Accurate estimation of surface normals in 3-d data sets

Abstract

A CT scanner or other medical diagnostic imager (A) generates data which is reconstructed (B) into a three-dimensional image representation that is stored in an image memory (C). Points on a surface (10) of a selected subregion, such as the surface of an internal organ, in the three-dimensional image representation are determined (12) which are visible from and correspond to pixels on a viewing plane (14). For each viewable point on the surface, a mean variation along an x, y, and z-coordinate system with its origin at the surface point in question is determined (20). A covariance matrix whose matrix elements along the diagonal are indicative of a rate of variance along each axis and whose other matrix values are indicative of a rate of variance relative to pairs of axes is defined (20). A rate of most rapid change through the 3D data is determined (22), by eigenvalue decomposition (24) of the covariance matrix. A vector along the rate of most rapid change is normalized (26). Gray scale shading for a pixel of a man-readable display (E) corresponding to the surface point is determined (28). In the preferred embodiment, the gray scale shading is proportional to the cosine of the angle between the normalized vector in a direction of most rapid gray scale change and a light source vector. In this manner, the surface normal to a surface at the points which correspond to each pixel of an image display are efficiently determined and provided with an appropriate gray scale value to make the two-dimensional image display appear as if it were three-dimensional.