Related papers: Cubical Ripser: Software for computing persistent …
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
We give an $O(n^2(k+\log n))$ algorithm for computing the $k$-dimensional persistent homology of a filtration of clique complexes of cyclic graphs on $n$ vertices. This is nearly quadratic in the number of vertices $n$, and therefore a…
$N$-body simulation serves as a critical method for modeling cosmic evolution and poses a significant challenge in high-performance computing. We present CUBE2, an open-source cosmological $N$-body code emphasizing memory efficiency,…
The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the…
Human volumetric capture is a long-standing topic in computer vision and computer graphics. Although high-quality results can be achieved using sophisticated off-line systems, real-time human volumetric capture of complex scenarios,…
We provide a comprehensive review of classical algorithms for compressive sensing of images, focused on Total variation methods, with a view to application in LiDAR systems. Our primary focus is providing a full review for beginners in the…
Along with predictive performance and runtime speed, reliability is a key requirement for real-world semantic segmentation. Reliability encompasses robustness, predictive uncertainty and reduced bias. To improve reliability, we introduce…
A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (in our case, a simplicial complex). Modern packages for persistent homology often construct Vietoris--Rips or other…
We have developed a method for the linear reconstruction of an image from undersampled, dithered data, which has been used to create the distributed, combined Hubble Deep Field images -- the deepest optical images yet taken of the universe.…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…
Computed Tomographic Imaging Spectrometers (CTIS) capture hyperspectral images in realtime. However, post processing the imagery can require enormous computational resources; thus, limiting its application to non-realtime scenarios. To…
The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…
Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be…
Remote sensing (RS) images are usually stored in compressed format to reduce the storage size of the archives. Thus, existing content-based image retrieval (CBIR) systems in RS require decoding images before applying CBIR (which is…
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
Mesh plays an indispensable role in dense real-time reconstruction essential in robotics. Efforts have been made to maintain flexible data structures for 3D data fusion, yet an efficient incremental framework specifically designed for…