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We consider the problem of computing persistent homology (PH) for large-scale Euclidean point cloud data, aimed at downstream machine learning tasks, where the exponential growth of the most widely-used Vietoris-Rips complex imposes serious…
Vision Transformers (ViTs) have emerged as a fundamental architecture and serve as the backbone of modern vision-language models. Despite their impressive performance, ViTs exhibit notable vulnerability to evasion attacks, necessitating the…
Recent advancements in mobile and wireless networks are unlocking the full potential of robotic autonomy, enabling robots to take advantage of ultra-low latency, high data throughput, and ubiquitous connectivity. However, for robots to…
Summarising distributed data is a central routine for parallel programming, lying at the core of widely used frameworks such as the map/reduce paradigm. In the IoT context it is even more crucial, being a privileged mean to allow long-range…
Industrial multi-label document understanding pipelines score candidate labels and threshold or rank them to form a label set per document. This early selection step directly affects the accuracy of downstream information extraction from…
Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by…
This is an unabridged version of a journal manuscript that has been submitted for publication [1]. (Due to length restrictions, we were forced to remove substantial amounts of content from the version that was submitted to the journal,…
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such…
A new parallel computing framework has been developed to use with general-purpose radiation transport codes. The framework was implemented as a C++ module that uses MPI for message passing. The module is significantly independent of…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
When it comes to clinical images, automatic segmentation has a wide variety of applications and a considerable diversity of input domains, such as different types of Magnetic Resonance Images (MRIs) and Computerized Tomography (CT) scans.…
Modern microscopy routinely produces gigapixel images that contain structures across multiple spatial scales, from fine cellular morphology to broader tissue organization. Many analysis tasks require combining these scales, yet most vision…
Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…
Extracting informative features from images has been of capital importance in computer vision. In this paper, we propose a way to extract such features from images by a method based on algebraic topology. To that end, we construct a…
Compressed Sensing MRI (CS-MRI) aims at reconstructing de-aliased images from sub-Nyquist sampling k-space data to accelerate MR Imaging, thus presenting two basic issues, i.e., where to sample and how to reconstruct. To deal with both…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
Multimodal image matching is an important prerequisite for multisource image information fusion. Compared with the traditional matching problem, multimodal feature matching is more challenging due to the severe nonlinear radiation…
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…
Persistent homology is a relatively new tool often used for \emph{qualitative} analysis of intrinsic topological features in images and data originated from scientific and engineering applications. In this paper, we report novel…