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Research Abstracts - 2006
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Experimental Analysis of BRDF Models

Addy Ngan, Fredo Durand & Wojciech Matusik


The Bidirectional Reflectance Distribution Function (BRDF) describes the appearance of a material by its interaction with light at a surface point. A variety of analytical models have been proposed to represent BRDFs. However, analysis of these models has been scarce due to the lack of high-resolution measured data. In this work we evaluate several well-known analytical models in terms of their ability to fit measured BRDFs. We use an existing high-resolution data set of a hundred isotropic materials and compute the best approximation for each analytical model. Furthermore, we have built a new setup for efficient acquisition of anisotropic BRDFs, which allows us to acquire anisotropic materials at high resolution. We have measured four samples of anisotropic materials (brushed aluminum, velvet, and two satins). Based on the numerical errors, function plots, and rendered images we provide insights into the performance of the various models. We conclude that for most isotropic materials physically-based analytic reflectance models can represent their appearance quite well. We illustrate the important difference between the two common ways of defining the specular lobe: around the mirror direction and with respect to the half-vector. Our evaluation shows that the latter gives a more accurate shape for the reflection lobe. Our analysis of anisotropic materials indicates current parametric reflectance models cannot represent their appearances faithfully in many cases. We show that using a sampled microfacet distribution computed from measurements improves the fit and qualitatively reproduces the measurements.


Figure 1: The normalized fitting errors (logarithmic scale) of five analytic models to our isotropic data set of 100 BRDFs. The BRDFs are sorted in the errors of the Lafortune model (Red) for visualization purpose.

We have analyzed the performance of several analytical BRDF models by their ability to fit real BRDFs. Our experimental results suggest that using a single specular lobe, the Cook-Torrance [4], Ashikhmin-Shirley [2] and the He [5] models perform well for most of the 100 isotropic BRDFs in the data set provided by Matusik et al. [7] (Figure 1). One factor of their good performance is probably their explicit modeling of the Fresnel effect. In the case of the He model, the number of degrees of freedom is also larger. In contrast the Blinn-Phong [3] and Ward [9] models consistently yield higher errors. The errors for the Lafortune model lie in between for a majority of the materials. To the left end of the plot are mostly diffuse or mildly glossy materials like fabrics, rubber and paints, while materials close to the right end are mostly smooth metals and highly specular plastics. The normalized errors span several order of magnitudes as the shape of the BRDF is vastly different for the wide spectrum of materials. Moreover, our results show that for a number of materials, the fit quality is much improved when an additional lobe is employed. This is mostly attributed to the multiple layer finish on these materials.

Figure 2: The VR lobe compared with the HN lobe remapped to the outgoing directions.

Figure 3: Acquisition setup for anisotropic materials. The cylinder tilt, surface normal variation, light position and strip orientation each contributes to one degree of freedom for acquiring the 4D BRDF.

Our study also illustrates that the difference between the two ways of modeling the specular lobes is profound (Figure 2). The HN formulation naturally corresponds to the microfacet-based theory, and its viability is confirmed by the data set. Meanwhile, models based on the VR lobes are visually inaccurate in a rendered scene. The fitting results of these models are systematically inferior to their counterparts. The Lafortune model [6], though highly expressive with its basis of generalized cosine lobes, cannot accurately model real BRDFs with a single lobe. While the computation for each generalized cosine lobe is cheaper relative to a Cook-Torrance lobe, fitting more than a few of these lobes to measured data is often unstable.

We have also built a new setup for high resolution measurement of anisotropic BRDFs using material strips on a rotating cylinder (Figure 3). We have used it to measure four typical anisotropic materials and have shown that only two of them can be modeled by parametric models. Our fabric measurements exhibit a complexity that cannot be accounted for by the elliptical functions used to introduce anisotropy in these models. Furthermore, we have shown how to estimate a tabulated microfacet distribution from these measurements, which yields good results with Ashikhmin et al.'s microfacet-based BRDF generator [1]. This model draws its expressive power from a general representation of microfacet distributions.

One of our measured material, the purple satin, shows an intriguing distribution (Figure 4): a large density around two great circles that are symmetrically slightly tilted from the vertical direction. This type of distribution can be caused by symmetric cone pairs. When we examine the macro photograph we note that the longest visible segments of thread are high in the middle and have a symmetrical slope that might be similar to a cone, as sketched on the right part of the image. Figure 5 shows comparisons between photographs of the measurement cylinder and renderings using the estimated microfacet distribution.

Figure 4: Left: Purple satin macro photograph with sketched double cones. Right: deduced microfacet distribution (log plot).

Figure 5: Left: Purple satin - one input photograph. Right: - reconstruction using sampled microfacet distribution.


This work was presented at the Eurographics Symposium on Rendering 2005 and published in the associated conference proceedings [8]. See here for more project details.


There are several directions for future work. First, we expect that a new set of basis functions, similar to the generalized cosine lobes, but expressed with the half-vector, would yield improved fitting results with fewer number of lobes. These basis functions should be reasonably inexpensive to compute and be flexible enough to represent complex reflectance phenomena, e.g. retro-reflection. Second, while our metric for BRDF fitting gives reasonable results in most cases, it does not directly correspond to perceptually important differences. Finally, a perceptually-based metric would improve the visual quality of the fits, especially when the fit is relatively poor and different choices of approximation tradeoffs are present.


We thank Eric Chan, Jan Kautz, Jaakko Lehtinen, Daniel Vlasic and the anonymous reviewers of the EGSR paper for valuable feedback on this work. This work was supported by an NSF CAREER award 0447561 Transient Signal Processing for Realistic Imagery, an NSF CISE Research Infrastructure Award (EIA9802220) and the Singapore-MIT Alliance.

  1. M. Ashikhmin, S. Premoze and P. Shirley. A microfacet-based BRDF generator. In Proceedings of SIGGRAPH 2000, pp. 65--75, July 2000.
  2. M. Ashikhmin, P. Shirley. An anisotropic Phong BRDF model. In Journal of Graphics Tools 5, 2 (2000), pp. 25--32, 2000.
  3. J. Blinn. Models of light reflection for computer synthesized pictures. In Proceedings of SIGGRAPH 1977, pp. 192--198, 1977.
  4. R. Cook and K. Torrance. A reflectance model for computer graphics. In Proceedings of SIGGRAPH 1981, pp. 307--316, 1981.
  5. X. He, K. Torrance, F. Sillion, D. Greenberg D. A comprehensive physical model for light reflection. In Proceedings of SIGGRAPH 1991, pp. 175--186, 1991.
  6. E. Lafortune, S. Foo, K. Torrance, D. Greenberg. Non-linear approximation of reflectance functions. In Proceedings of SIGGRAPH 1997, pp. 117--126, 1997.
  7. W. Matusik, H. Pfister, M. Brand, L. McMillan. A data-driven reflectance model. In ACM Transactions on Graphics, 3 (2003), pp. 759--769, 2003.
  8. A. Ngan, F. Durand and W. Matusik. Experimental Analysis of BRDF Models. In Proceedings of the Eurographics Symposium on Rendering 2005, pp. 117--126, Konstanz, Germany, June 2005.
  9. G. Ward. Measuring and modeling anisotropic reflection. In Proceedings of SIGGRAPH 1992, pp. 265--272, 1992.
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