Related papers: A Geometric Approach to Steerable Convolutions
Contemporary deep neural networks exhibit impressive results on practical problems. These networks generalize well although their inherent capacity may extend significantly beyond the number of training examples. We analyze this behavior in…
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…
Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…
We present TetGAN, a convolutional neural network designed to generate tetrahedral meshes. We represent shapes using an irregular tetrahedral grid which encodes an occupancy and displacement field. Our formulation enables defining…
This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…
This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being…
We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…
Mesh-based learning is one of the popular approaches nowadays to learn shapes. The most established backbone in this field is MeshCNN. In this paper, we propose infusing MeshCNN with geometric reasoning to achieve higher quality learning.…
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…
We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural…
Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features,…
Deformable image registration poses a challenging problem where, unlike most deep learning tasks, a complex relationship between multiple coordinate systems has to be considered. Although data-driven methods have shown promising…
A new geometric shaping method is proposed, leveraging unsupervised machine learning to optimize the constellation design. The learned constellation mitigates nonlinear effects with gains up to 0.13 bit/4D when trained with a simplified…
Convolutional kernels are basic and vital components of deep Convolutional Neural Networks (CNN). In this paper, we equip convolutional kernels with shape attributes to generate the deep Irregular Convolutional Neural Networks (ICNN).…
It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
Neural implicit functions have achieved impressive results for reconstructing 3D shapes from single images. However, the image features for describing 3D point samplings of implicit functions are less effective when significant variations…
Standard convolutional neural networks assume a grid structured input is available and exploit discrete convolutions as their fundamental building blocks. This limits their applicability to many real-world applications. In this paper we…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…