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A Spectral Analysis of Function Composition and its Implications for Sampling in Direct Volume Visualization


In this paper we investigate the effects of function composition in the form g( f (x)) = h(x) by means of a spectral analysis of h. We decompose the spectral description of h(x) into a scalar product of the spectral description of g(x) and a term that solely depends on f(x) and that is independent of g(x). We then use the method of stationary phase to derive the essential maximum frequency of g(f(x)) bounding the main portion of the energy of its spectrum. This limit is the product of the maximum frequency of g(x) and the maximum derivative of f (x). This leads to a proper sampling of the composition h of the two functions g and f . We apply our theoretical results to a fundamental open problem in volume rendering?the proper sampling of the rendering integral after the application of a transfer function. In particular, we demonstrate how the sampling criterion can be incorporated in adaptive ray integration, visualization with multi-dimensional transfer functions, and pre-integrated volume rendering.

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Supplemental Material
Paper in Conference Proceedings or in Workshop Proceedings (Full Paper in Proceedings)
Event Title
IEEE Visualization (VIS) 2006
Visualization and Data Analysis
Event Location
Baltimore, Maryland
Event Type
Event Dates
Oct 29 - Nov 3
October 2006
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