Related papers: Nonlinear Invariants of Planar Point Clouds Transf…

In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are…

We propose a general method for deep learning based point cloud analysis, which is invariant to rotation on the inputs. Classical methods are vulnerable to rotation, as they usually take aligned point clouds as input. Principle Component…

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…

The convenience of 3D sensors has led to an increase in the use of 3D point clouds in various applications. However, the differences in acquisition devices or scenarios lead to divergence in the data distribution of point clouds, which…

The networks for point cloud tasks are expected to be invariant when the point clouds are affinely transformed such as rotation and reflection. So far, relative to the rotational invariance that has been attracting major research attention…

Recently, many deep neural networks were designed to process 3D point clouds, but a common drawback is that rotation invariance is not ensured, leading to poor generalization to arbitrary orientations. In this paper, we introduce a new…

In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…

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…

Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data…

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…

This paper focuses on a novel generative approach for 3D point clouds that makes use of invertible flow-based models. The main idea of the method is to treat a point cloud as a probability density in 3D space that is modeled using a…

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…

Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks…

A basic representation of any real molecule is a finite cloud of unordered atoms, many of which are chemically indistinguishable. A natural equivalence on point clouds in any metric space is defined by isometries that are…

The intrinsic rotation invariance lies at the core of matching point clouds with handcrafted descriptors. However, it is widely despised by recent deep matchers that obtain the rotation invariance extrinsically via data augmentation. As the…

The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. For each order metric perturbation, we define the variable which is defined by the appropriate combination with…

Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry. Recently, there has been a growing interest in neural architectures that are invariant or equivariant…

We present a learning-based method for interpolating and manipulating 3D shapes represented as point clouds, that is explicitly designed to preserve intrinsic shape properties. Our approach is based on constructing a dual encoding space…

Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…

Point clouds have grown in importance in the way computers perceive the world. From LIDAR sensors in autonomous cars and drones to the time of flight and stereo vision systems in our phones, point clouds are everywhere. Despite their…