5,337
edits
Advanced Computer Graphics: Difference between revisions
→Advanced Sampling Techniques
| Line 79: | Line 79: | ||
==Advanced Sampling Techniques== | ==Advanced Sampling Techniques== | ||
===Multiple Importance Sampling=== | |||
Weighted sampling between <math>F_a</math> <math>F_d</math> | |||
* Take <math>N</math> samples from each technique (j=1,...,N) | |||
* <math>F=\frac{1}{N} \sum_{j=1}^{N} \sum_{i=1}^{n} w_i(X_{i,j}) \frac{f(X_{i,j})}{p_i(X_{i,j})}</math> | |||
** Make sure <math>\sum_{i=1}^{n}w_i(x) = 1</math> | |||
* Weights for provable variance reduction | |||
** Balance heuristics: <math>w_i(x)=\frac{p_i(x)}{\sum_{k=1}^{n}p_k(x)}</math> | |||
** Power heuristics: <math>w_i(x)=\frac{p_i^2(x)}{\sum_{k=1}^{n}p_k^2(x)}</math> | |||
==Ignore== | ==Ignore== | ||
[[Visible to::users]] | [[Visible to::users]] | ||