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

Applying image processing algorithms independently to each frame of a video often leads to undesired inconsistent results over time. Developing temporally consistent video-based extensions, however, requires domain knowledge for individual…

This paper develops a framework for conceptualizing, visualizing, and measuring regularities in rhythmic data. I propose to think about rhythmic data in terms of interval segments: fixed-length groups of consecutive intervals, which can be…

Unpaired video-to-video translation aims to translate videos between a source and a target domain without the need of paired training data, making it more feasible for real applications. Unfortunately, the translated videos generally suffer…

Objective: Breathing pattern variability (BPV), as a universal physiological feature, encodes rich health information. We aim to show that, a high-quality automatic sleep stage scoring based on a proper quantification of BPV extracting from…

We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic manifolds which are as aperiodic as…

In this work, we investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces, namely arrays of mechanical oscillators arranged over the free surface of an elastic half-space according to a…

In this paper, we propose Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data by integrating multiparameter persistence and zigzag persistence. To this end, we introduce a stable topological invariant that…

In this paper, we propose a method that learns a general representation of periodic signals from unlabeled facial videos by capturing subtle changes in skin tone over time. The proposed framework employs the video masked autoencoder to…

For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…

We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that…

We employ a typical genetic circuit model to explore how noise can influence the dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure…

Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…

In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of…

We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data.…

The goal of video segmentation is to turn video data into a set of concrete motion clusters that can be easily interpreted as building blocks of the video. There are some works on similar topics like detecting scene cuts in a video, but…

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…

Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…

Detecting salient objects from a video requires exploiting both spatial and temporal knowledge included in the video. We propose a novel region-based multiscale spatiotemporal saliency detection method for videos, where static features and…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

Video generation has many unique challenges beyond those of image generation. The temporal dimension introduces extensive possible variations across frames, over which consistency and continuity may be violated. In this study, we move…