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The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…

Many works in the recent literature introduce semantic mapping methods that use CNNs (Convolutional Neural Networks) to recognize semantic properties in images. The types of properties (eg.: room size, place category, and objects) and their…

In the literature, it has been shown that the evolution of the known explicit 3D surface to the target one can be learned from 2D images using the instantaneous flow field, where the known and target 3D surfaces may largely differ in…

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…

Deep generative models have emerged as a powerful tool for learning useful molecular representations and designing novel molecules with desired properties, with applications in drug discovery and material design. However, most existing deep…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

Enhancement is an important step in post-processing digital images for personal use, in medical imaging, and for object recognition. Most existing manual techniques rely on region selection, similarity, and/or thresholding for editing,…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

Face is one of the most important things for communication with the world around us. It also forms our identity and expressions. Estimating the face structure is a fundamental task in computer vision with applications in different areas…

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…