Related papers: Continuation of Point Clouds via Persistence Diagr…
Point cloud segmentation and classification are some of the primary tasks in 3D computer vision with applications ranging from augmented reality to robotics. However, processing point clouds using deep learning-based algorithms is quite…
Point clouds are often sparse and incomplete. Existing shape completion methods are incapable of generating details of objects or learning the complex point distributions. To this end, we propose a cascaded refinement network together with…
Point clouds data, as one kind of representation of 3D objects, are the most primitive output obtained by 3D sensors. Unlike 2D images, point clouds are disordered and unstructured. Hence it is not straightforward to apply classification…
In this paper we define, implement, and investigate a simplicial complex construction for computing persistent homology of Euclidean point cloud data, which we call the Delaunay-Rips complex (DR). Assigning the Vietoris-Rips weights to…
This paper introduces a new method for 3D point cloud registration based on deep learning. The architecture is composed of three distinct blocs: (i) an encoder composed of a convolutional graph-based descriptor that encodes the immediate…
Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed…
Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D…
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with 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…
3D point-cloud recognition with PointNet and its variants has received remarkable progress. A missing ingredient, however, is the ability to automatically evaluate point-wise importance w.r.t.\! classification performance, which is usually…
3D point cloud completion, the task of inferring the complete geometric shape from a partial point cloud, has been attracting attention in the community. For acquiring high-fidelity dense point clouds and avoiding uneven distribution,…
The ever-increasing 3D application makes the point cloud compression unprecedentedly important and needed. In this paper, we propose a patch-based compression process using deep learning, focusing on the lossy point cloud geometry…
A method is presented for the distributed computation of persistent homology, based on an extension of the generalized Mayer-Vietoris principle to filtered spaces. Cellular cosheaves and spectral sequences are used to compute global…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
The increasing demand for accurate representations of 3D scenes, combined with immersive technologies has led point clouds to extensive popularity. However, quality point clouds require a large amount of data and therefore the need for…
Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning.…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
Three dimensional (3D) object recognition is becoming a key desired capability for many computer vision systems such as autonomous vehicles, service robots and surveillance drones to operate more effectively in unstructured environments.…
Current learning-based methods predict NeRF or 3D Gaussians from point clouds to achieve photo-realistic rendering but still depend on categorical priors, dense point clouds, or additional refinements. Hence, we introduce a novel point…
Graph convolutional neural networks (Graph-CNNs) extend traditional CNNs to handle data that is supported on a graph. Major challenges when working with data on graphs are that the support set (the vertices of the graph) do not typically…