Anisotropic 3-D Distance Transform Based on Contour Propagation

Anisotropic three dimensional (3-D) Euclidean distance transform (EDT) has important applications in medical image processing, but few algorithms have been reported so far. An anisotropic 3-D EDT algorithm is designed and realized based on Eggers´s 2-D algorithm. The characteristic of the algorithm is that all voxels in the propagation contour have the same chessboard distance from the feature voxels. The voxels in the surface of the feature voxel set constitute the initial propagation contour. The voxels in the contour propagate the distance information to the neighbors in special directions, which constitute the new propagation contour. The voxels in the contour are classified into three types, and propagate to seven, three, and one neighbors respectively. The proposed algorithm can generate exact signed and unsigned EDT. The validity of the algorithm is proved theoretically. The speed and efficiency of the algorithm is evaluated, and compared to other algorithm. Methods to reduce the memory requirements are discussed.