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5 August 2004 Frequency space techniques for BRDF shading
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The Bi-directional Reflectance Distribution Function (BRDF) is a general way to represent reflection from surfaces. However, even when ignoring variations in location and wavelength, the BRDF is still a 4-dimensional function and the number of BRDF samples necessary for direct utilization can impose severe computational requirements. To address these and other problems, analytical BRDF equations have been developed for computer image simulations. Limitations remain since they may be empirical, appropriate only for specific surfaces, or require difficult-to-obtain physical parameters. BRDF shading based on signal processing methods has recently been presented in computer graphics that projects any BRDF onto an orthogonal basis set and then employs a truncated linear series for shading with controlled accuracy. This paper presents an overview of BRDF shading and frequency-space representations using orthogonal polynomials as basis functions. Techniques are then described that utilize the resulting linear shading equations to factor lighting and geometry components of a scene for image-based re-lighting. Statistical properties of images may then be partially computed for fixed views in a pre-process phase and employed to rapidly compute view properties for arbitrary lighting distributions and different BRDFs. Techniques are also described for producing correct blended BRDFS aimed at level-of-detail frequency-space shading.
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Randy K. Scoggins and Raghu Machiraju "Frequency space techniques for BRDF shading", Proc. SPIE 5431, Targets and Backgrounds X: Characterization and Representation, (5 August 2004);

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