Using distance maps for accurate surface representation in sampled volumes

Figure 1: Shaded, volume rendered spheres stored with two values per voxel: a value indicating the distance to the closest surface point; and a binary intensity value. The sphere in a) has radius 30 voxels and is stored in an array of size. The spheres in b), c), and d) have radii 3 voxels, 2 voxels and 1.5 voxels respectively and are stored in arrays of size. The surface normal used in surface shading was calculated using a 6-point central difference operator on the distance values. Remarkably smooth shading can be achieved for these low resolution data volumes because the function of the distance-to-closest surface varies smoothly across surfaces. (See color plate.) High quality rendering and physics-based modeling in volume graphics have been limited because intensity-based volumetric data do not represent surfaces well. High spatial frequencies due to abrupt intensity changes at object surfaces result in jagged or terraced surfaces in rendered images. The use of a distance-to-closestsurface function to encode object surfaces is proposed. This function varies smoothly across surfaces and hence can be accurately reconstructed from sampled data. The zero-value iso-surface of the distance map yields the object surface and the derivative of the distance map yields the surface normal. Examples of rendered images are presented along with a new method for calculating distance maps from sampled binary data.