Several algorithms in image processing involve spatio-range filtering of images and high-dimensional data derived from them. The exact computation of these so-called high-dimensional filters is challenging, especially for real-time processing of high-resolution images. In this paper, a simple yet accurate approximation of high-dimensional filters is obtained using a mix of clustering and fast convolutions. The resulting algorithm is competitive with state-of-the-art methods and importantly comes with guaranteed error bounds. The algorithm will be discussed in short in this presentation. To emphasise the practical speed-up obtained using our fast algorithm, a demo will be presented at the end.