Matrix row-column sampling for the many-light problem

Abstract

2.2m triangles: 300 rows, 900 columns, 16.9 s 388k triangles: 432 rows, 864 columns, 13.5 s 869k triangles: 100 rows, 200 columns, 3.8 s Figure 1: In the above images, over 1.9 million surface samples are shaded from over 100 thousand point lights in a few seconds. This is achieved by sampling a few hundred rows and columns from the large unknown matrix of surface-light interactions. AbstractRendering complex scenes with indirect illumination, high dynamic range environment lighting, and many direct light sources remains a challenging problem. Prior work has shown that all these effects can be approximated by many point lights. This paper presents a scalable solution to the many-light problem suitable for a GPU implementation. We view the problem as a large matrix of samplelight interactions; the ideal final image is the sum of the matrix columns. We propose an algorithm for approximating this sum by sampling entire rows and columns of the matrix on the GPU using shadow mapping. The key observation is that the inherent structure of the transfer matrix can be revealed by sampling just a small number of rows and columns. Our prototype implementation can compute the light transfer within a few seconds for scenes with indirect and environment illumination, area lights, complex geometry and arbitrary shaders. We believe this approach can be very useful for rapid previewing in applications like cinematic and architectural lighting design.

Kernel Nyström method for light transport

“…Similar to [Hašan et al 2007], we pack the r sparse elements in each row to a vectorr i = (T i, j 1 , T i, j 2 , . .…”

GPU-based out-of-core many-lights rendering

“…The latest work was to apply such a scalable framework to capture light transports in bidirectional ray paths [Walter et al 2012]. An alternative formulation of the many-lights problem is the matrix representation, where each row represents an individual sample shaded by each of lights, while each column represents each of samples lit by an individual light [Hašan et al 2007]. The final image is computed by summing each row in the matrix.…”

“…The many-lights rendering problem has been formulated in matrix form [Hašan et al 2007], where matrix A of size M × N represents the light transport from N lights to M surface samples. The shading of one surface sample is calculated by summing one column as…”

“…The basic principle of matrix sampling in previous methods [Walter et al 2006;Hašan et al 2007;Ou and Pellacini 2011] is to find representative lights so as to reduce the rendering computation. In our method, we need to partition the matrix into submatrices satisfying our data management requirements.…”

“…In this framework, scenes with diffuse and low-gloss materials can be rendered by approximating direct and indirect illumination from a large number of virtual point lights (VPLs) [Keller 1997]. By viewing the integration of these lights as surface sample-light interactions of the light transport matrix, the rendering is formulated into a matrix sampling problem [Walter et al 2005;Walter et al 2006;Hašan et al 2007], where elements of the matrix are first sampled to obtain representative lights and then these representative lights are integrated to samples (pixels). These two steps require different kinds of data: lights and geometry.…”