Dense deformation reconstruction via sparse coding

Many image registration algorithms need to interpolate dense deformations from a small set of sparse deformations or correspondences established on the landmark points. Previous methods generally use a certain pre-defined deformation model, e.g., B-Spline or Thin-Plate Spline, for dense deformation interpolation, which may affect the final registration accuracy since the actual deformation may not exactly follow the pre-defined model. To address this issue, we propose a novel leaning-based method to represent the to-be-estimated dense deformations as a linear combination of sample dense deformations in the pre-constructed dictionary, with the combination coefficients computed from sparse representation of their respective correspondences on the same set of landmarks. Specifically, in the training stage, for each training image, we register it to the selected template by a certain registration method and obtain correspondences on a fixed set of landmarks in the template, as well as the respective dense deformation field. Then, we can build two dictionaries to, respectively, save the landmark correspondences and their dense deformations from all training images at the same indexing order. Thus, in the application stage, after estimating the landmark correspondences for a new subject, we can first represent them by all instances in the dictionary of landmark correspondences. Then, the estimated sparse coefficients can be used to reconstruct the dense deformation field of the new subject by fusing the corresponding instances in the dictionary of dense deformations. We have demonstrated the advantage of our proposed deformation interpolation method in two applications, i.e., CT prostate registration in the radiotherapy and MR brain registration in the neuroscience study. In both applications, our learning-based method can achieve higher accuracy and potentially faster computation, compared to the conventional method.