An algorithm for efficient determination of the 3D coordinates for a spatial point selected on a 2D surface-rendered image

In 3-dimension (3D) reformatting of multi-slice 2 dimensional (2D) images, algorithms such as the marching cubes or its variants can be used to form surface triplets of a specified region of the anatomy. The reformatted image can then be displayed in 3D on a computer screen. For certain clinical applications, it is necessary to measure the distance between two points selected with a mouse on the screen, and to determine the geometrical angle between two lines formed by three spatial points in the 3D image. In this paper, we present an algorithm that enables these desired operations by computing the 3D coordinate of a point on a surface-rendered image and selected with a mouse on the screen. Further, we describe and analyze some technical factors that affect the computational process of the algorithm.