### Questions on BDPT and Sampling

Posted:

**Wed Dec 31, 2014 5:46 am**Hello all

I've got a question with regards to BDPT and sampling. In BDPT in order to efficiently generate paths, we do a correlated path sampling scheme by connecting all vertices of the camera path to all the vertices of the light path. Assume the length of eye path as N_E and the light path as N_L. So in essence we have N_E x N_L connections done and resulting in the same number of paths. Assume all paths are valid (visibility is true for all connected pairs). In order to simplify lets take an example case of N_E = 3 and N_L = 3. We can derive the following table to understand this better.

Assume 'k' to be the path length. Assume that we cannot directly intersect with the camera and the light source (pinhole camera and point light) thereby making the connections explicit.

-------------------------

E | L | K |

-------------------------

1 1 1

1 2 2

1 3 3

2 1 2

2 2 3

2 3 4

3 1 3

3 2 4

3 3 5

-------------------------

As we can see we have the following counts of paths of various lengths

-----------------------

K | n_K |

-----------------------

1 1

2 2

3 3

4 2

5 1

------------------------

All these paths now contribute to the same pixel. My questions are the following.

1. Should we average the path contributions on per path length basis? For example we are considering '3' different path lengths of 'k = 3'. By monte carlo sampling framework this represents three different random paths which would mean that we do an average of all three f(x)/p(x) of each path.

2. Assume we are generating a lot of camera samples for each pixel. How do we go about correctly averaging the results for the entire pixel.?

I've got a question with regards to BDPT and sampling. In BDPT in order to efficiently generate paths, we do a correlated path sampling scheme by connecting all vertices of the camera path to all the vertices of the light path. Assume the length of eye path as N_E and the light path as N_L. So in essence we have N_E x N_L connections done and resulting in the same number of paths. Assume all paths are valid (visibility is true for all connected pairs). In order to simplify lets take an example case of N_E = 3 and N_L = 3. We can derive the following table to understand this better.

Assume 'k' to be the path length. Assume that we cannot directly intersect with the camera and the light source (pinhole camera and point light) thereby making the connections explicit.

-------------------------

E | L | K |

-------------------------

1 1 1

1 2 2

1 3 3

2 1 2

2 2 3

2 3 4

3 1 3

3 2 4

3 3 5

-------------------------

As we can see we have the following counts of paths of various lengths

-----------------------

K | n_K |

-----------------------

1 1

2 2

3 3

4 2

5 1

------------------------

All these paths now contribute to the same pixel. My questions are the following.

1. Should we average the path contributions on per path length basis? For example we are considering '3' different path lengths of 'k = 3'. By monte carlo sampling framework this represents three different random paths which would mean that we do an average of all three f(x)/p(x) of each path.

2. Assume we are generating a lot of camera samples for each pixel. How do we go about correctly averaging the results for the entire pixel.?