Related papers: Efficient two-parameter persistence computation vi…
We construct worst-case examples for the standard reduction algorithm for computing persistent homology. Our constructions are similar to the worst-case examples introduced by Morozov, but we replace the single-triangle arrangement with a…
The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would permit multi-parameter…
The homography matrix is a key component in various vision-based robotic tasks. Traditionally, homography estimation algorithms are classified into feature- or intensity-based. The main advantages of the latter are their versatility,…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…
We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data…
We introduce a new algorithm to parallelise the computation of persistent homology of 2D alpha complexes. Our algorithm distributes the input point cloud among the cores which then compute a cover based on a rectilinear grid. We show how to…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…
Persistent homology is a tool of topological data analysis that has been used in a variety of settings to characterize different dimensional holes in data. However, persistent homology computations can be memory intensive with a…
Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena…
We develop novel methods for using persistent homology to infer the homology of an unknown Riemannian manifold $(M, g)$ from a point cloud sampled from an arbitrary smooth probability density function. Standard distance-based filtered…
Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for…
We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct…
In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been…
In this paper, we propose a improved 2D-PEH based on double prediction-error. First,different from previous 2D-PEH, the proposed 2D-DPEH is established by selecting two distinct predictors with low correlation to calculate double prediction…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes.…
A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…
The Hough transform is a popular and classical technique in computer vision for the detection of lines (or more general objects). It maps a pixel into a dual space -- the Hough space: each pixel is mapped to the set of lines through this…
Persistence diagrams are useful displays that give a summary information regarding the topological features of some phenomenon. Usually, only one persistence diagram is available, and replicated persistence diagrams are needed for…