Box Splines for Image Edge Detection

With bivariate box splines, we can construct tight wavelet frames. See paper by Lai and Stoeckler for a detailed construction method. Dr. Kyunglim Nam has implemented this constructive method in MATLAB for several box spline functions. We use these programs to obtain the edges of images by decomposing an image into low frequencies (box spline functions) and high frequencies (wavelet frames) and reconstructing the image by using zero for low frequencies. Choose an appropriate threshold to divide the reconstructed image into two values, either 0 or 1. The resulting image contains only the edges of the image. It is simple and elegant. The following are examples of images (left) and "edges"(right) based on box spline tight wavelet frames.