Hello Here is a little update on what I have done recently on denoising. My work on a "new" raw denoise module is still ongoing, but it takes a lot of time (as expected), as I have to try various things before getting correct ones. So no news on this side.
Yet, I found a quicker and easier way to improve darktable's denoising capabilities. In fact, it does not even change the algorithm! The idea is to give equalizer-like GUI for all wavelets based modules, and to allow the user to change the force for red, green and blue channel, as these channels usually suffer from different levels on noise (especially after demosaic, where red and blue channel have coarser noise due to the fact that errors propagated during the demosaic). This way, the user can reduce coarse grain noise while keeping fine grain noise if he wants, or whatever fits its need. I have implemented this idea both for denoiseprofile and rawdenoise modules, and I have just opened two pull requests for them: https://github.com/darktable-org/darktable/pull/1752 https://github.com/darktable-org/darktable/pull/1753 Using these updated GUIs, I personally found that the existing algorithm had plenty of hidden power (especially in case of high ISO images where the coarse grain noise is more important)! I hope you will enjoy this as much as I do. rawfiner Le dim. 22 juil. 2018 à 20:50, rawfiner <rawfi...@gmail.com> a écrit : > Thank you Aurélien, that is a great answer. > I think I will try to incorporate this in the weight computation of non > local means to use only "non noisy" pixels in the computations of the > weights, in addition to trying to use this as a (parametric?) mask. > > rawfiner > > > Le samedi 21 juillet 2018, Aurélien Pierre <rese...@aurelienpierre.com> a > écrit : > >> The TV is the norm (L1, L2, or something else) of the gradient along the >> dimensions. Here, we have TV = || du/dx ; du/dy||. The discretized gradient >> of a function u along a direction x is a simple forward or backward finite >> difference such as du/dx = [u(i) - u(i-1)] / [x(i) - x(i-1)] (backward) or >> du/dx = [u(i +1) - u(i)] / [x(i+1) - x(i)] (forward). >> >> For contiguous pixels on main directions, the distance between 2 pixels >> is x(i) - x(i-1) = 1 (I don't divide explicitely by 1 in the code though), >> on diagonals it's = sqrt(2) (result of Pythagore's theorem). Hence the >> division by sqrt(2). >> >> Now, imagine a 2D problem where we have an inconsistent pixel in a smooth >> sub-area of a picture with 0 all around: >> >> [0 ; 0 ; 0] >> [0 ; 1 ; 0] >> [0 ; 0 ; 0] >> >> That is the matrix of a 2D Dirac delta function (impulse). Computing the >> TV L1 in forward difference leads to : >> >> ([0.0 ; 0.5 ; 0.0] >> [0.5 ; 1.0 ; 0.0] >> [0.0 ; 0.0 ; 0.0])*2 >> >> Doing the same backwards leads to : >> >> ([0.0 ; 0.0 ; 0.0] >> [0.0 ; 1.0 ; 0.5] >> [0.0 ; 0.5 ; 0.0])*2 >> >> So what happens is in both cases, the immediate neighbours of the noisy >> pixel are detected as somewhat noisy as well because of the first order >> discretization, but they are not noise. That's a limit of the discrete >> computation. Also the derivative of a Dirac delta function is supposed to >> be an even function, obviously that property is broken here. If you compute >> the L2 norm of these arrays, you get 1.22. A delta function should have a >> L2 norm = 1. Actually, the best approximation of the TV of the delta >> function would be the original delta function itself. >> >> If we average the both TV norms, we get : >> >> ([0.00 ; 0.25 ; 0.00] >> [0.25 ; 1.00 ; 0.25] >> [0.00 ; 0.25 ; 0.00])*4 >> >> So, now, we have an error on more neighbours, but smaller in magnitude >> and the TV map is now even. Also, the L2 norm of the array is now 1.12, >> which is closer to 1. So we have a better approximation of the delta >> derivative. >> >> With that in mind, on the 8 neighbours variant, we also compute the TV L1 >> norms (average of backward and forward) on diagonals, meaning : >> >> ([0.25 ; 0.00 ; 0.25] >> [0.00 ; 1.00 ; 0.00] >> [0.25 ; 0.00 ; 0.25])*4/sqrt(2) >> >> And… you are right, there is a problem of normalization because we should >> divide by 4*(1 + 1/sqrt(2)) instead of 4. Then, our TV L1 map will be : >> >> [0.1036 ; 0.1464 ; 0.1036] >> [0.1464 ; 1.0000 ; 0.1464] >> [0.1036 ; 0.1464 ; 0.1036] >> >> That's an even better approximation to the Dirac delta. Now, the L2 norm >> is 1.06. And now that I see it, that could lead to a separable kernel to >> compute the TV L1 with two 1D convolutions… >> >> I didn't plan on going full math here, but, here we are… >> >> I will correct my code soon. >> >> 16/07/2018 à 01:51, rawfiner a écrit : >> >> I went through Aurélien's study again >> I wonder why the result of TV is divided by 4 (in case of 8 neighbors, " >> out[i, j, k] /= 