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High-Quality Wavelet Splatting for Volume Rendering

S. Horbelt, M. Vetterli, M. Unser

Wavelet Applications Workshop, Monte Verità TI, Swiss Confederation, September 28-October 2, 1998.



We extended Gross's et al. [1, 2] method of volume wavelet rendering by computing splats via least-squares approximation. The method decomposes the volume data into a wavelet pyramid representation in the B-spline domain. The splats of the basis functions are projected onto a multiresolution grid. The approximation error on the grid is derived, applying [3, 4], as a function of the sampling step h. Choosing at each step the appropriate wavelet space and spatial resolution produces the smallest possible filters and reduces computation. Our approach ensures a maximal image quality when rendering at low resolution.

References

  1. M.H. Gross, L. Lippert, R. Dittrich, S. Häring, "Two Methods for Wavelet-Based Volume Rendering," Computer & Graphics, vol. 21, no. 2, pp. 237-252, March/April 1997.

  2. R. Westermann, "A Multiresolution Framework for Volume Rendering," Proceedings of the 1994 ACM Symposium on Volume Visualization, Washington DC, USA, October 17-18, 1994, pp. 51-58.

  3. T. Blu, M. Unser, "Quantitative Fourier Analysis of Approximation Techniques: Part I—Interpolators and Projectors," IEEE Transactions on Signal Processing, vol. 47, no. 10, pp. 2783-2795, October 1999.

  4. T. Blu, M. Unser, "Quantitative Fourier Analysis of Approximation Techniques: Part II—Wavelets," IEEE Transactions on Signal Processing, vol. 47, no. 10, pp. 2796-2806, October 1999.


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