Related papers: Deep neural networks on diffeomorphism groups for …

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color…

In this work, a 2D contour generation algorithm is proposed for irregular regions. The contour of the physical domain is approximated by mesh segments using the known coordinates of the contour. For this purpose, the algorithm uses a…

Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…

We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…

3D object reconstruction from a single-view image is a long-standing challenging problem. Previous work was difficult to accurately reconstruct 3D shapes with a complex topology which has rich details at the edges and corners. Moreover,…

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…

We propose a novel tree-like curvilinear structure reconstruction algorithm based on supervised learning and graph theory. In this work we analyze image patches to obtain the local major orientations and the rankings that correspond to the…

Diffeomorphic image registration (DIR) is a fundamental task in 3D medical image analysis that seeks topology-preserving deformations between image pairs. To ensure diffeomorphism, a common approach is to model the deformation field as the…

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…

We introduce \emph{ReMatching}, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate \emph{re}-meshing paradigm, can target shape-\emph{matching} tasks even on meshes…

Current methods for 3D object reconstruction from a set of planar cross-sections still struggle to capture detailed topology or require a considerable number of cross-sections. In this paper, we present, to the best of our knowledge the…

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

This paper presents a predictive model for estimating regularization parameters of diffeomorphic image registration. We introduce a novel framework that automatically determines the parameters controlling the smoothness of diffeomorphic…

Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…

In computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has become a central tool for modeling smooth, invertible transformations between shapes such as curves or landmarks. In this paper, we extend…

With the explosive growth of web-based cameras and mobile devices, billions of photographs are uploaded to the internet. We can trivially collect a huge number of photo streams for various goals, such as image clustering, 3D scene…

We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

Diffeomorphisms play a crucial role while searching for shapes with fixed topological properties, allowing for smooth deformation of template shapes. Several approaches use diffeomorphism for shape search. However, these approaches employ…