4.") >> >> I guess it is kind of a normalisation. >> But as we divided the differences along diagonals by sqrt(2), the maximum >> achievable (supposing the values of the image are in [0,1], thus taking a >> difference of 1 along each direction) are: >> sqrt(1 + 1) + sqrt(1 + 1) + sqrt(1/2+1/2) + sqrt(1/2+1/2) = 2*sqrt(2) + 2 >> in case of L2 norm >> 2 + 2 + 2*1/sqrt(2) + 2*1/sqrt(2) = 4 + 2*sqrt(2) in case of L1 norm >> >> So why this 4 and not a 4.83 and a 6.83 for L2 norm and L1 norm >> respectively? >> Or is it just a division by the number of directions? (if so, why are the >> diagonals difference divided by sqrt(2)?) >> >> Thanks! >> >> rawfiner >> >> >> 2018-07-02 21:34 GMT+02:00 rawfiner <rawfi...@gmail.com>: >> >> Thank you for all these explanations! >> Seems promising to me. >> >> Cheers, >> >> rawfiner >> >> 2018-07-01 21:26 GMT+02:00 Aurélien Pierre <rese...@aurelienpierre.com>: >> >> You're welcome ;-) >> >> That's true : the multiplication is equivalent to an "AND" operation, the >> resulting mask has non-zero values where both TV AND Laplacian masks has >> non-zero values, which - from my tests - is where the real noise is. >> >> That is because TV alone is too sensitive : when the image is noisy, it >> works fine, but whenever the image is clean or barely noisy, it detect >> edges as well, thus false-positive in the case of noise detection. >> >> The TV × Laplacian is a safety jacket that allows the TV to work as >> expected on noisy images (see the example) but will protect sharp edges on >> clean images (on the example, the masks barely grabs a few pixels in the >> in-focus area). >> >> I have found that the only way we could overcome the oversensibility of >> the TV alone is by setting a window (like a band-pass filter) instead of a >> threshold (high-pass filter) because, in a noisy picture, depending on the >> noise level, the TV values of noisy and edgy pixels are very close. From an >> end-user perspective, this is tricky. >> >> Using TV × Laplacian, given that the noise stats should not vary much for >> a given sensor at a given ISO, allows to confidently set a simple threshold >> as a factor of the standard deviation. It gives more reproductibility and >> allows to build preset/styles for given camera/ISO. Assuming gaussian >> noise, if you set your threshold factor to X (which means "unmask >> everything above the mean (TV × Laplacian) + X standard deviation), you >> know beforehand how many high-frequency pixels will be affected, no matter >> what : >> >> - X = -1 => 84 %, >> - 0 => 50 %, >> - 1 => 16 % , >> - 2 => 2.5 %, >> - 3 => 0.15 % >> - … >> >> Le 01/07/2018 à 14:13, rawfiner a écrit : >> >> Thank you for this study Aurélien >> >> As far as I understand, TV and Laplacians are complementary as they >> detect noise in different regions of the image (noise in sharp edge for >> Laplacian, noise elsewhere for TV). >> Though, I do not understand why you multiply the TV and Laplacian results >> to get the mask. >> Multiplying them would result in a mask containing non-zero values only >> for pixels that are detected as noise both by TV and Laplacian. >> Is there a particular reason for multiplying (or did I misunderstood >> something?), or could we take the maximum value among TV and Laplacian for >> each pixel instead? >> >> Thanks again >> >> Cheers, >> rawfiner >> >> >> 2018-07-01 3:45 GMT+02:00 Aurélien Pierre <rese...@aurelienpierre.com>: >> >> Hi, >> >> I have done experiments on that matter and took the opportunity to >> correct/test further my code. >> >> So here are my attempts to code a noise mask and a sharpness mask with >> total variation and laplacian norms : >> https://github.com/aurelienpierre/Image-Cases-Studies/blob/master/notebooks/Total%20Variation%20masking.ipynb >> >> Performance benchmarks are at the end. >> >> Cheers, >> >> Aurélien. >> >> Le 17/06/2018 à 15:03, rawfiner a écrit : >> >> >> >> Le dimanche 17 juin 2018, Aurélien Pierre <rese...@aurelienpierre.com> a >> écrit : >> >> >> >> Le 13/06/2018 à 17:31, rawfiner a écrit : >> >> >> >> Le mercredi 13 juin 2018, Aurélien Pierre <rese...@aurelienpierre.com> a >> écrit : >> >> >> >> On Thu, Jun 14, 2018 at 12:23 AM, Aurélien Pierre >> <rese...