Metropolis Light Transport

1. Slides by Yimin LiSlides by Yimin Li
Metropolis Light Transport
Eric Veach, Leonidas J. Guibas
Computer Science Department
Stanford University

2. 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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3. A good example
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4. Basics
Given a function f, and an equation y=f(x)
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5. Basics
Given an image, input becomes (x,y)
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6. Basics
Gray = 0.29900*R+0.58700*G+0.11400*B
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7. Basics
f may appear in any form. It can be the
difference of samples
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8. Metropolis Light Transport
= ray tracing + metropolis sampling
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9. Bidirectional Path Tracing
= path tracing + light tracing
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10. Mutation
choose a path
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11. Mutation
mutate this path by adding new vertices
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12. Mutation
mutate this path by perturbing a vertex
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13. 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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14. 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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15. 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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16. Advantages
· Unbiased
· Infinite dimensions
· Faster convergence
· Efficient for
glossy surfaces,
caustics,
and strong indirect lighting
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17. Demo
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18. Thank you!
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