Related papers: Delaunay-Rips filtration: a study and an algorithm

Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…

We propose a framework for distributed robust statistical learning on {\em big contaminated data}. The Distributed Robust Learning (DRL) framework can reduce the computational time of traditional robust learning methods by several orders of…

Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be…

As incremental Structure from Motion algorithms become effective, a good sparse point cloud representing the map of the scene becomes available frame-by-frame. From the 3D Delaunay triangulation of these points, state-of-the-art algorithms…

In this paper, we address the problem of estimating dense depth from a sequence of images using deep neural networks. Specifically, we employ a dense-optical-flow network to compute correspondences and then triangulate the point cloud to…

This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe…

We propose a robust normal estimation method for both point clouds and meshes using a low rank matrix approximation algorithm. First, we compute a local feature descriptor for each point and find similar, non-local neighbors that we…

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A…

Retinal vessels are important biomarkers for many ophthalmological and cardiovascular diseases. Hence, it is of great significance to develop automatic models for computer-aided diagnosis. Existing methods, such as U-Net follow the…

Convolutional networks for image classification progressively reduce resolution until the image is represented by tiny feature maps in which the spatial structure of the scene is no longer discernible. Such loss of spatial acuity can limit…

We propose DeepMapping, a novel registration framework using deep neural networks (DNNs) as auxiliary functions to align multiple point clouds from scratch to a globally consistent frame. We use DNNs to model the highly non-convex mapping…

The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult…

In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…

We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the…

Recovering high quality surfaces from noisy point clouds, known as point cloud denoising, is a fundamental yet challenging problem in geometry processing. Most of the existing methods either directly denoise the noisy input or filter raw…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

The task of learning from point cloud data is always challenging due to the often occurrence of noise and outliers in the data. Such data inaccuracies can significantly influence the performance of state-of-the-art deep learning networks…

Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…

Recurrent Neural Networks (RNNs) are a class of machine learning algorithms used for applications with time-series and sequential data. Recently, there has been a strong interest in executing RNNs on embedded devices. However, difficulties…

This paper presents some of our findings on the scalability of parallel 3D mesh generation on distributed memory machines. The primary objective of this study was to evaluate a distributed memory approach for implementing a 3D parallel…