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

Motivated by the recent discovery that the interpretation maps of CNNs could easily be manipulated by adversarial attacks against network interpretability, we study the problem of interpretation robustness from a new perspective of \Renyi…

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…

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

Efficiently identifying accurate correspondences between point clouds is crucial for both rigid and non-rigid point cloud registration. Existing methods usually rely on geometric or semantic feature embeddings to establish correspondences…

The proposed RMS-FlowNet is a novel end-to-end learning-based architecture for accurate and efficient scene flow estimation which can operate on point clouds of high density. For hierarchical scene flow estimation, the existing methods…

Convolutional neural networks (CNN) have achieved impressive performance on the wide variety of tasks (classification, detection, etc.) across multiple domains at the cost of high computational and memory requirements. Thus, leveraging CNNs…

Dense pixel matching problems such as optical flow and disparity estimation are among the most challenging tasks in computer vision. Recently, several deep learning methods designed for these problems have been successful. A sufficiently…

We study metrics that assess how close a triangulation is to being a Delaunay triangulation, for use in contexts where a good triangulation is desired but constraints (e.g., maximum degree) prevent the use of the Delaunay triangulation…

The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn-Hilliard Volume-of-Fluid model to capture the dynamics of the air-sea interface at geophysically relevant Reynolds numbers. It…

We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…

3D point cloud registration is a fundamental problem in computer vision and robotics. There has been extensive research in this area, but existing methods meet great challenges in situations with a large proportion of outliers and time…

ResNets and its variants play an important role in various fields of image recognition. This paper gives another variant of ResNets, a kind of cross-residual learning networks called C-ResNets, which has less computation and parameters than…

The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…

Determinantal point processes (DPPs) have emerged as a kernelized alternative to vanilla independent sampling for generating efficient minibatches, coresets and other parsimonious representations of large-scale datasets. While theoretical…

Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation.…

This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…

Nonlinear photonic delay systems present interesting implementation platforms for machine learning models. They can be extremely fast, offer great degrees of parallelism and potentially consume far less power than digital processors. So far…

3D motion estimation including scene flow and point cloud registration has drawn increasing interest. Inspired by 2D flow estimation, recent methods employ deep neural networks to construct the cost volume for estimating accurate 3D flow.…