Efficient Normal Estimation Using Variable-size Operator

Shading an object is to simulate the behaviour of light incident on its surfaces. It is necessary to calculate normal vectors on the surfaces of the object for shading it. Since objects do not contain surface inclination in voxel-based representation, a normal vector for each voxel must be estimated from the relative position of its neighbouring voxels that have the same data value. The previously devised methods that use fixed-size gradient operators can estimate normal vectors accurately only in a limited area and may cause some errors and artefacts. In this paper we propose an efficient normal estimation method using an extended central difference operator whose size can vary according to the arrangement of surface-comprising voxels. This method calculates normals more accurately than the previous methods and its 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 method and the previous methods and then applying them to some volume data.