Efficient normal estimation using variable-size operator

Shading an object is to simulate the behaviour of light incident on its sur faces. It is necessary to calculate normal vectors on the surfaces of the o bject for shading it. Since objects do not contain surface inclination in v oxel-based representation, a normal vector for each voxel must be estimated from the relative position of its neighbouring voxels that have the same d ata value. The previously devised methods that use fixed-size gradient oper ators can estimate normal vectors accurately only in a limited area and may cause some errors and artefacts. In this paper we propose an efficient nor mal estimation method using an extended central difference operator whose s ize can vary according to the arrangement of surface-comprising voxels. Thi s method calculates normals move accurately than the previous methods and i ts computation time is shorter than that of methods that guarantee the same image quality. In order to show the improvement, we compare the quality of resulting images and processing time by implementing the newly proposed me thod and the previous methods and then applying them to some volume data. C opyright (C) 1999 John Wiley & Sons, Ltd.