New method of three-dimensional Euclidean distance transform

Most existing algorithms of three-dimensional distance transform are extensions of two-dimensional approximate Euclidean distance transform algorithms of such as the city block/chessboard. Such algorithms can only get the approximate Euclidean distance. A new method of three-dimensional true Euclidean distance transform is presented in this paper. The proposed method can get the true Euclidean distance with time complexity O (n³·log n). Moreover, this method is used to render the soft tissue in three-dimensional medical CT images, and good result has been obtained.