Space-Time Signal Analysis and the 3D Shearlet Transform

Damiano Malafronte, Ernesto De Vito, Francesca Odone

Abstract: In this work, we address the problem of analyzing video sequences by representing meaningful local space–time neighborhoods. We propose a mathematical model to describe relevant points as local singularities of a 3D signal, and we show that these local patterns can be nicely highlighted by the 3D shearlet transform, which is at the root of our work. Based on this mathematical framework, we derive an algorithm to represent space–time points which is very effective in analyzing video sequences. In particular, we show how points of the same nature have a very similar representation, allowing us to compute different space–time primitives for a video sequence in an unsupervised way.