Factor Analysis (FA) is a well established method for factors separation in analysis of dynamic medical imaging. However, its assumptions are valid only in limited regions of interest (ROI) in the images which must be selected manually or using heuristics. The resulting quality of separation is sensitive to the choice of these ROI. We propose a new probabilistic model for functional analysis with inherent estimation of probabilistic ROI. The model is solved using the Variational Bayes method which provides also automatic relevance determination of the estimated factors. Performance of the method is demonstrated on data from renal scintigraphy, where a significant improvement is achieved. Since there are no scintigraphy-related assumptions, the method can be used in any other imaging modality.