Multidimensional biomedical image representation using a linear hypertree

Biomedical structures such as the beating heart are inherently multi-dimensional in nature. In addition to the three spatial directions which represent the object location and orientation, higher order dimensions can be assigned to represent various object parameters such as time and tissue density. In this paper, we propose a hierarchical data structure which can be mapped into a computer architecture that will efficiently store, manipulate, and display time varying images of multi-dimensional biomedical structures. This n-D object representation scheme which is called a linear hypertree is a generalization of the linear quadtree and octree from their respective 2-D and 3-D spaces to n-D environment. It is a hierarchical data structure which represents multi-dimensional volumetric information in a 2'-way branching tree. The basic properties of a linear hypertree are briefly presented along with the procedure for encoding the node rectangular coordinates into a hierarchical locational code. Two decoding techniques that transform the node locational code into its rectangular coordinate format are introduced. Some adjacency concepts in a multi-dimensional environment are defined. A neighbor finding algorithm which identifies the locational code of the adjacent hypertree node in a given direction is also presented. This algorithm does not convert the locational code to its rectangular coordinate form; instead, it operates directly on the node locational code in order to determine the neighbor's identification. Finally, Procedures for computing the locational codes of larger and smaller size neighbors are also included.