Continuation of point clouds via persistence diagrams
نویسندگان
چکیده
منابع مشابه
Continuation of Point Clouds via Persistence Diagrams
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P , its persistence di...
متن کاملTopological Measurement of Protein Compressibility via Persistence Diagrams
We exploit recent advances in computational topology to study the compressibility of various proteins found in the Protein Data Bank (PDB). Our fundamental tool is the persistence diagram, a topological invariant which captures the sizes and robustness of geometric features such as tunnels and cavities in protein molecules. Based on certain physical and chemical properties conjectured to impact...
متن کاملFast Resampling of 3D Point Clouds via Graphs
To reduce the cost of storing, processing and visualizing a large-scale point cloud, we propose a randomized resampling strategy that selects a representative subset of points while preserving application-dependent features. The strategy is based on graphs, which can represent underlying surfaces and lend themselves well to efficient computation. We use a general feature-extraction operator to ...
متن کاملApproximating Gradients for Meshes and Point Clouds via Diffusion Metric
The gradient of a function defined on a manifold is perhaps one of the most important differential objects in data analysis. Most often in practice, the input function is available only at discrete points sampled from the underlying manifold, and the manifold is approximated by either a mesh or simply a point cloud. While many methods exist for computing gradients of a function defined over a m...
متن کاملBatched Point Location in SINR Diagrams via Algebraic Tools
The SINR model for the quality of wireless connections has been the subject of extensiverecent study. It attempts to predict whether a particular transmitter is heard at a specificlocation, in a setting consisting of n simultaneous transmitters and background noise. The SINRmodel gives rise to a natural geometric object, the SINR diagram, which partitions the spaceinto n regions...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2016
ISSN: 0167-2789
DOI: 10.1016/j.physd.2015.11.011