A computer-controlled procedure is outlined here that first determines the position of the amorphous-crystalline interface in an image. Subsequently, from a time series of these images, the velocity of the crystal growth front is quantified. The procedure presented here can be useful for a wide range of applications, and we apply the new approach to determine growth rates in a so-called fast-growth-type phase-change material. The growth rate (without nucleation) of this material is of interest for comparison with identical material used in phase-change random access memory cells. Crystal growth rates in the amorphous phase-change layers have been measured at various temperatures using in situ heating in a transmission electron microscope. Doped SbTe films (20 nm thick) were deposited on silicon nitride membranes, and samples with and without silicon oxide capping layer were studied. The activation energy for growth was found to be 3.0 eV. The samples without capping layer exhibit a nucleation rate that is an order of magnitude higher than the samples with a silicon oxide capping layer. This difference can be attributed to the partial oxidation of the phase-change layer in air. However, the growth rates of the samples with and without capping are quite comparable.