extensible, and simple to incorporate into the workflow of the data scientist, practitioner, and applied researcher.…
We introduce a novel numerical framework for the exploration of Blaschke--Santal\'o diagrams, which are efficient tools characterizing the possible inequalities relating some given shape functionals. We introduce a parametrization of convex…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Deep Implicit Functions (DIFs) represent 3D geometry with continuous signed distance functions learned through deep neural nets. Recently DIFs-based methods have been proposed to handle shape reconstruction and dense point correspondences…
Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…
Many imaging problems can be formulated as mapping problems. A general mapping problem aims to obtain an optimal mapping that minimizes an energy functional subject to the given constraints. Existing methods to solve the mapping problems…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…
In this paper we consider the problem of constructing numerical algorithms for approximating of convex compact bodies in d-dimensional Euclidean space by polytopes with any given accuracy. It is well known that optimal with respect to the…
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…