Bidirectional Light Transport with Vertex Merging

彬彬

Abstract

We present vertex merging – a bidirectional path sampling technique

for Monte Carlo light transport integration. Vertex merging

is simple and more computationally efficient for specular-diffusespecular

effects than the currently available techniques in bidirectional

path tracing. It brings the advantages of photon mapping to

the path integral framework, while avoiding the concept of density

estimation altogether. This makes it possible for the first time

to quantitatively reason about the efficiency of two rendering approaches

that have been historically considered conceptually different.

The practical result is a combined bidirectional rendering algorithm

that efficiently handles a wide variety of lighting conditions,

ranging from direct illumination and diffuse inter-reflections to the

notoriously problematic reflected caustics. This algorithm also has

a higher order of convergence than progressive photon mapping.

1 Light Path Sampling

Veach [Veach 1997] formulated the rendering problem mathematically

as a radiance measurement function integrated over the space

of all light transport paths. This tidy path integral framework made

it possible to combine different Monte Carlo light transport estimators

in an efficient way using multiple importance sampling (MIS).

Veach then developed bidirectional path tracing (BDPT) as a family

of path sampling techniques whose corresponding estimators are

weighted with the power heuristic [Veach 1997]. This heuristic assumes

that higher probability density function (pdf) values result in

lower variance, and weights estimators proportionally to the pdf of

their corresponding sampling technique.

The two basic building blocks of BDPT are the unbiased unidirectional

sampling and vertex connection techniques. Unidirectional

sampling cons***cts a path connecting a light source with the camera

by performing a random walk from either end until termination.

Vertex connection joins the endpoints of a camera and a light subpaths

deterministically by a ray, saving one random sampling step.

Vertex connection works best if the two vertices are far apart and

both have low frequency BSDFs. Unidirectional sampling is in

contrast superior for specular paths, and inferior for diffuse interreflections.

Therefore, specular-diffuse-specular (SDS) vertex sequences

are ill-suited for both techniques, and result in low sampling

pdfs. Such paths occur, e.g., when looking at a car’s interior

or at a glass-enclosed object from the outside, as shown in Figure 1.

Photon mapping has been shown to efficiently handle SDS interactions

in a consistent way [Hachisuka et al. 2008]. Unfortunately, it

is inefficient for diffuse illumination and has a lower order of convergence

than the unbiased BDPT estimators [Knaus and Zwicker

2011]. Furthermore, the flux density estimator has been derived in a

framework that cannot be easily mapped to the path integral. These

different theoretical foundations have prevented the rigorous comparison,

C.R.CAN

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菜刀吻电线

很有心,部分已收录自用,谢谢

晃晃

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奇

有意思！学习了！

晃晃

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C.R.CAN

呵呵，很好，方便罗。

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