An algorithm for multidimensional nonlinear registration is proposed. The deformation field between two elastic bodies is represented by a multi-resolution separable wavelet. Using a progressive approach that reduces algorithm complexity the registration parameters are recovered in a coarse to fine order. A custom wavelet that approximates threefold orthogonality is developed. The performance of the algorithm is evaluated by the alignment of sections from mouse brains. The wavelet registration algorithm demonstrated on average fourfold improvement in section alignment over linear alignment.
A significant problem in 3D reconstruction of biological tissue from histological material is alignment of the individual sections. We are developing a method to determine the surface of the tissue prior to cryosectioning and then utilize that information to guide registration. Toward that end, we have developed a structured light techniuqe for imaging frozen rat brains. The imaging approach relies on a novel coding scheme for the projected light which is based on 2D perfect submaps. Perhaps submaps are r by v c-ary arrays in which every n by m c-ary submatrix is unique. This coding scheme offers two major advantages over previous structured light patterns critical in the present application. It permits rapid image capture and, because each subwindow is unique, is robust in the presence of partial occlusion. To examine the accuracy of this technique, we compare the points mapped using it to the surface produced by block-face imaging. In the later approach, the tissue block is imaged prior to collecting each of the tissue sections. Since the block can be accurately repositioned after each cutting stroke, reconstruction of the surface from the block-face images is straightforward.