@aurelienpierre.com> wrote: >> > Hi, >> > >> > The problem of a 2-passes denoising method involving 2 differents >> > algorithms, the later applied where the former failed, could be the >> grain >> > structure (the shape of the noise) would be different along the picture, >> > thus very unpleasing. >> >> >> I agree that the grain structure could be different. Indeed, the grain >> could be different, but my feeling (that may be wrong) is that it would be >> still better than just no further processing, that leaves some pixels >> unprocessed (they could form grain structures far from uniform if we are >> not lucky). >> If you think it is only due to a change of algorithm, I guess we could >> apply non local means again on pixels where a first pass failed, but with >> different parameters to be quite confident that the second pass will work. >> >> That sounds better to me… but practice will have the last word. >> >> >> Ok :-) >> >> >> >> > >> > I thought maybe we could instead create some sort of total variation >> > threshold on other denoising modules : >> > >> > compute the total variation of each channel of each pixel as the >> divergence >> > divided by the L1 norm of the gradient - we then obtain a "heatmap" of >> the >> > gradients over the picture (contours and noise) >> > let the user define a total variation threshold and form a mask where >> the >> > weights above the threshold are the total variation and the weights >> below >> > the threshold are zeros (sort of a highpass filter actually) >> > apply the bilateral filter according to this mask. >> > >> > This way, if the user wants to stack several denoising modules, he could >> > protect the already-cleaned areas from further denoising. >> > >> > What do you think ? >> >> >> That sounds interesting. >> This would maybe allow to keep some small variations/details that are not >> due to noise or not disturbing, while denoising the other parts. >> Also, it may be computationally interesting (depends on the complexity of >> the total variation computation, I don't know it), as it could reduce the >> number of pixels to process. >> I guess the user could use something like that also the other way?: to >> protect high detailed zones and apply the denoising on quite smoothed zones >> only, in order to be able to use stronger denoising on zones that are >> supposed to be background blur. >> >> >> The noise is high frequency, so the TV (total variation) threshold will >> have to be high pass only. The hypothesis behind the TV thresholding is >> noisy pixels should have abnormally higher gradients than true details, so >> you isolate them this way. Selecting noise in low frequencies areas would >> require in addition something like a guided filter, which I believe is what >> is used in the dehaze module. The complexity of the TV computation depends >> on the order of accuracy you expect. >> >> A classic approximation of the gradient is using a convolution product >> with Sobel or Prewitt operators (3×3 arrays, very efficient, fairly >> accurate for edges, probably less accurate for punctual noise). I have >> developped myself optimized methods using 2, 4, and 8 neighbouring pixels >> that give higher order accuracy, given the sparsity of the data, at the >> expense of computing cost : >> https://github.com/aurelienpierre/Image-Cases-Studies/blob/947fd8d5c2e4c3384c80c1045d86f8cf89ddcc7e/lib/deconvolution.pyx#L342 >> (ignore the variable ut in the code, only u is relevant for us here). >> >> Great, thanks for the explanations. >> Looking at the code of the 8 neighbouring pixels, I wonder if we would >> make sense to compute something like that on raw data considering only >> neighbouring pixels of the same color? >> >> >> the RAW data are even more sparse, so the gradient can't be computed this >> way. One would have to tweak the Taylor theorem to find an expression of >> gradient for sparse data. And that would be different for Bayer and X-Trans >> patterns. It's a bit of a conundrum. >> >> >> Ok, thank you for these explainations >> >> >> >> Also, when talking about the mask formed from the heat map, do you mean >> that the "heat" would give for each pixel a weight to use between input and >> output? (i.e. a mask that is not only ones and zeros, but that controls how >> much input and output are used for each pixel) >> If so, I think it is a good idea to explore! >> >> yes, exactly, think of it as an opacity mask where you remap the >> user-input TV threshold and the lower values to 0, the max magnitude of TV >> to 1, and all the values in between accordingly. >> >> >> Ok that is really cool! It seems a good idea to try to use that! >> >> rawfiner >> >> >> >> >> rawfiner >> >> >> >> >> > >> > Aurélien. >> > >> > >> > Le 13/06/2018 à 03:16, rawfiner a écrit : >> > >> > Hi, >> > >> > I don't have the feeling that increasing K is the best way to improve >> noise >> > reduction anymore. >> > I will upload the raw next week (if I don't forget to), as I am not at >> home >> > this week. >> > My feeling is that doing non local means on raw data gives much bigger >> > improvement than that. >> > I still have to work on it yet. >> > I am currently testing some raw downsizing ideas to allow a fast >> execution >> > of the algorithm. >> > >> > Apart of that, I also