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Fast LIC with Higher Order Filter Kernels

Please always quote using this URN: urn:nbn:de:0297-zib-3439
  • Line integral convolution (LIC) has become a well-known and popular method for visualizing vector fields. The method works by convolving a random input texture along the integral curves of the vector field. In order to accelerate image synthesis significantly, an efficient algorithm has been proposed that utilizes pixel coherence in field line direction. This algorithm, called ``fast LIC'', originally was restricted to simple box-type filter kernels. Here we describe a generalization of fast LIC for piecewise polynomial filter kernels. Expanding the filter 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 filter kernels, e.g.\ of B-spline type, is very low. Such filter kernels produce smoother, less noisier results than a box filter. 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.

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Author:Hans-Christian HegeORCiDGND, Detlev Stalling
Document Type:ZIB-Report
Date of first Publication:1998/02/03
Series (Serial Number):ZIB-Report (SC-97-74)
Published in:A revised version appeared under the title: Fast LIC with Piecewise Polynomial Filter Kernels in: Mathematical Visualization - Algorithms, Applications, and Numerics. Hege, H.-C., Polthier, K. (eds.) Springer 1998, pp 295-312
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