Related papers: Baby Morse Theory in Data Analysis
Characterizing microstructure-material-property relations calls for software tools which extract point-cloud- and continuum-scale-based representations of microstructural objects. Application examples include atom probe, electron, and…
We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…
Change detection and irregular object extraction in 3D point clouds is a challenging task that is of high importance not only for autonomous navigation but also for updating existing digital twin models of various industrial environments.…
Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…
We propose a systematic approach for registering cross-source point clouds. The compelling need for cross-source point cloud registration is motivated by the rapid development of a variety of 3D sensing techniques, but many existing…
The time-series data of sea level rise and fall contains crucial information on the variability of sea level patterns. Traditional $k$-means clustering is commonly used for categorizing regional variability of sea level, however, its…
High quality upsampling of sparse 3D point clouds is critically useful for a wide range of geometric operations such as reconstruction, rendering, meshing, and analysis. In this paper, we propose a data-driven algorithm that enables an…
Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…
Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial…
Three-dimensional data have become increasingly present in earth observation over the last decades. However, many 3D surveys are still underexploited due to the lack of accessible and explainable automatic classification methods, for…
Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…
Unstructured point clouds with varying sizes are increasingly acquired in a variety of environments through laser triangulation or Light Detection and Ranging (LiDAR). Predicting a scalar response based on unstructured point clouds is a…
Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…
We introduce an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. We represent these edges as a collection of parametric curves (i.e.,lines, circles, and B-splines). Accordingly, our deep neural…
In this paper, we consider a simple class of stratified spaces -- 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from…
Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD),…
Point cloud completion is a generation and estimation issue derived from the partial point clouds, which plays a vital role in the applications in 3D computer vision. The progress of deep learning (DL) has impressively improved the…
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…
Geometric graphs form an important family of hidden structures behind data. In this paper, we develop an efficient and robust algorithm to infer a graph skeleton of a high-dimensional point cloud dataset (PCD). Previously, there has been…