  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.
