Antialiased Voxelization of Geometric Objects

In this technical report we analyze different filters used for the voxelization of analytically described objects. We show that, when the voxel model is used for visualization, the filter design is related to the subsequent rendering phase, namely the gradient estimation technique. Further, we introduce a new concept for alias-free voxelization of geometric objects based on a Voxelization model (V-model). The V-model of an object is its representation in three dimensional continuous space by a trivariate density function. This function is sampled during the voxelization and the resulting values are stored in a volume buffer. This concept enables us to study general issues of sampling and rendering separately from object specific design issues. It provides us with a possibility to design such V-models, which are correct from the point of view of both the sampling and rendering, thus leading to both alias-free volumetric representation and alias-free rendered images. We performed numerous experiments with different combinations of V-models and reconstruction techniques. We have shown that the V-model with a Gaussian surface density profile combined with tricubic interpolation and Gabor derivative reconstruction outperforms the previously published technique with a linear density profile. This enables higher fidelity of images rendered from volume data due to increased sharpness of edges and thinner surface patches. We describe the vxt library for filtered voxelization of objects, being developed at SUNY Stony Brook. It provides the user with an extensible set of easy-to-use tools and routines for alias-free voxelization of analytically defined monochromatic and color objects. Thus, resulting volumetric data represent a suitable input for both software and hardware volume rendering systems. The library provides for voxelization of primitive objects; however, when supplemented by a suitable parser, it represents a basis for voxelization of complex models defined in various graphics formats.