<title>Spectral BRDF modeling using wavelets</title>

Abstract

The Bi-directional Reflectance Distribution Function (BRDF) is a complex function characterizing the reflection of light on a surface. It depends on five variables: four angles (lighting direction and observer direction) and the wavelength. A complete measurement campaign generates a large data set difficult to model. One way to proceed is to fit an analytical model on this data set. A numerical optimization technique, like simplex, allows to retrieve the best parameters of the model by minimizing the error with regard to measurements. Most of the analytical models obtain poor results for specular surfaces, and no wavelength dependent model actually exists.These reasons lead us to choose a numerical approach and particularly wavelets. This paper shows how wavelets can be used to provide an efficient BRDF model. Results of modeling are presented over a large collection of measurement data sets. At fixed wavelength, wavelet model has pretty good results, comparable to the best analytical models for diffuse surfaces, and much better for specular surfaces. The global relative error is lower than 5% with a compression ratio better than 90%. For spectral data sets, the wavelet model also presents very interesting performances with compression ratios greater than 95% and error lower than 2%.

Compact Representation of Spectral BRDFs Using Fourier Transform and Spherical Harmonic Expansion

“…Claustres et al . [39, 40] represented spectral BRDFs in both geometrical (incident and outgoing directions) and spectral (wavelength) components using wavelets.…”

“…Multidimensional wavelets are constructed from one-dimensional wavelet bases using the products of basis functions. Claustres et al [39,40] represented spectral BRDFs in both geometrical (incident and outgoing directions) and spectral (wavelength) components using wavelets.…”

“…In spectral rendering, the wavelength information should be preserved, and finally be transferred into color components for display in a device. Although the Claustres' method [39, 40] can represent the spectral BRDFs, to enhance representation compactness, the method removes the wavelet coefficients lower than a given threshold and introduces a sparse array to save the remained coefficients; this reduces the representation accuracy and increases the complexity of implementation.…”

Wavelet-based modeling of spectral bidirectional reflectance distribution function data

“…However, the specular peak is wellpreserved with a medium compression rate. Moreover, we have shown in [41] that wavelet modelling has similar performances than the analytical modelling at fixed wavelength for diffuse surfaces, and better ones for specular surfaces. Figure 7 shows the plots of the BRDF of three different samples (cloth, sand, and dry grass) for a fixed incoming direction and azimuth angle.…”

Physically based reflectance model utilizing polarization measurement

“…Claustres et al proposed wavelet models, which can effectively reduce the number of modeling parameters. 8 The theoretical modeling approach is to resolve the reflected light into distinctive features, e.g., a diffuse component and a specular component, based on physical phenomena. Then each component of the model is parameterized in terms of the measured BRDF data.…”