GLoG: Laplacian of Gaussian for Spatial Pattern Detection in Spatio-Temporal Data

TL;DR

This paper introduces GLoG, a graph-based Laplacian of Gaussian filter for detecting spatial patterns in spatio-temporal data, aiding visual analysis of complex dynamic phenomena.

Contribution

It develops a novel graph signal processing filter inspired by image edge detection, enabling spatial pattern detection and entropy analysis in spatio-temporal datasets.

Findings

Effectively uncovers spatial patterns in synthetic and real data

Supports entropy-based analysis of temporal data slices

Enhances visual analytic tasks for spatio-temporal phenomena

Abstract

Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel boundary detection filter in the context of graphs, having as main application scenario the visual analysis of spatio-temporal data. More specifically, we propose the equivalent for graphs of the so-called Laplacian of Gaussian edge detection filter, which is widely used in image processing. The proposed filter is able to reveal interesting spatial patterns while still enabling the definition of entropy of time slices. The entropy reveals the degree of randomness of a time slice, helping users to identify expected and unexpected phenomena over time. The effectiveness of our approach appears in applications involving synthetic and real data sets, which show that the proposed methodology is able to uncover interesting spatial and temporal phenomena. The provided examples and case studies make clear the usefulness of our approach as a mechanism to support visual analytic tasks involving spatio-temporal data.