Specular Lobe‐Aware Filtering and Upsampling for Interactive Indirect Illumination

Abstract

Although geometry‐aware filtering and upsampling have often been used for interactive or real‐time rendering, they are unsuitable for glossy surfaces because shading results strongly depend on the bidirectional reflectance distribution functions. This paper proposes a novel weighting function of cross bilateral filtering and upsampling to measure the similarity of specular lobes. The difficulty is that a specular lobe is represented with a distribution function in directional space, whereas conventional cross bilateral filtering evaluates similarities using the distance between two points in a Euclidean space. Therefore, this paper first generalizes cross bilateral filtering for the similarity of distribution functions in a non‐Euclidean space. Then, the weighting function is specialized for specular lobes. Our key insight is that the weighting function of bilateral filtering can be represented with the product integral of two distribution functions corresponding to two pixels. In addition, we propose spherical Gaussian‐based approximations to calculate this weighting function analytically. Our weighting function detects the edges of glossiness, and adapts to all‐frequency materials using only a camera position and G‐buffer. These features are not only suitable for path tracing, but also deferred shading and non‐ray tracing–based methods such as voxel cone tracing.Although geometry‐aware filtering and upsampling have often been used for interactive or real‐time rendering, they are unsuitable for glossy surfaces because shading results strongly depend on the bidirectional reflectance distribution functions. This paper proposes a novel weighting function of cross bilateral filtering and upsampling to measure the similarity of specular lobes. The difficulty is that a specular lobe is represented with a distribution function in directional space, whereas conventional cross bilateral filtering evaluates similarities using the distance between two points in a Euclidean space. Therefore, this paper first generalizes cross bilateral filtering for the similarity of distribution functions in a non‐Euclidean space. Then, the weighting function is specialized for specular lobes. Our key insight is that the weighting function of bilateral filtering can be represented with the product integral of two distribution functions corresponding to two pixels. In addition, we propose spherical Gaussian‐based approximations to calculate this weighting function analytically.