Fast LIC with Piecewise Polynomial Filter Kernels

Line integral convolution (LIC) has become a well-known and popular method for visualizing vector elds. The method works by convolving a random input texture along the integral curves of the vector eld. In order to accelerate image synthesis signiicantly, an eecient algorithm has been proposed that utilizes pixel coherence in eld line direction. This algorithm, called \fast LIC", originally was restricted to simple box-type lter kernels. Here we describe a generalization of fast LIC for piecewise polynomial lter kernels. Expanding the lter kernels in terms of truncated power functions allows us to exploit a certain convolution theorem. The convolution integral is expressed as a linear combination of repeated integrals (or repeated sums in the discrete case). Compared to the original algorithm the additional expense for using higher order lter kernels, e.g. of B-spline type, is very low. Such lter kernels produce smoother, less noisier results than a box lter. This is evident from visual investigation, as well as from analysis of pixel correlations. Thus, our method represents a useful extension of the fast LIC algorithm for the creation of high-quality LIC images.