Related papers: Topological Data Analysis with $\epsilon$-net Indu…

Computation of persistent homology of simplicial representations such as the Rips and the C\v{e}ch complexes do not efficiently scale to large point clouds. It is, therefore, meaningful to devise approximate representations and evaluate the…

The efficiency of extracting topological information from point data depends largely on the complex that is built on top of the data points. From a computational viewpoint, the most favored complexes for this purpose have so far been…

Capitalizing on the intuitive premise that shape characteristics are more robust to perturbations, we bridge adversarial graph learning with the emerging tools from computational topology, namely, persistent homology representations of…

Appearance-based gaze estimation frequently relies on deep Convolutional Neural Networks (CNNs). These models are accurate, but computationally expensive and act as "black boxes", offering little interpretability. Geometric methods based on…

Point cloud completion aims at completing geometric and topological shapes from a partial observation. However, some topology of the original shape is missing, existing methods directly predict the location of complete points, without…

Benefiting from the continuous representation ability, deep implicit functions can represent a shape at infinite resolution. However, extracting high-resolution iso-surface from an implicit function requires forward-propagating a network…

The task of a visual landmark recognition system is to identify photographed buildings or objects in query photos and to provide the user with relevant information on them. With their increasing coverage of the world's landmark buildings…

Landmark detection is a critical component of the image processing pipeline for automated aortic size measurements. Given that the thoracic aorta has a relatively conserved topology across the population and that a human annotator with…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

3D object classification is a crucial problem due to its significant practical relevance in many fields, including computer vision, robotics, and autonomous driving. Although deep learning methods applied to point clouds sampled on CAD…

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 (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…

A methodology is proposed for inferring the topology underlying point cloud data. The approach employs basic elements of Morse Theory, and is capable of producing not only a point estimate of various topological quantities (e.g., genus),…

Automatically selecting the best performing algorithm for a given dataset or ranking multiple algorithms by their expected performance supports users in developing new machine learning applications. Most approaches for this problem rely on…

We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical…

An efficient 3D point cloud learning architecture, named EfficientLO-Net, for LiDAR odometry is first proposed in this paper. In this architecture, the projection-aware representation of the 3D point cloud is proposed to organize the raw 3D…

Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

Point cloud-based object/place recognition remains a problem of interest in applications such as autonomous driving, scene reconstruction, and localization. Extracting a meaningful global descriptor from a query point cloud that can be…

It is laborious to manually label point cloud data for training high-quality 3D object detectors. This work proposes a weakly supervised approach for 3D object detection, only requiring a small set of weakly annotated scenes, associated…