Related papers: Elastic Shape Registration of Surfaces in 3D Space…

The computation of the elastic shape registration of two simple surfaces in 3-dimensional space and therefore of the elastic shape distance between them has been investigated by Kurtek, Jermyn, et al. who have proposed algorithms to carry…

The computation of the elastic registration of two simple curves in higher dimensions and therefore of the elastic shape distance between them has been investigated by Srivastava et al. Assuming the first curve has one or more starting…

As the continuation of the contour mean calculation - designed for averaging the manual delineations of 3D layer stack images - in this paper, the most important equations: a) the reparameterization equations to determine the minimizing…

We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a…

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…

We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…

Reverse Engineering a CAD shape from other representations is an important geometric processing step for many downstream applications. In this work, we introduce a novel neural network architecture to solve this challenging task and…

We propose a novel algorithm for the fitting of 3D human shape to images. Combining the accuracy and refinement capabilities of iterative gradient-based optimization techniques with the robustness of deep neural networks, we propose a…

We present a performance analysis for image registration with gradient descent methods. We consider a typical multiscale registration setting where the global 2-D translation between a pair of images is estimated by smoothing the images and…

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…

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…

We propose a new Riemannian gradient descent method for computing spherical area-preserving mappings of topological spheres using a Riemannian retraction-based framework with theoretically guaranteed convergence. The objective function is…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

We review the theory of, and develop algorithms for transforming a finite point set in ${\bf R}^d$ into a set in \emph{radial isotropic position} by a nonsingular linear transformation followed by rescaling each image point to the unit…

Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interations deform vesicle membrane is a fundamental question in biophysics. In this article we developed a fast algorithm to…

Surface registration is a technique that is used in various areas such as object recognition and 3D model reconstruction. Problem of surface registration can be analyzed as an optimization problem of seeking a rigid motion between two…

Reparameterization aims to improve the generalization of deep neural networks by transforming convolutional layers into equivalent multi-branched structures during training. However, there exists a gap in understanding how…

We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…

We study the implicit regularization of gradient descent towards structured sparsity via a novel neural reparameterization, which we call a diagonally grouped linear neural network. We show the following intriguing property of our…