An Incremental Method for Computing the Intersection of Discretely Sampled m-Dimensional Images with n-Dimensional Boundaries

This paper describes an algorithm for clipping of m-dimensional objects that intersect a compact n-dimensional rectangular area. The new algorithm is an extension of a method for line clipping in three dimensions. Motivated by the need for efficient algorithms for example when comparing three-dimensional (3-D) images to each other, our method allows for the incremental computation of the subset of voxels in a discretely sampled image which are located inside a second image. Limited fields of view (rectangular regions of interest) in either image are easily supported. Application of our algorithm does not require the generation of an explicit geometrical description of the image intersection. Besides its generality with respect to the dimensions of the objects under consideration, our clipping method solves the problem of discriminating between points inside the clipping region and points on its edge, which is important when problems such as voxel intensity interpolation are only well-defined within the clipping area.