Related papers: Vertex characterization via second-order topologic…

Vortices and their analysis play a critical role in the understanding of complex phenomena in turbulent flows. Traditional vortex extraction methods, notably region-based techniques, often overlook the entanglement phenomenon, resulting in…

We introduce and study strongly vertex dismissible, vertex dismissible, and scalable simplicial complexes as non-pure extensions of vertex decomposability and shellability. Strong vertex dismissibility is defined recursively by relaxing the…

We introduce a proper notion of 2-dimensional signature for images. This object is inspired by the so-called rough paths theory, and it captures many essential features of a 2-dimensional object such as an image. It thus serves as a…

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…

Recent research on learnable neural representations has been widely adopted in the field of 3D scene reconstruction and neural rendering applications. However, traditional feature grid representations often suffer from substantial memory…

Subspace representation is a fundamental technique in various fields of machine learning. Analyzing a geometrical relationship among multiple subspaces is essential for understanding subspace series' temporal and/or spatial dynamics. This…

Treating images as data has become increasingly popular in political science. While existing classifiers for images reach high levels of accuracy, it is difficult to systematically assess the visual features on which they base their…

Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here we showcase…

Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features…

Image recognition is the need of the hour. In order to be able to recognize an image, it is of immense importance that the image should be distinguishable from the background. In the present work, an approach is presented for automatic…

This paper addresses how to construct features for the problem of image correspondence, in particular, the paper addresses how to construct features so as to maintain the right level of invariance versus discriminability. We show that…

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.

Over the past decade, the importance of the 1D signature which can be seen as a functional defined along a path, has been pivotal in both path-wise stochastic calculus and the analysis of time series data. By considering an image as a…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

This paper is devoted to study a characterization of (strong) local maximal monotonicity in terms of a property involving the graphical derivative of a set-valued mapping defined on a Hilbert space. As a consequence, a second-order…

Texture is a visual attribute largely used in many problems of image analysis. Currently, many methods that use learning techniques have been proposed for texture discrimination, achieving improved performance over previous handcrafted…

Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…

For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…

Fast and light-weight methods for animating 3D characters are desirable in various applications such as computer games. We present a learning-based approach to enhance skinning-based animations of 3D characters with vivid secondary motion…

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…