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Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
A key step in any scanning-based asset creation workflow is to convert unordered point clouds to a surface. Classical methods (e.g., Poisson reconstruction) start to degrade in the presence of noisy and partial scans. Hence, deep learning…
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…
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,…
Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…
Current methodologies in point cloud analysis predominantly explore 3D geometries, often achieved through the introduction of intricate learnable geometric extractors in the encoder or by deepening networks with repeated blocks. However,…
Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural…
The precision of shape representation and the dimensionality of the design space significantly influence the cost and outcomes of aerodynamic optimization. The design space can be represented more compactly by maintaining geometric…
We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
Advanced 3D metrology technologies such as Coordinate Measuring Machine (CMM) and laser 3D scanners have facilitated the collection of massive point cloud data, beneficial for process monitoring, control and optimization. However, due to…
Point clouds, as a form of Lagrangian representation, allow for powerful and flexible applications in a large number of computational disciplines. We propose a novel deep-learning method to learn stable and temporally coherent feature…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
Reconstructing the 3D shape of an object from a single RGB image is a long-standing and highly challenging problem in computer vision. In this paper, we propose a novel method for single-image 3D reconstruction which generates a sparse…
In this paper, we propose a new algorithm for point cloud denoising based on the tensor Tucker decomposition. We first represent the local surface patches of a noisy point cloud to be matrices by their distances to a reference point, and…
3D point cloud (PC) -- a collection of discrete geometric samples of a physical object's surface -- is typically large in size, which entails expensive subsequent operations like viewpoint image rendering and object recognition. Leveraging…
One major challenge in 3D reconstruction is to infer the complete shape geometry from partial foreground occlusions. In this paper, we propose a method to reconstruct the complete 3D shape of an object from a single RGB image, with…
Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from 3D object recognition to reconstruction. We propose a novel approach to the alignment problem that utilizes Bayesian nonparametrics to…
In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces. Traditionally the middle surface is obtained by detecting singularities in computed distance…
We proposed a generalized method, NeuralSSD, for reconstructing a 3D implicit surface from the widely-available point cloud data. NeuralSSD is a solver-based on the neural Galerkin method, aimed at reconstructing higher-quality and accurate…