The quality of an estimator is not measured using just bias or variance. It is a combination of both, i.e. Root Mean Squared error
RMS Error = bias^2 + variance
so if you can trade a small amount of bias for a large amount of variance you are doing quite well. Add consistency (i.e. the bias of the estimator goes to zero as the sample size increases) to that and you are golden.
This is what lies at the heart of Photon Mapping. The photon map based estimate of the scene radiance is biased but consistent quantity and has a much smaller variance as compared to a pure monte carlo path traced version.
As for final gather, you can make yet another bias for variance tradeoff using irradiance caches (greg ward) and irradiance gradients. This can speed up a typical final gather routine by more than an order of magnitude.
As for depth of field he will have to simulate a finite aperture in anycase, so I do not see how this is a disadvantage of photon mapping. The direct lighting from spherical sources is not a big deal I do not see what complication you are referring to there.
So in summary, the goal of an unbiased simulation is nice, but since what you are really after is an accurate image, for the same amount of computational effort photon mapping will give you better results.
Two words: Photon Mapping The simulation you are trying to run does not the kind of compute effort that you are planning on using. I implemented a photon map based renderer for a rendering class last year and it can render a room like the one you showed in a couple of minutes.
The reference you are looking for is:
Realistic Image Synthesis using Photon Mapping By Henrik Wann Jensen
He is the guy who got the technical oscar this year for being one of the inventors of a method to render materials which display subsurface scattering, e.g. skin and marble.
now that I have your attention. I have been using matlab for almost exactly an year now and my primary occupation is doing various kinds of machine learning and computer vision related stuff. I have used Mathematica for doing simulations of chemical reactors in the past, so I have some experience with it.
If you are going to deal with experimental data, and your needs include lots of data visualization MATLAB is truly the way to go. People who like to refer to matlab as just another matrix language miss the point. Just about anyone can put a interpreter around LAPACK and give you a matrix language. What makes MATLAB so popular and powerful is the availability of very high quality libraries and the fantastic visualization tools that come with MATLAB. It is a good idea to invest in a good set of toolboxes when you buy you matlab license. Plus there is a ton of free stuff out there.
Writing iterative code used to be quite slow, but with the latest MATLAB release mathworks has included a JIT compiler which can convert some not all of your loops to machine code and give you quite a bit of speedups.
The C interface is clean, and very easy to learn. You can add existing C libraries or write new code and integrate it into your matlab setup very quickly.
The matlab programming language itself has an extremely powerful syntax. You will be surprised how much you can do in a line of matlab code.
Finally, if you need to do symbolic computations, there is the symbolic computations toolbox, which I as far as I recall is a wrapper around a maple interpreter, so you have the full power of maple available in MATLAB. I have used it and its pretty good.
My experience with Mathematica suggests that unless you are going to deal with mathematical structures, and do a lot of symbolic computation in particular, you are better of using like MATLAB.
Exactly what is ethically dubious about being a dataminer ?
Isn't it like saying that guns are ethically dubious ?
Datamining as a profession has nothing to do with what use the mined information is put to.. or how the information was collected. A data miner is a specialized professional like any other engineer.
I would hope that you would be a tad bit more careful before you make such irresponsible statements.
Slashdot Mirror
You have obviously never heard of fMRI studies, have you?
One word for you my brother
netTunes
Stop yawning and start reading. http://graphics.stanford.edu/papers/rtongfx http://graphics.stanford.edu/papers/tpurcell_thesi s/
http://graphics.stanford.edu/papers/photongfx
The quality of an estimator is not measured using just bias or variance. It is a combination of both, i.e. Root Mean Squared error RMS Error = bias^2 + variance so if you can trade a small amount of bias for a large amount of variance you are doing quite well. Add consistency (i.e. the bias of the estimator goes to zero as the sample size increases) to that and you are golden. This is what lies at the heart of Photon Mapping. The photon map based estimate of the scene radiance is biased but consistent quantity and has a much smaller variance as compared to a pure monte carlo path traced version. As for final gather, you can make yet another bias for variance tradeoff using irradiance caches (greg ward) and irradiance gradients. This can speed up a typical final gather routine by more than an order of magnitude. As for depth of field he will have to simulate a finite aperture in anycase, so I do not see how this is a disadvantage of photon mapping. The direct lighting from spherical sources is not a big deal I do not see what complication you are referring to there. So in summary, the goal of an unbiased simulation is nice, but since what you are really after is an accurate image, for the same amount of computational effort photon mapping will give you better results.
Two words: Photon Mapping
The simulation you are trying to run does not the kind of compute effort that you are planning on using. I implemented a photon map based renderer for a rendering class last year and it can render a room like the one you showed in a couple of minutes.
The reference you are looking for is:
Realistic Image Synthesis using Photon Mapping
By Henrik Wann Jensen
He is the guy who got the technical oscar this year for being one of the inventors of a method to render materials which display subsurface scattering, e.g. skin and marble.
now that I have your attention.
I have been using matlab for almost exactly an year now and my primary occupation is doing various kinds of machine learning and computer vision related stuff. I have used Mathematica for doing simulations of chemical reactors in the past, so I have some experience with it.
If you are going to deal with experimental data, and your needs include lots of data visualization MATLAB is truly the way to go. People who like to refer to matlab as just another matrix language miss the point. Just about anyone can put a interpreter around LAPACK and give you a matrix language. What makes MATLAB so popular and powerful is the availability of very high quality libraries and the fantastic visualization tools that come with MATLAB. It is a good idea to invest in a good set of toolboxes when you buy you matlab license. Plus there is a ton of free stuff out there.
Writing iterative code used to be quite slow, but with the latest MATLAB release mathworks has included a JIT compiler which can convert some not all of your loops to machine code and give you quite a bit of speedups.
The C interface is clean, and very easy to learn. You can add existing C libraries or write new code and integrate it into your matlab setup very quickly.
The matlab programming language itself has an extremely powerful syntax. You will be surprised how much you can do in a line of matlab code.
Finally, if you need to do symbolic computations, there is the symbolic computations toolbox, which I as far as I recall is a wrapper around a maple interpreter, so you have the full power of maple available in MATLAB. I have used it and its pretty good.
My experience with Mathematica suggests that unless you are going to deal with mathematical structures, and do a lot of symbolic computation in particular, you are better of using like MATLAB.
Exactly what is ethically dubious about being a dataminer ? Isn't it like saying that guns are ethically dubious ? Datamining as a profession has nothing to do with what use the mined information is put to.. or how the information was collected. A data miner is a specialized professional like any other engineer. I would hope that you would be a tad bit more careful before you make such irresponsible statements.