Low-complexity maximum intensity projection

Abstract

Many techniques have already been proposed to improve the efficiency of maximum intensity projection (MIP) volume rendering, but none of them considered the possible hypothesis of a better complexity than either O( n ) for finding the maximum value of n samples along a ray or O( n 3 ) for an object-order algorithm. Here, we fully model and analyze the use of octrees for MIP, and we mathematically show that the average MIP complexity can be reduced to O( n 2 ) for an object-order algorithm, or to O(log( n )) per ray when using the image-order variant of our algorithm. Therefore, this improvement establishes a major advance for interactive MIP visualization of large-volume data.In parallel, we also present an object-order implementation of our algorithm, satisfying the theoretical O( n 2 ) result. It is based on hierarchical occlusion maps that perform on-the-fly visibility of the data, and our results show that it is the most efficient solution for MIP available to date.