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An Extension of Fourier-Wavelet Volume Rendering by View Interpolation

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Abstract

This paper describes an extension to Fourier-wavelet volume rendering (FWVR), which is a Fourier domain implementation of the wavelet X-ray transform. This transform combines integration along the line of sight with a simultaneous 2-D wavelet transform in the view plane perpendicular to this line. During user interaction, only low resolution images are computed based on wavelet approximation coefficients. When user interaction ceases, the images are refined incrementally with the wavelet detail coefficients. The extension proposed in this paper is similar to a technique called view interpolation, which originates from the field of computer graphics. View interpolation is used to speed up rendering of complex scenes by precomputing images from a number of selected viewpoints. For intermediate viewpoints, rendering is performed by interpolating the precomputed images. In this paper, we show that for FWVR the speed of rendering low resolution images is increased by interpolation of precomputed sets of wavelet approximation coefficients in the Fourier domain. The differences with traditional view interpolation are that (i) interpolation is performed on the wavelet approximation coefficients in the Fourier domain and not on images, and (ii) interpolation is performed during user interaction only. When interaction ceases, ordinary FWVR progressively renders an image at high quality. Medical CT data are used to assess the accuracy and performance of the method. We use regular angular sampling of spherical coordinates which determine the viewing direction. The results show that angle increments as large as 10 degrees result in only a small degradation of image quality.

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Authors and Affiliations

  1. Institute for Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    Michel A. Westenberg & Jos B.T.M. Roerdink

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  1. Michel A. Westenberg
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  2. Jos B.T.M. Roerdink
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Westenberg, M.A., Roerdink, J.B. An Extension of Fourier-Wavelet Volume Rendering by View Interpolation. Journal of Mathematical Imaging and Vision 14, 103–115 (2001). https://doi.org/10.1023/A:1011255130846

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