Unwrapping phase images by propagating probabilities across graphs

Phase images are derived from source images by applying a modulus operation to each pixel value. Phase unwrapping is the problem of inferring the original, unwrapped values from the wrapped values, using prior knowledge about the smoothness of the image. One approach to solving this problem is to infer the gradient vector field of the unwrapped image and then integrate the gradient field. The gradient in a particular direction at a pixel is equal to the observed pixel difference plus an unknown integer number of shifts. We introduce a technique for inferring these shifts using the low-complexity probability propagation algorithm, applied in a graphical model that prefers shifts that match the phase image and that constrains the shifts to satisfy the properties of a gradient field. We present results for a phase image from the region of the Sandia National Laboratories.