Related papers: Multi-directional Geodesic Neural Networks via Equ…
This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
3D shape models are naturally parameterized using vertices and faces, \ie, composed of polygons forming a surface. However, current 3D learning paradigms for predictive and generative tasks using convolutional neural networks focus on a…
The majority of descriptor-based methods for geometric processing of non-rigid shape rely on hand-crafted descriptors. Recently, learning-based techniques have been shown effective, achieving state-of-the-art results in a variety of tasks.…
Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to…
We propose DualConvMesh-Nets (DCM-Net) a family of deep hierarchical convolutional networks over 3D geometric data that combines two types of convolutions. The first type, geodesic convolutions, defines the kernel weights over mesh surfaces…
Multimodal data provide complementary information of a natural phenomenon by integrating data from various domains with very different statistical properties. Capturing the intra-modality and cross-modality information of multimodal data is…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…
In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…
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…
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
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…
Contour detection has been a fundamental component in many image segmentation and object detection systems. Most previous work utilizes low-level features such as texture or saliency to detect contours and then use them as cues for a…
Graph convolution operators bring the advantages of deep learning to a variety of graph and mesh processing tasks previously deemed out of reach. With their continued success comes the desire to design more powerful architectures, often by…
We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes…
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…
Convolutional Neural Network (CNN) has demonstrated impressive ability to represent hyperspectral images and to achieve promising results in hyperspectral image classification. However, traditional CNN models can only operate convolution on…
Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…