Distance Transform Based Surface Registration

A modification of the head-and-hat algorithm pre-computes a distance transform of the source image surface. A distance transform is applied to a binary image in which voxels inside an object have the value 1 and voxels outside an object have the value 0. The distance transform labels each voxel in the image with its distance from the surface. Computation of the transform proceeds by taking a starting estimate of the transformation and looking up the distance from the surface in the distance transform image for each surface point in the target image. The cost of this transformation is computed as the sum of squares of these distances. A process of optimization is used to find the transformation that minimizes this cost. The chamfer filter defined by Borgefors [29] is widely used and efficient and has been successfully used in image registration applications [30-32]. More recently exact distance transforms have been used in place of the chamfer transform [33]. Surface-based registration is prone to finding local minima during the optimization process and presenting these as the solution rather than the true global optimum. The physical analogy is that small features on the surface "lock together" at the incorrect registration. To partially alleviate the risk of this occurring, multiscale representations have been used [30].

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