Two-dimensional generalisations of dynamic programming for image analysis

Dynamic programming (DP) is a fast, elegant method for solving many one-dimensional optimisation problems but, unfortunately, most problems in image analysis, such as restoration and warping, are two-dimensional. We consider three generalisations of DP. The first is iterated dynamic programming (IDP), where DP is used to recursively solve each of a sequence of one-dimensional problems in turn, to find a local optimum. A second algorithm is an empirical, stochastic optimiser, which is implemented by adding progressively less noise to IDP. The final approach replaces DP by a more computationally intensive Forward-Backwards Gibbs Sampler, and uses a simulated annealing cooling schedule. Results are compared with existing pixel-by-pixel methods of iterated conditional modes (ICM) and simulated annealing to restore a synthetic aperture radar (SAR) image and are also used to warp a pulsed-field electrophoresis gel in order to align with a reference image. We find that IDP and its stochastic variant outperform the remaining algorithms.