Continuous Regression

Welcome to the Continuous Regression framework site!

This site intends to gather all work done up to date about Continuous Regression. Continuous Regression brings a Functional Regression framework to the imaging domain, by solving the typically-used Least-Squares problem over a continuous set of target dimensions. It was first sparked by Fernando De la Torre, with whom I brought the Levin and Sashua [ECCV2002] framework to present the Continuous Regression over i.i.d. non-rigid shape parameters. Our work was successfully presented at ECCV2012.

However, a single FR extension was assuming that a uniform distribution was being used. One may argue that, as long as all infinite samples are being taken, the way they’re taken is not a big deal. However, such assumption implies that the space of target variables is uncorrelated. This means that discrete sampling would have been done by assuming that target dimensions are i.i.d., which is not always the case.

In order to overcome such problem, I proposed a fully mathematical derivation, that includes a data term, which accounts for how samples are supposed to be taken. This term helps correlate the target dimensions. This way, and thanks to the great help of Brais Martinez, Yorgos Tzimiropoulos, and Michel Valstar, we could bring a real-time incremental face tracking algorithm, built completely upon a novel framework for Continuous Regression!