Slides by Yimin LiSlides by Yimin Li

Metropolis Light Transport

Eric Veach, Leonidas J. Guibas

Computer Science DepartmentStanford University

Intuition

In Monte Carlo Ray Tracing, most paths do not contribute significantly to the image.

We need more samples where f is large.

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A good example

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Basics

Given a function f, and an equation y=f(x)

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Basics

Given an image, input becomes (x,y)

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Basics

Gray = 0.29900*R+0.58700*G+0.11400*B

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Basics

f may appear in any form. It can be the difference of samples

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Metropolis Light Transport

= ray tracing + metropolis sampling

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Bidirectional Path Tracing

= path tracing + light tracing

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Mutation

choose a path

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Mutation

mutate this path by adding new vertices

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Mutation

mutate this path by perturbing a vertex

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Mutation

The algorithm finds an important, but hard to find, path. Once this path is found, it explores other paths “near” that path

through mutations, which guarantees faster convergence.

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Basic MTL algorithm

MTL(){ image = 0; // zero matrix x_bar = random_path(); // a path generated by ray tracing for i = 1 to N // N is the length of path x_bar { y_bar = mutate( x_bar ); a = acceptProbability ( x_bar, y_bar ); if ( (float)rand()/RAND_MAX < a ) x_bar = y_bar; recordSample( image, f(x_bar) ); }

return image;}

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Acceptance Probability

Detailed balance:

f(x_bar)T(y_bar|x_bar)a(y_bar|x_bar) = f(y_bar)T(x_bar|y_bar)a(x_bar|y_bar)

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Advantages

· Unbiased· Infinite dimensions· Faster convergence· Efficient for glossy surfaces, caustics,

and strong indirect lighting

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Demo

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Thank you!

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