As mentioned in the paper, dimensionality reduction techniques could be used to find an approximate isometric transformation. However, such approximations lead to artifacts in the filtered image. For this example we used Laplacian Eigenmaps [Belkin and Niyogi 2003] to reduce the dimensionality of the color image in (a) from 5D to 2D. Notice how the red flower got clustered into the middle of the domain, and the background foliage got compressed to the sides. When filtering the dimensionality-reduced image with a 2D Gaussian kernel, as shown in (c), edges in the background are not correctly preserved, as in the case of the branch and foliage edges on the right of the image. Generating the dimensionality-reduced image shown in (b) took 25 minutes on a MATLAB implementation. Our approach takes 0.015 seconds to produce its result, shown in (d), and correctly handles all image edges. Finally, we note that approximate solutions for the transformation produce worse results for more complex images.