Superpixel decomposition methods are generally used as a pre-processing step to speed up image processing tasks. They group the pixels of an image into homogeneous regions while trying to respect existing contours. For all state-of-the-art superpixel decomposition methods, a trade-off is made between 1) computational time, 2) adherence to image contours and 3) regularity and compactness of the decomposition. In this paper, we propose a fast method to compute Superpixels with Contour Adherence using Linear Path (SCALP) in an iterative clustering framework. The distance computed when trying to associate a pixel to a superpixel during the clustering is enhanced by considering the linear path to the superpixel barycenter. The proposed framework produces regular and compact superpixels that adhere to the image contours. We provide a detailed evaluation of SCALP on the standard Berkeley Segmentation Dataset. The obtained results outperform state-of-the-art methods in terms of standard superpixel and contour detection metrics.