metropolis light transport
TRANSCRIPT
![Page 1: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/1.jpg)
Slides by Yimin LiSlides by Yimin Li
Metropolis Light Transport
Eric Veach, Leonidas J. Guibas
Computer Science DepartmentStanford University
![Page 2: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/2.jpg)
Intuition
In Monte Carlo Ray Tracing, most paths do not contribute significantly to the image.
We need more samples where f is large.
2
![Page 3: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/3.jpg)
A good example
3
![Page 4: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/4.jpg)
Basics
Given a function f, and an equation y=f(x)
4
![Page 5: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/5.jpg)
Basics
Given an image, input becomes (x,y)
5
![Page 6: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/6.jpg)
Basics
Gray = 0.29900*R+0.58700*G+0.11400*B
6
![Page 7: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/7.jpg)
Basics
f may appear in any form. It can be the difference of samples
7
![Page 8: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/8.jpg)
Metropolis Light Transport
= ray tracing + metropolis sampling
8
![Page 9: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/9.jpg)
Bidirectional Path Tracing
= path tracing + light tracing
9
![Page 10: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/10.jpg)
Mutation
choose a path
10
![Page 11: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/11.jpg)
Mutation
mutate this path by adding new vertices
11
![Page 12: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/12.jpg)
Mutation
mutate this path by perturbing a vertex
12
![Page 13: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/13.jpg)
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.
13
![Page 14: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/14.jpg)
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;}
14
![Page 15: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/15.jpg)
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)
15
![Page 16: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/16.jpg)
Advantages
· Unbiased· Infinite dimensions· Faster convergence· Efficient for glossy surfaces, caustics,
and strong indirect lighting
16
![Page 17: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/17.jpg)
Demo
17
![Page 18: Metropolis Light Transport](https://reader033.vdocuments.us/reader033/viewer/2022060122/5596257d1a28ab614a8b457c/html5/thumbnails/18.jpg)
Thank you!
18