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Deformable registration is needed for a variety of tasks in establishing the voxel correspondence between respiratory phases. Most registration algorithms assume or imply that the deformation field is smooth and continuous everywhere. However, the lungs are contained within closed invaginated sacs called pleurae and are allowed to slide almost independently along the chest wall. This sliding motion is characterized by a discontinuous vector field, which cannot be generated using standard deformable registration methods. The authors have developed a registration method that can create discontinuous vector fields at the boundaries of anatomical subregions. Registration is performed independently on each subregion, with a boundary-matching penalty used to prevent gaps. This method was implemented and tested using both the B-spline and Demons registration algorithms in the Insight Segmentation and Registration Toolkit. The authors have validated this method on four patient 4DCT data sets for registration of the end-inhalation and end-exhalation volumes. Multiple experts identified homologous points in the lungs and along the ribs in the two respiratory phases. Statistical analyses of the mismatch of the homologous points before and after registration demonstrated improved overall accuracy for both algorithms.

SUMMARYThe accurate reconstruction of three-dimensional (3D) boundary surfaces from two-dimensional (2D) medical images is a crucial procedure in most applications of computational biomedical engineering. This paper addresses an innovative system that e ciently reconstructs accurate, multiple-material, 3D surface meshes from 2D medical images. It is based on an enhanced marching cubes algorithm, the multi-material marching cubes algorithm (M3C), which extracts boundary surfaces between di erent materials within one sweep of the image stack in an integrated manner. The continuity and integrity of the surfaces are ensured with this robust algorithm. Surface adjustment algorithms were also revised to adapt to the multiple-material nature of the system.