think that to improve noise reduction such as the >> > denoise profile in nlm mode and the denoise non local means, we could >> do a 2 >> > passes algorithm, with non local means applied first, and then a >> bilateral >> > filter (or median filter or something else) applied only on pixels >> where non >> > local means failed to find suitable patches (i.e. pixels where the sum >> of >> > weights was close to 0). >> > The user would have a slider to adjust this setting. >> > I think that it would make easier to have a "uniform" output (i.e. an >> output >> > where noise has been reduced quite uniformly) >> > I have not tested this idea yet. >> > >> > Cheers, >> > rawfiner >> > >> > Le lundi 11 juin 2018, johannes hanika <hana...@gmail.com> a écrit : >> >> >> >> hi, >> >> >> >> i was playing with noise reduction presets again and tried the large >> >> neighbourhood search window. on my shots i could very rarely spot a >> >> difference at all increasing K above 7, and even less so going above >> >> 10. the image you posted earlier did show quite a substantial >> >> improvement however. i was wondering whether you'd be able to share >> >> the image so i can evaluate on it? maybe i just haven't found the >> >> right test image yet, or maybe it's camera dependent? >> >> >> >> (and yes, automatic and adaptive would be better but if we can ship a >> >> simple slider that can improve matters, maybe we should) >> >> >> >> cheers, >> >> jo >> >> >> >> >> >> >> >> On Mon, Jan 29, 2018 at 2:05 AM, rawfiner <rawfi...@gmail.com> wrote: >> >> > Hi >> >> > >> >> > Yes, the patch size is set to 1 from the GUI, so it is not a >> bilateral >> >> > filter, and I guess it corresponds to a patch window size of 3x3 in >> the >> >> > code. >> >> > The runtime difference is near the expected quadratic slowdown: >> >> > 1,460 secs (8,379 CPU) for 7 and 12,794 secs (85,972 CPU) for 25, >> which >> >> > means about 10.26x slowdown >> >> > >> >> > If you want to make your mind on it, I have pushed a branch here that >> >> > integrates the K parameter in the GUI: >> >> > https://github.com/rawfiner/darktable.git >> >> > The branch is denoise-profile-GUI-K >> >> > >> >> > I think that it may be worth to see if an automated approach for the >> >> > choice >> >> > of K may work, in order not to integrate the parameter in the GUI. >> >> > I may try to implement the approach of Kervann and Boulanger (the >> >> > reference >> >> > from the darktable blog post) to see how it performs. >> >> > >> >> > cheers, >> >> > rawfiner >> >> > >> >> > >> >> > 2018-01-27 13:50 GMT+01:00 johannes hanika <hana...@gmail.com>: >> >> >> >> >> >> heya, >> >> >> >> >> >> thanks for the reference! interesting interpretation how the >> blotches >> >> >> form. not sure i'm entirely convinced by that argument. >> >> >> your image does look convincing though. let me get this right.. you >> >> >> ran with radius 1 which means patch window size 3x3? not 1x1 which >> >> >> would be a bilateral filter effectively? >> >> >> >> >> >> also what was the run time difference? is it near the expected >> >> >> quadratic slowdown from 7 (i.e. 15x15) to 25 (51x51) so about 11.56x >> >> >> slower with the large window size? (test with darktable -d perf) >> >> >> >> >> >> since nlmeans isn't the fastest thing, even with this coalesced way >> of >> >> >> implementing it, we should certainly keep an eye on this. >> >> >> >> >> >> that being said if we can often times get much better results we >> >> >> should totally expose this in the gui, maybe with a big warning that >> >> >> it really severely impacts speed. >> >> >> >> >> >> cheers, >> >> >> jo >> >> >> >> >> >> On Sat, Jan 27, 2018 at 7:34 AM, rawfiner <rawfi...@gmail.com> >> wrote: >> >> >> > Thank you for your answer >> >> >> > I perfectly agree with the fact that the GUI should not become >> >> >> > overcomplicated. >> >> >> > >> >> >> > As far as I understand, the pixels within a small zone may suffer >> >> >> > from >> >> >> > correlated noise, and there is a risk of noise to noise matching. >> >> >> > That's why this paper suggest not to take pixels that are too >> close >> >> >> > to >> >> >> > the >> >> >> > zone we are correcting, but to take them a little farther (see the >> >> >> > caption >> >> >> > of Figure 2 for a quick explaination): >> >> >> > >> >> >> > >> >> >> > >> >> >> > >> https://pdfs.semanticscholar.org/c458/71830cf535ebe6c2b7656f6a205033761fc0.pdf >> >> >> > (in case you ask, unfortunately there is a patent associated with >> >> >> > this >> >> >> > approach, so we cannot implement it) >> >> >> >> ___________________________________________________________________________ darktable developer mailing list to unsubscribe send a mail to darktable-dev+unsubscr...@lists.darktable.org
