heya, sorry for the delay, i had half of this mail sitting in my drafts folder for quite some time now.
On Tue, May 10, 2016 at 12:54 AM, Wolfgang Mader <wolfgang_ma...@brain-frog.de> wrote: > Hi Johannes, > > I write this mail personally to you since I am not sure if my excerpt of the > paper is too detailed for the list. As you send me the paper, I assumed you > the expert on the topic. heh. i did see the talk five years ago, and thought i would understand it back then. let's see how much detail i remember :) > I hope this is fine for you. If you think the list > would benefit from this mail, feel free to forward it or let me know, such > that > I can post it. > > I have summarized my current understanding of the algorithm and pointed out > points which are unclear to me. I hope this gives us a nice basis for > discussion w/o assuming something the other might not know/be aware of. > > > 1) Obtain the Gaussian pyramid > ------------------------------ > Starting from the original image I with i rows and j columns, the n-th level > of the Gaussian pyramid is a downsampled version of I with i/(2**n) rows and > j/(2**n) columns, yielding ij/(4**n) pixels at n-th level; x**y denotes x > raised to the power of y. In order to avoid aliasing, the image must be > downsampled such that the Nyquist-frequency is halved from level n to n+1. The > filter doing this must not introduce spurious structures at a coarser > scale.[1] yes. > To this end, the scale space community (if there such a thing) has mainly > settled on Gaussian filters, which has been claimed the unique solution for > this problem. This claim, however, seems disputable.[1] right. i don't think it matters much in practice as long as you're blurring (and not introducing frequency by some ringing filter). > In the reference code, downsampling is performed by a 2D separable low pass > filter constructed as the outher product of the parameter vectors of a 1D > 5-tab > low pass filter. I guess, separable meens that the covariance matrix of the 2D > Gaussian function is has zero off-diagonal entries. Is this correct? separable means you can first do a 1D blur in x and another 1D blur in y direction. that is, you separate the 5x5 2D filter into two 5-wide 1D filters. which is of course a little bit faster. i think you can show that a gaussian is pretty much the only thing that separates from a radially symmetric filter kernel to two 1D gaussians, without introducing some square-shaped artifacts. > This is the first point where we can play with parameters. However, whatever > we > implement here, we must respect the Nyquist frequency. it's really kind of hard not to, no? i mean, you have a signal with 2 pixels, so the maximum frequency you get out of this is just under wavelength=2. now you average those two and get a signal with max wavelength=1 ..? > 2) Obtaining the Laplacian pyramid > ---------------------------------- > The n-th level of the Laplacian pyramid is defined as > L(n) = G(n) - upsample(G(n+1)) > where upsample() is an operator that doubles the image size in each dimension. > Thus G(n) and upsample(G(n+1)) have the same number of pixels. The top-most > level L(N) equals G(N), while L(0) = G(0) - upsample(G(1)). Starting with > G(N), the Laplacian pyramid can be collapsed > G(n) = L(n) + upsample(G(n+1)) > such that finally > G(0) = L(0) + upsample(G(1)) > the original image is resurrected. yes, multiresolution, much like wavelets would work, too. > 3) Detecting edges > ------------------ > Edges are detected in a color space (rgb, luminosity, etc.) appropriate for > the problem at hand. As darktable already offers many different color spaces, > this should nicely fit darktable's design. It is assumed, that fine detail > generates smaller discontinuities in this color space than edges do. As we > probably want to keep detail, this is the second point of interaction we can > play with. yeah, i would try to do it in our Lab pipeline, and detect edges mainly via L. not sure whether we want the pyramid to work on 3d colour at all, or just on the lightness. > 4) Altering edges > ----------------- > The amplitude of detected edges shall be adjusted while the shape of the edge > (position, shape, direction of its gradient) shall remain unmodified. Edges > with different profiles end up in different levels L(n). Therefore, altering > the coefficients in the Laplacian pyramid directly while preserving the > properties of the edge is tricky. yes. > An easier approach is to alter the original image in its color space is such a > way that it locally equals our target. This can be compression or enhancement > or whatever else comes to mind. New Laplacian coefficients from this altered > image are then determined and replace the original ones in the Laplacian > pyramid. This operation is local as further discussed in 6). yes, the tricky part is to make the laplacians local. > 5) Preserve detail > ------------------ > Detail is lost by the compression of the original image. by compression you mean reduction of overall contrast by compressing dynamic range with, for instance, a tonecurve on L. > The paper mentions a > nifty trick to avoid this (Paragraph: Detail preservation). However, for the > current discussion, this is not that important. I skip it for now and have a > closer look at it once the rest of the algorithm is clear to me. okay. > 6) Local Laplacian filtering > ---------------------------- > Each pixel (k,l,n) of the n-th level of the Laplacian pyramid is obtained from > an intermediate image I' which is explicitly generated to obtain this single > pixel. Here, the paper is a bit blurry, such that I have to consult the > reference code in order to figure out what really is going on. If you can fill > me in here, I would appreciate. However, the transformation applied to I in > order to obtain I' is key to the local Laplacian filter. By adjusting the > parameters of this local transformation, detail, tone or both can be either > smoothed or enhanced. did you see https://youtu.be/t4mbrKYRmvs ? i think it nicely visualises the optimised version of creating the laplacian pyramids (by in fact only computing the gaussian pyramids and evaluating the laplacians on the fly). the sampling step in the end is of course not explained in this video, but i think it's probably a good idea to follow the paper with the optimised implementation that is cited below this video (your [2]). > 7) Conclusion > ------------- > To me, a variate of applications seem possible. Depending on which information > of the image (color, luminosity, etc.) we include in the pyramids, different > aspects of the image should be affected. Also, by selecting only some of all > possible levels of the Laplacian pyramid, we can limit the effects to specific > frequency bands of the image. This should be similar to what we can do in the > wavelet-based Equalizer module. indeed. > 8) Plan of action > ----------------- > I found another publication about a fast implementation of the algorithm.[2] I > want to read this and further dig through the code, both the Matlab version > and what you send me. > > Meanwhile, I would be happy to read your comments if you have any. Once I am > all clear on the algorithm, I for sure have some questions on how to manage > the entire image and parts of it in the pixel pipeline. It would be great if > you could help me there. absolutely. i would consider that the easy part :) cheers, jo > > > This is all for now from my side. > Cheers, > Wolfgang > > > > > [1] https://en.wikipedia.org/wiki/Scale_space#Why_a_Gaussian_filter.3F > [2] http://www.di.ens.fr/~aubry/llf.html ___________________________________________________________________________ darktable developer mailing list to unsubscribe send a mail to darktable-dev+unsubscr...@lists.darktable.org
