相关论文: ZerNet: Convolutional Neural Networks on Arbitrary…

In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…

Convolutional neural networks (ConvNets) have demonstrated an exceptional capacity to discern visual patterns from digital images and signals. Unfortunately, such powerful ConvNets do not generalize well to arbitrary-shaped manifolds, where…

Surface meshes are widely used shape representations and capture finer geometry data than point clouds or volumetric grids, but are challenging to apply CNNs directly due to their non-Euclidean structure. We use parallel frames on surface…

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…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids…

Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…

Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…

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…

An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…

Convolutional Neural Networks have revolutionized vision applications. There are image domains and representations, however, that cannot be handled by standard CNNs (e.g., spherical images, superpixels). Such data are usually processed…

Convolutional neural networks (CNNs) have massively impacted visual recognition in 2D images, and are now ubiquitous in state-of-the-art approaches. CNNs do not easily extend, however, to data that are not represented by regular grids, such…

We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…

Neural networks are omnipresent, but remain poorly understood. Their increasing complexity and use in critical systems raises the important challenge to full interpretability. We propose to address a simple well-posed learning problem:…

In Convolutional Neural Networks (CNNs) information flows across a small neighbourhood of each pixel of an image, preventing long-range integration of features before reaching deep layers in the network. We propose a novel architecture that…

Geometric deep learning has attracted significant attention in recent years, in part due to the availability of exotic data types for which traditional neural network architectures are not well suited. Our goal in this paper is to…

We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of a translation operator on a graph structure. In regular settings such as images, convolutional layers are designed by translating a…

Existing techniques to encode spatial invariance within deep convolutional neural networks only model 2D transformation fields. This does not account for the fact that objects in a 2D space are a projection of 3D ones, and thus they have…

This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions…

With the impressive capability to capture visual content, deep convolutional neural networks (CNN) have demon- strated promising performance in various vision-based ap- plications, such as classification, recognition, and objec- t…