Related papers: Cubical Ripser: Software for computing persistent …
Persistent homology, an algebraic method for discerning structure in abstract data, relies on the construction of a sequence of nested topological spaces known as a filtration. Two-parameter persistent homology allows the analysis of data…
The computation of Vietoris-Rips persistence barcodes is both execution-intensive and memory-intensive. In this paper, we study its computational structure and identify several unique mathematical properties and algorithmic opportunities…
This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…
We present CuMPerLay, a novel differentiable vectorization layer that enables the integration of Cubical Multiparameter Persistence (CMP) into deep learning pipelines. While CMP presents a natural and powerful way to topologically work with…
The Vietoris-Rips filtration for an $n$-point metric space is a sequence of large simplicial complexes adding a topological structure to the otherwise disconnected space. The persistent homology is a key tool in topological data analysis…
Persistent homology (PH) is a powerful mathematical method to automatically extract relevant insights from images, such as those obtained by high-resolution imaging devices like electron microscopes or new-generation telescopes. However,…
Incorporating semantic information into the codecs during image compression can significantly reduce the repetitive computation of fundamental semantic analysis (such as object recognition) in client-side applications. The same practice…
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond…
We propose a real-time and lightweight single-image super-resolution (SR) network named Bicubic++. Despite using spatial dimensions of the input image across the whole network, Bicubic++ first learns quick reversible downgraded and lower…
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Image compression using neural networks have reached or exceeded non-neural methods (such as JPEG, WebP, BPG). While these networks are state of the art in ratedistortion performance, computational feasibility of these models remains a…
We present theory and practice for robust implementations of bivariate Jacobi set and Reeb space algorithms. Robustness is a fundamental topic in computational geometry that deals with the issues of numerical errors and degenerate cases in…
In this work, we conducted a survey on different registration algorithms and investigated their suitability for hyperspectral historical image registration applications. After the evaluation of different algorithms, we choose an intensity…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…
Quantitative analysis of multidimensional biological images is useful for understanding complex cellular phenotypes and accelerating advances in biomedical research. As modern microscopy generates ever-larger 2D and 3D datasets, existing…
Randomized neural networks for representation learning have consistently achieved prominent results in texture recognition tasks, effectively combining the advantages of both traditional techniques and learning-based approaches. However,…
Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…