Deformable Image Registration via Multi-Scale Markov Fields

The patent segments the deformation field into discrete labels representing different deformation states. By formulating the problem as a discrete optimization task where each voxel is assigned one of a finite set of labels, the method can capture discontinuities while avoiding the combinatorial explosion of fully continuous approaches. The segmentation is achieved through defining a label set that includes both smooth deformation labels and discontinuity labels.

The patent changes the parameter representation from continuous deformation vectors to discrete labels. This parameter transformation allows the use of discrete optimization techniques that can efficiently handle the labeling problem. The energy function is designed to work with these discrete parameters, using regularization terms that encourage smoothness while allowing discontinuities where the data strongly indicates them.

The patent substitutes the continuous mechanical deformation model with a discrete labeling model. Instead of solving differential equations or using iterative optimization on continuous fields, the method uses discrete optimization with an energy function that can be minimized using graph-cut or dynamic programming algorithms. This substitution maintains computational efficiency while enabling accurate capture of discontinuities through the discrete label structure.

The patent introduces dynamics by allowing the deformation model to adapt locally - being smooth in some regions and discontinuous in others. The energy function includes data fidelity terms that drive the solution toward discontinuities where the image data indicates sharp changes, while regularization terms maintain smoothness elsewhere. This dynamic adaptation allows the model to automatically adjust its behavior based on local image characteristics.