Volume rendering with least squares spline reconstruction

This paper presents a volume rendering procedure with embedded least square spline reconstruction. The first part of this paper describes a technique for the continuous representation of discrete signals by using B-splines. Volume element space is an example of the discrete signal which can be continuously represented in terms of the B-spline. Volume rendering is a very time-consuming procedure and therefore we down-sample the initial size of the volume. Before the down-sampling, some low-pass prefiltering is required. Our prefilter design is based on considering the combined operation of the prefiltering and the reconstruction postfiltering. The second part of this paper deals with embedding of the least square spline filter into the volume rendering procedure. The position of the reconstruction point is arbitrary in the volume element space. Reconstruction of the normal vector required for shading could be easily derived from the continuous reconstruction function.