Axis-aligned filtering for interactive physically-based diffuse indirect lighting

We introduce an algorithm for interactive rendering of physically-based global illumination, based on a novel frequency analysis of indirect lighting. Our method combines adaptive sampling by Monte Carlo ray or path tracing, using a standard GPU-accelerated raytracer, with real-time reconstruction of the resulting noisy images. Our theoretical analysis assumes diffuse indirect lighting, with general Lambertian and specular receivers. In practice, we demonstrate accurate interactive global illumination with diffuse and moderately glossy objects, at 1-3 fps. We show mathematically that indirect illumination is a structured signal in the Fourier domain, with inherent band-limiting due to the BRDF and geometry terms. We extend previous work on sheared and axis-aligned filtering for motion blur and shadows, to develop an image-space filtering method for interreflections. Our method enables 5--8X reduced sampling rates and wall clock times, and converges to ground truth as more samples are added. To develop our theory, we overcome important technical challenges---unlike previous work, there is no light source to serve as a band-limit in indirect lighting, and we also consider non-parallel geometry of receiver and reflecting surfaces, without first-order approximations.