Related papers: (Quasi)Periodicity Quantification in Video Data, U…

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…

We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…

In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure, and their validity and comprehensibility remain elusive. The integration of topological methods, despite its relatively…

A function is called quasiperiodic if its fundamental frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window point clouds of such functions can be shown to be dense in tori with dimension…

Generic motion understanding from video involves not only tracking objects, but also perceiving how their surfaces deform and move. This information is useful to make inferences about 3D shape, physical properties and object interactions.…

Persistent homology, the study of holes that appear in data as one thickens balls centered around its points over time, has theoretically guaranteed stability. That is, small data perturbations guarantee small changes in the lifetimes of…

Action repetition counting is to estimate the occurrence times of the repetitive motion in one action, which is a relatively new, important but challenging measurement problem. To solve this problem, we propose a new method superior to the…

Periodic point sets model all solid crystalline materials (crystals) whose atoms can be considered zero-sized points with or without atomic types. This paper addresses the fundamental problem of checking whether claimed crystals are novel,…

We present a new test-time optimization method for estimating dense and long-range motion from a video sequence. Prior optical flow or particle video tracking algorithms typically operate within limited temporal windows, struggling to track…

Despite the recent success of neural networks in image feature learning, a major problem in the video domain is the lack of sufficient labeled data for learning to model temporal information. In this paper, we propose an unsupervised…

Generating geometrically consistent videos remains an open challenge: text-to-video diffusion models trained on web-scale data treat geometry only implicitly, leading to object deformation, texture drift, and non-rigid backgrounds under…

Quantifying patterns in visual or tactile textures provides important information about the process or phenomena that generated these patterns. In manufacturing, these patterns can be intentionally introduced as a design feature, or they…

We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground…

Topological boundary and interface modes are generated in an acoustic waveguide by simple quasi-periodic patternings of the walls. The procedure opens many topological gaps in the resonant spectrum and qualitative as well as quantitative…

We consider a signal composed of several periods of a periodic function, of which we observe a noisy reparametrisation. The phase estimation problem consists of finding that reparametrisation, and, in particular, the number of observed…

Quasiperiodicity, a partially synchronous state that precedes the onset of forced synchronization in hydrodynamic systems, exhibits distinct geometrical patterns based on the specific route to lock-in. In this study, we explore these…

We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…

This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…

We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…