Questions on MH algorithm and Spherical Harmonics illumination

[Luke]

Dear,

Thanks for the nice probabilistic fitting tutorial. It is very interesting and inspiring. After going through the material, I got couple of questions:

1) The section of Unaligned Landmarks Posterior in the chapter of Stochastic Sampling. I found it uses independent Gaussian likelihood model to model the target pdf with MH algorithm.

But we typically have very efficient way to sample Gaussian or normal distribution's pdf, why we still need to use MH algorithm in the case ? I thought MH is good if the desired pdf is special (i.e. not uniform or normal distribution).

2) In the section of Model Rendering of the chapter of Computer Graphics. It's nice that scalismoLab-faces provides a library for shading, lighting etc. The Spherical Harmonics illumination is used to encode a whole environment map. 

I was wondering if it includes diffuse interreflection, i.e. illumination is not only from direct light but also from secondary reflected light from other points on the face. If so, how many bounces do you take into account ?

If there is a open-source code, please let me know. I am thinking about implementing the tricky part in python.

Hope to hear your expertise.

Best Regards,

Luke

   

[Andreas Forster]

Hi Luke,

Thank you for your positive feedback. Now to your questions:

1. The main Idea of this part of the tutorial is to introduce the sampling with a simpler problem than the full face fitting. In addition, I doubt that the Gaussian likelihood from the 2d image, the Gaussian model prior and the uninformative uniform prior for the pose result in a Gaussian posterior over all the model and pose parameters due to the coupling through the perspective projection and the model in 3d. But maybe I miss understood your idea how to sample more efficiently from the resulting posterior.

2. We have different local shaders in scalismo.faces.renderer.PixelShaders. But we have not yet explored too much different illumination models considering light reflections. The most closely related work is a linear model considering self-occlusion (see https://ieeexplore.ieee.org/document/8237679/ ). However, this code is not open-sourced, but if I am right, it is planned to be a freely available tutorial soon. In the meantime, you could directly write the first author if you have questions about it.

Best regards,

Andreas

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Dr. Andreas Morel-Forster
Departement Mathematik und Informatik
Spiegelgasse 1
CH-4051 Basel
PHONE: +41 61 207 05 52

MAIL: Andreas.Forster@unibas.ch
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