Related papers: Core Bifiltration
This paper proposes the Parallel Residual Bi-Fusion Feature Pyramid Network (PRB-FPN) for fast and accurate single-shot object detection. Feature Pyramid (FP) is widely used in recent visual detection, however the top-down pathway of FP…
(Abridged) Context. Core condensation is a critical step in the star-formation process, but is still poorly characterized observationally. Aims. We have studied the 10 pc-long L1495/B213 complex in Taurus to investigate how dense cores have…
New multi-core imaging fibre bundles -- hexabundles -- being developed at the University of Sydney will provide simultaneous integral field spectroscopy for hundreds of celestial sources across a wide angular field. These are a natural…
A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider the case where a sample is drawn from a properly embedded C1-submanifold without boundary in…
The alpha complex efficiently computes persistent homology of a point cloud $X$ in Euclidean space when the dimension $d$ is low. Given a subset $A$ of $X$, relative persistent homology can be computed as the persistent homology of the…
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…
We have performed 2D hydromagnetic simulations with an adaptive mesh refinement code to examine the response of a pre-existing initially spherical dense core to a non-linear fast-mode wave. One key parameter is the ratio of the wavelength…
Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…
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…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
We study detection of collapse in high-dimensional point clouds, where mass concentrates near a lower-dimensional set relative to a non-collapsed geometry. We propose persistent homology-based test statistics under two well-studied…
In this work we investigate the parallel computation of homology using the Mayer-Vietoris principle. We present a two stage approach for parallelizing persistence. In the first stage, we produce a cover of the input cell complex by…
Reconstructing building wireframe from airborne LiDAR point clouds yields a compact, topology-centric representation that enables structural understanding beyond dense meshes. Yet a key limitation persists: conventional methods have failed…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
The Hilbert metric is a distance function defined for points lying within the interior of a convex body. It arises in the analysis and processing of convex bodies, machine learning, and quantum information theory. In this paper, we show how…
We consider the Voronoi tessellation associated to a stationary simple point process on $\mathbb{R}^d$ with finite and positive intensity. We introduce the Delaunay triangulation as its dual graph, i.e.~the graph with vertex set given by…
Rigid shapes should be naturally compared up to rigid motion or isometry, which preserves all inter-point distances. The same rigid shape can be often represented by noisy point clouds of different sizes. Hence the isometry shape…
Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returning an algebraic object that can be vizualised as a…
Two important tasks in the field of Topological Data Analysis are building practical multifiltrations on objects and using TDA to detect the geometry. Motivated by the tasks, we build multiparameter filtrations by operators on images named…
Finding a suitable density function is essential for density-based clustering algorithms such as DBSCAN and DPC. A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in these…