Fundamental relationship between bilateral Kernel and locally adaptive regression Kernel

The relationship between the bilateral kernel function and the recently proposed locally adaptive regression kernel is examined. Despite the difference in implementation, both locally adaptive approaches are designed to prevent averaging across edges while smoothing an image. Their similarity suggests that they can reasonably be linked although both filtering approaches have grown to become well-established theories in their fields. First, the locally adaptive regression kernel is analysed theoretically. Then, the connection between the methods is explored by applying the spectral distance measure to the bilateral kernel. Finally, a direct relation is established between the bilateral kernel and the locally adaptive regression kernel.