Related papers: A Distributed Approach for Persistent Homology Com…
The parallel and distributed processing are becoming de facto industry standard, and a large part of the current research is targeted on how to make computing scalable and distributed, dynamically, without allocating the resources on…
Recent applications in computer vision have come to heavily rely on superpixel over-segmentation as a pre-processing step for higher level vision tasks, such as object recognition, image labelling or image segmentation. Here we present a…
Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…
Recently, some hypergraph-based methods have been proposed to deal with the problem of model fitting in computer vision, mainly due to the superior capability of hypergraph to represent the complex relationship between data points. However,…
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…
The Persistent Homology Transform (PHT) summarizes a shape in $\mathbb{R}^m$ by collecting persistence diagrams obtained from linear height filtrations in all directions on $\mathbb{S}^{m-1}$. It enjoys strong theoretical guarantees,…
Sparse coding of images is traditionally done by cutting them into small patches and representing each patch individually over some dictionary given a pre-determined number of nonzero coefficients to use for each patch. In lack of a way to…
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…
The hierarchical distribution matching (Hi-DM) approach for probabilistic shaping is described. The potential of Hi-DM in terms of trade-off between performance,complexity, and memory is illustrated through three case studies.
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…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or…
This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…
Holographic representations of data enable distributed storage with progressive refinement when the stored packets of data are made available in any arbitrary order. In this paper, we propose and test patch-based transform coding…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
We seek to accelerate and increase the size of simulations for fluid-structure interactions (FSI) by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two-way…
With the growth of image on the web, research on hashing which enables high-speed image retrieval has been actively studied. In recent years, various hashing methods based on deep neural networks have been proposed and achieved higher…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
We introduce a novel matching algorithm, called DeepMatching, to compute dense correspondences between images. DeepMatching relies on a hierarchical, multi-layer, correlational architecture designed for matching images and was inspired by…
Persistent homology is a crucial invariant that is used in many areas to understand data. The $O(N^4)$ run time is a hindrance to its use on most large datasets. We give a parallelization method to utilize multi-core machines and clusters.…