FM filters for modulation domain image processing

For the first time, we demonstrate modulation domain image filters that achieve perceptually motivated image processing goals by directly manipulating the FM functions in a multi-component AM-FM image model. The action of previous modulation domain filters has been limited to modification of the AM functions based on the values of the AM and FM functions. This is because reconstruction of the modified phase from the filtered frequency modulation vectors was an unsolved problem. Here, we present two new algorithms capable of reconstructing the phase from the processed frequencies, one based on a least squares solution of the discrete Poisson equation with Neumann boundary condition and one based on cubic tensor product spline integration. New modulation domain FM filters are designed to modify both the orientations and magnitudes of the visually important emergent image frequency vectors. In our most dramatic example, we demonstrate an FM filter that autonomously changes the stripes on the pants in the well known Barbara image from vertical to horizontal.