A penalized likelihood approach to image warping

A warping is a function that deforms images by mapping between image domain s. The choice of function is formulated statistically as maximum penalized likelihood, where the likelihood measures the similarity between images aft er warping and the penalty is a measure of distortion of a warping. The pap er addresses two issues simultaneously, of how to choose the warping functi on and how to assess the alignment. A new, Fourier-von Mises image model is identified, with phase differences between Fourier-transformed images havi ng von Mises distributions. Also, new, null set distortion criteria are pro posed, with each criterion uniquely minimized by a particular set of polyno mial functions. A conjugate gradient algorithm is used to estimate the warp ing function, which is numerically approximated by a piecewise bilinear fun ction. The method is motivated by, and used to solve, three applied problem s: to register a remotely sensed image with a map, to align microscope imag es obtained by using different optics and to discriminate between species o f fish from photographic images.