A survey on deep geometry learning: from a representation perspective

Researchers have achieved great success in dealing with 2D images using deep learning. In recent years, 3D computer vision and geometry deep learning have gained ever more attention. Many advanced techniques for 3D shapes have been proposed for different applications. Unlike 2D images, which can be uniformly represented by a regular grid of pixels, 3D shapes have various representations, such as depth images, multi-view images, voxels, point clouds, meshes, implicit surfaces, etc. The performance achieved in different applications largely depends on the representation used, and there is no unique representation that works well for all applications. Therefore, in this survey, we review recent developments in deep learning for 3D geometry from a representation perspective, summarizing the advantages and disadvantages of different representations for different applications. We also present existing datasets in these representations and further discuss future research directions

BeyondPixels: A Comprehensive Review of the Evolution of Neural Radiance Fields

Neural rendering combines ideas from classical computer graphics and machine learning to synthesize images from real-world observations. NeRF, short for Neural Radiance Fields, is a recent innovation that uses AI algorithms to create 3D objects from 2D images. By leveraging an interpolation approach, NeRF can produce new 3D reconstructed views of complicated scenes. Rather than directly restoring the whole 3D scene geometry, NeRF generates a volumetric representation called a ``radiance field,'' which is capable of creating color and density for every point within the relevant 3D space. The broad appeal and notoriety of NeRF make it imperative to examine the existing research on the topic comprehensively. While previous surveys on 3D rendering have primarily focused on traditional computer vision-based or deep learning-based approaches, only a handful of them discuss the potential of NeRF. However, such surveys have predominantly focused on NeRF's early contributions and have not explored its full potential. NeRF is a relatively new technique continuously being investigated for its capabilities and limitations. This survey reviews recent advances in NeRF and categorizes them according to their architectural designs, especially in the field of novel view synthesis.Comment: 22 page, 1 figure, 5 tabl

Length Constrained Multiresolution Deformation for Surface Wrinkling

International audienceWe present a method for deforming piescewise linear 3D curves on surfaces with constant length constraint. We show how this constraint can be integrated into a multiresolution editing tool allowing an intuitive control of the deformation's extent and aspect. The constraint is enforced following two steps. A first step consists in approximating the initial length by modifying the multiresolution decomposition at some specified scale. In a second step the constraint is axactly enforced by constrained minimization of a smoothness criterion. This process then provides the core of an integrated wrinkling tool for soft tissues modelling. A curve on the mesh is deformed, providing a deformation profile which is propagated in a user-defined neighbourhood

Implementation of a level-set based volume penalization method for solving fluid flows around bluff bodies in OpenFOAM

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an Open Source Field Operation and Manipulation (OpenFOAM). For capturing the fluid-solid interface more accurately, the grid is refined near the solid surface using topoSetDict and refineMeshDict utilities in OpenFOAM. In order to avoid any numerical oscillation, the present volume penalization method (VPM) is integrated with a signed distance function, which is also referred to as a level-set function. Benchmark problems, such as flows around a cylinder and a sphere, are considered and thoroughly validated with the results available in the literature. For the flow over a stationary cylinder, the Reynolds number is varied so that it covers from a steady 2D (two-dimensional) flow to an unsteady 3D (three-dimensional) flow. The capability of the present solver has been further verified by considering the flow past a vibrating cylinder in the cross-stream direction. In addition, a flow over a sphere, which is inherently three-dimensional due to its geometrical shape, is validated in both steady and unsteady regimes. The results obtained by the present VPM show good agreement with those obtained by a body-fitted grid using the same numerical scheme as that of the VPM, and also with those reported in the literature. The present results indicate that the VPM-based immersed boundary technique can be widely applicable to scientific and engineering problems involving flow past stationary and moving bluff bodies of arbitrary geometry