Related papers: The Manifold Scattering Transform for High-Dimensi…

Deep neural networks are widely used for understanding 3D point clouds. At each point convolution layer, features are computed from local neighborhoods of 3D points and combined for subsequent processing in order to extract semantic…

3D point clouds deep learning is a promising field of research that allows a neural network to learn features of point clouds directly, making it a robust tool for solving 3D scene understanding tasks. While recent works show that point…

Hypergraph spectral analysis has emerged as an effective tool processing complex data structures in data analysis. The surface of a three-dimensional (3D) point cloud and the multilateral relationship among their points can be naturally…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point…

Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go,…

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…

In this paper we propose a rotation-invariant deep network for point clouds analysis. Point-based deep networks are commonly designed to recognize roughly aligned 3D shapes based on point coordinates, but suffer from performance drops with…

Point clouds are characterized by irregularity and unstructuredness, which pose challenges in efficient data exploitation and discriminative feature extraction. In this paper, we present an unsupervised deep neural architecture called…

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…

The concept of a Point Cloud has played an increasingly important role in many areas of Engineering, Science, and Mathematics. Examples are: LIDAR, 3D-Printing, Data Analysis, Computer Graphics, Machine Learning, Mathematical Visualization,…

High quality upsampling of sparse 3D point clouds is critically useful for a wide range of geometric operations such as reconstruction, rendering, meshing, and analysis. In this paper, we propose a data-driven algorithm that enables an…

Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…

This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…

In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…

We recover the Riemannian gradient of a given function defined on interior points of a Riemannian submanifold in the Euclidean space based on a sample of function evaluations at points in the submanifold. This approach is based on the…

Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. However, their invertibility constraint imposes limitations on data distributions that reside on…

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…

We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…