Time-resolved medical data has important applications in a large variety of medical applications. In this paper we study automatic analysis of dynamical renal scintigraphies. The traditional analysis pipeline for dynamical renal scintigraphies is to use manual or semiautomatic methods for segmentation of pixels into physical compartments, extract their corresponding time-activity curves and then compute the parameters that are relevant for medical assessment. In this paper we present a fully automatic system that incorporates spatial smoothing constraints, compartment modelling and positivity constraints to produce an interpretation of the full time-resolved data. The method has been tested on renal dynamical scintigraphies with promising results. It is shown that the method indeed produces more compact representations, while keeping the residual of fit low. The parameters of the time activity curve, such as peak-time and time for half activity from peak, are compared between the previous semiautomatic method and the method presented in this paper. It is also shown how to obtain new and clinically relevant features using our novel system.