Related papers: Representation Learning on Unit Ball with 3D Roto-…

Establishing correspondences between 3D shapes is a fundamental task in 3D Computer Vision, typically addressed by matching local descriptors. Recently, a few attempts at applying the deep learning paradigm to the task have shown promising…

A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…

Deep learning models develop successive representations of their input in sequential layers, the last of which maps the final representation to the output. Here we investigate the informational content of these representations by observing…

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…

A unified construction of high order shape functions is given for all four classical energy spaces ($H^1$, $H(\mathrm{curl})$, $H(\mathrm{div})$ and $L^2$) and for elements of "all" shapes (segment, quadrilateral, triangle, hexahedron,…

Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…

Recently, deep learning approach has achieved promising results in various fields of computer vision. In this paper, a new framework called Hierarchical Depth Motion Maps (HDMM) + 3 Channel Deep Convolutional Neural Networks (3ConvNets) is…

3D geometry is a very informative cue when interacting with and navigating an environment. This writing proposes a new approach to 3D reconstruction and scene understanding, which implicitly learns 3D geometry from depth maps pairing a deep…

Like other applications in computer vision, medical image segmentation has been most successfully addressed using deep learning models that rely on the convolution operation as their main building block. Convolutions enjoy important…

In this paper, we propose a simple yet effective method to endow deep 3D models with rotation invariance by expressing the coordinates in an intrinsic frame determined by the object shape itself. Key to our approach is to find such an…

We present e3nn, a generalized framework for creating E(3) equivariant trainable functions, also known as Euclidean neural networks. e3nn naturally operates on geometry and geometric tensors that describe systems in 3D and transform…

Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…

Solving image-to-3D from a single view is an ill-posed problem, and current neural reconstruction methods addressing it through diffusion models still rely on scene-specific optimization, constraining their generalization capability. To…

Convolutional Neural Networks (CNNs) have been providing the state-of-the-art performance for learning-related problems involving 2D/3D images in Euclidean space. However, unlike in the Euclidean space, the shapes of many structures in…

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…

Computer vision is a growing field with a lot of new applications in automation and robotics, since it allows the analysis of images and shapes for the generation of numerical or analytical information. One of the most used method of…

Human motion retargeting aims to transfer the motion of one person in a "driving" video or set of images to another person. Existing efforts leverage a long training video from each target person to train a subject-specific motion transfer…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

In this paper, we propose a novel 3D graph convolution based pipeline for category-level 6D pose and size estimation from monocular RGB-D images. The proposed method leverages an efficient 3D data augmentation and a novel vector-based…

Extending the translation equivariance property of convolutional neural networks to larger symmetry groups has been shown to reduce sample complexity and enable more discriminative feature learning. Further, exploiting additional symmetries…