3D non-rigid registration by gradient descent on a Gaussian-windowed similarity measure using convolutions

Non-rigid registration of medical images is usually presented as a physical model driven by forces deriving from a measure of similarity of the images. These forces can be computed using a gradient-descent scheme for simple intensity-based similarity measures. However, for more complex similarity measures, using for instance local statistics, the forces are usually found using a block matching scheme. Here, the authors introduce a Gaussian window scheme, where the local statistics (here the sum of local correlation coefficients) are weighted with Gaussian kernels. The authors show that the criterion can be deducted easily to obtain forces to guide the registration. Moreover, these forces can be computed very efficiently by global convolutions inside the real image of the Gaussian window in a time independent of the size of the Gaussian window. The authors also present two minimization strategies by gradient descent to optimize the similarity measure: a linear search and a Gauss-Newton-like scheme. Experiments on synthetic and real 3D data show that the sum of local correlation coefficients optimized using a Gauss-Newton scheme is a fast and accurate method to register images corrupted by a non-uniform bias.