Macrofacet Theory for Gaussian Process Statistical Surfaces
For computer graphics researchers, this work bridges microfacet models and Gaussian processes, offering a new rendering method for surfaces, volumes, and in-betweens.
The paper extends microfacet theory to macro-space by transforming surfaces into volumetric representations, enabling efficient rendering of Gaussian process statistical surfaces without realizations. The approach improves performance over realization-based methods.
We present macrofacet theory to extend microfacet theory from the micro-space to the macro-space. This is achieved by transforming surfaces into volumetric representations that preserve microfacet characteristics. Therefore, we formulate a macroscopic microfacet model using a classic exponential participating medium. Meanwhile, we observe that traditional microfacet models are equivalent to Gaussian processes by definition but ignore the correlation along the geometric normal of the macro-surface. We extend microfacet theory to address this limitation. Our formulation represents Gaussian process implicit surfaces in a statistical manner, which we refer to as Gaussian process statistical surfaces. As a result, our approach converts Gaussian process statistical surfaces into classic exponential media to render surfaces, volumes and in-betweens without realizations. This enables efficient rendering and improves performance compared to realization-based approaches, while theoretically bridging microfacet models and Gaussian processes. Moreover, our approach is easy to implement.