Gaussian mean-shift (GMS) is a clustering algorithm that has been shown to produce good image segmentations (where each pixel is represented as a feature vector with spatial and range components). GMS operates by defining a Gaussian kernel density estimate for the data and clustering together points that converge to the same mode under a fixed-point iterative scheme. However, the algorithm is slow, since its complexity is O(kN2), where N is the number of pixels and k the average number of iterations per pixel. We study four acceleration strategies for GMS based on the spatial structure of images and on the fact that GMS is an expectation-maximisation (EM) algorithm: spatial discretisation, spatial neighbourhood, sparse EM and EM-Newton algorithm. We show that the spatial discretisation strategy can accelerate GMS by one to two orders of magnitude while achieving essentially the same segmentation; and that the other strategies attain speedups of less than an order of magnitude.