A variational method for the classification, segmentation and denoising of a time series field

Applied and Computational Mathematics Seminar
Monday, March 30, 2009 - 13:00
1 hour (actually 50 minutes)
Skiles 255
Istituto per le Applicazioni del Calcolo "Mauro Picone" of C.N.R.
We consider ordered sequences of digital images. At a given pixel a time course is observed which is related to the time courses at neighbour pixels. Useful information can be extracted from a set of such observations by classifying pixels in groups, according to some features of interest. We assume to observe a noisy version of a positive function depending on space and time, which is parameterized by a vector of unknown functions (depending on space) with discontinuities which separate regions with different features in the image domain. We propose a variational method which allows to estimate the parameter functions, to segment the image domain in regions, and to assign to each region a label according to the values that the parameters assume on the region. Approximation by \Gamma-convergence is used to design a numerical scheme. Numerical results are reported for a dynamic Magnetic Resonance imaging problem.