In this paper we present a new approach for curve clus- tering designed for analysis of spatiotemporal data. Such kind of data contains both spatial and temporal patterns that we desire to capture. The proposed methodology is based on regression and Gaussian mixture modeling and the novelty of the herein work is the incorporation of spa- tial smoothness constraints in the form of a prior for the data labels. This enables the proposed model to take into account the underlying property of spatiotemporal data that spatially adjacent data points most likely should belong to the same cluster. A maximum a posteriori Expectation Max- imization (MAP-EM) algorithm is used for learning this model. We present numerical experiments with simulated data where the ground truth is known in order to assess the value of the introduced smoothness constraint, and also with real cardiac perfusion MRI data. The results are very promising and demonstrate the value of the proposed con- straint for analysis of such data .