Surface alignment of an elastic body using a multiresolution wavelet representation

An algorithm for nonlinear registration of an elastic body is developed. Surfaces (outlines) of known anatomic structures are used to align all other (internal) points. The deformation field is represented with a multiresolution wavelet expansion and is modeled by the partial differential equations of linear elasticity. A hierarchical approach that reduces algorithm complexity is adopted. The performance of the algorithm is evaluated by two-dimensional alignment of sections from mouse brains located in the olfactory bulbs. The registration algorithm was guided by manually delineated contours of a subset of brain structures and validated based on another subset of brain structures. The wavelet alignment algorithm produced a twofold to fivefold improvement in accuracy over an affine (linear) alignment algorithm.