We propose a supervised approach to the classification and segmentation of material regions in hyperspectral imagery. Our algorithm is a two-stage process, combining a pixelwise classification step with a segmentation step aiming to minimise the total perimeters of the resulting regions. Our algorithm is distinctive in its ability to ensure label consistency within local homogeneous areas and to generate material segments with smooth boundaries. Furthermore, we establish a new hyperspectral benchmark dataset to demonstrate the advantages of the proposed approach over several state-of-the-art methods.