Self-similarity weighted mutual information: a new nonrigid image registration metric.

Mutual information (MI) has been widely used as a similarity measure for rigid registration of multi-modal and uni-modal medical images. However, robust application of MI to deformable registration is challenging mainly because rich structural information, which are critical cues for successful deformable registration, are not incorporated into MI. We propose a self-similarity weighted graph-based implementation of α-mutual information (α-MI) for nonrigid image registration. We use a self-similarity measure that uses local structural information and is invariant to rotation and to local affine intensity distortions, and therefore the new Self Similarity α-MI (SeSaMI) metric inherits these properties and is robust against signal nonstationarity and intensity distortions. We have used SeSaMI as the similarity measure in a regularized cost function with B-spline deformation field to achieve nonrigid registration. Since the gradient of SeSaMI can be derived analytically, the cost function can be efficiently optimized using stochastic gradient descent methods. We show that SeSaMI produces a robust and smooth cost function and outperforms the state of the art statistical based similarity metrics in simulation and using data from image-guided neurosurgery.