Posted by: hxtang | May 1, 2009

Comparison of Non-Blind Deconvolution Algorithm?

Although lots of study has been conducted on blind deconvolution, I was frustrated to see that even state-of-art convolution algorithms don’t work very well.
Of course this has something to deal with the illposedness of the original problem (say, the Fourier Spectrum of PSF can have lots of zeros), I found the devil also resides in the formulation of the problems, e.g. noise model, prior to use, etc.

IMHO the algorithm that works best in practice is Richardson-Lucy algorithm developed in 1970s. I bet it is because this algorithm uses a Poisson distribution to model the shot noise in camera. Wavelet regularized algorithm is my second favorite because it also produces natural results, although because of the wavelet bases, they do produce noise.

I personally don’t like diffusion based approach since the output image would be piecewise linear. If that is the case, why not just do edge detection and then inpaint? I would rather do L2-regularized or Wiener deconvolution in that case.

Posted by: hxtang | April 26, 2009

CHDK

http://chdk.wikia.com/wiki/CHDK_firmware_usage

It seems that this software is pretty safe because it does not replace the original software, and it extends the ability of your original camera.
I am interested in embeding several recent CP algorithms into the camera to enhance its capability in challenging circumstances, e.g.shutter-flutter photography (to remove motion) and light efficient photography (to remove defocus).

Posted by: hxtang | April 16, 2009

Spectral Matting

http://www.vision.huji.ac.il/SpectralMatting/

A very influential paper that does matting almost automatically. I was very excited on seeing this paper as I am tired of excusing bad algorithms with unneccessary user-interactions…

The contribution of the paper is only in combining matting Laplacian with spectral clustering theory. The former came in the author’s eariler paper, while the latter is almost a small area in machine learning(?). But the assumptions behind these two components are both interesting. For the matting Laplacian, the author was actually shows that local linear models could be very powerful models to describe edges and boundaries, even if they’re of some very complicated shape. For spectral clustering, it’s interesting to see how eigenvectors specify the affinity of samples. My favorite way of seeing this is from the stochastic process aspect: Imagine a particle wandering over the image, and it has preference to traveling between similar pixels. The alpha value is then just, given its starting point(s), the probability it will end up with staying at a specific pixel, and it’s a linear combination to the eigen-vectors.

One may dislike this paper because the actual algorithm is slow, but I bet it can be accelerated with some multiscale techniques. And I like this paper because it provides an in-depth discussion about spectral matting. Although it might not be detailed enough in comparison to relevant papers from theoretical machine learning side, it is a better introduction for vision students than the spectral segmentation paper I think.

http://graphics.stanford.edu/papers/lfwigner/

This is not a task-oriented paper so you can barely expect any “novel techniques”. The real product is just equivalence between light field and Wigner distribution : no magic knowing geometric optics an extreme case of Fourier optics. I personally see this as an enhancement of light field to work in the microcopy domain, to account for oscillation, or at least as claimed by the author, to see what has already been done by the optics people and avoiding doing it again with light field.

Despite the tough mathematics in the paper, the path of equivalence is straightforward. As in Fourier Slice Photography it uses shift and slope to specify a wave, but with a bit different interpretations for both of them. The shift is no longer a pinhone on the exit pupil but a small aperture to avoid argument that single point light sources emit un-directed waves; and the slope corresponds to a specific angular spectrum, or a planar wave component of that specific direction defined by the virtual “light ray”. If one understands that the image formation process in wave optics is quadratic (integrating over squared norm of the scalar field), the derivation of the equivalence now becomes straight-forward. And one might not be surprised that conherence of light plays a central role in this formulation.

The applications in this paper can all be found in previous works. Interestingly, just like Levin et.al. downgraded Fourier optics to geometric optics to analyze wavefront coding with light field, this paper shows how uncertainty principle, which due to the quantum nature of light, can be intepretated in wave optics. And the authors have already done that in the context of geometric optics! It’s still a question to me how this is going to be useful somehow, besides keeping CP and optics people closer and closer.

After all I would still say it’s a well-grounded paper and requires struggling for sometime to really get anything from the paper. And it’s worth the price if you want to understand light and camera in depth.

Posted by: hxtang | November 17, 2008

use screen to run experiments on the server

It is not always necessary to use VNC sessions to allow running experiments on the server while shutting off my laptop for a while. This is by firstly screen on the server, run the experiment, and use “ctrl+ A D” to detach the screen.Later on, you can just log off and shut off the local machine. To go back to the screen, simply screen -r.

Posted by: hxtang | November 4, 2008

Notes on depth of field

The DOF is determined by the subject distance, the lens focal length, and the lens f-number (relative aperture).

\displaystyle DOF \thickapprox \frac{2Hs^2}{H^2-s^2} for s \geq H

DOF \thickapprox \displaystyle \frac{2Ncf^2s^2}{f^4 - N^2c^2s^2} for s > H

At close-up distances, DOF is approximately determined by the subject-magnification and the lens f-number.

DOF \thickapprox 2Nc\left(\displaystyle \frac{m+1}{m^2}\right)


References:

[1] Depth of field – Wikipedia

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