Presentation on theme: "Manuel Gomez-Rodriguez* Jens Kober† Bernhard Schölkopf†"— Presentation transcript:
1Denoising photographs using dark frames optimized by quadratic programming Manuel Gomez-Rodriguez*Jens Kober†Bernhard Schölkopf††Max Planck Institute for Biological CyberneticsTübingen*Electrical Engineering DepartmentStanford University
2Long exposure photographs Long exposure photographs (e.g., astronomical photographs) contain substantial amounts of noise.Dark current noise is the dominant source of noise in long exposure photographs.We have access to samples of the joint distribution of the noise of our camera using bias frames and dark frames
3Noise profileA bias frame – raw image taken with closed shutter and exposure time ~ 0 seconds. The bias value is cased by the readout noise.A dark frame – raw image taken with closed shutter and nonzero exposure time. It contains a bias frame plus a component that increases with exposure time, in a way that depends on several other factors (i.e. temperature, ISO setting, …)A light frame – raw image to denoise.
4The problemGiven the observed image I + D and a few points sampled from the multidimensional noise distribution, we want to estimate I.X1X2XNDINoise distribution
5The problemWe want to include the joint statistics of the sensor noise in our denoising methodHow should we combine the dark frames?Does it generalize to different conditions?Is the problem computationally tractable?Given a noisylong exposure settingA library of darkframesDenoised image
6Naïve approachSingle dark frame: record a dark frame of matching exposure time after each long exposure. This dark frame is subtracted from the light frameIt is implemented on commercial camerasIt doubles the amount of timeThe temperature tends to changeOne-point sample from the joint distribution of the noise
7Average of dark frames approach Average of dark frames: a set of dark frames under conditions matching the ones of the light frame. The mean of the set is substracted from the light frame.Used, for example, in astrophotographyWorks well for professional cooled CCDs with precise temperature controlBetter estimate of the expected noise (multi-point sample)
8Our approachThe distribution of noise for a given camera depends on various conditions, including temperature, ISO settings and exposure time.If we knew the conditions for the image to be denoised, we should ideally use a library that matches the conditions of the image. But,The exact temperature is usually unknownWe cannot store dark frames for every possible condition
9Our approachOur method generates a synthetic dark frame from the convex hull of the dark frames D(1)…D(N), taken under different conditions,such that subtracting it from a noisy image optimizes a quality measure or prior for the class of images to denoiseX1X2XNDINoise distributionImage prior
10Optimization problemIf the quality measure is the smoothness of the image (i.e. discrete derivative), the convex optimization problem can be formulated as,whereis the variable, is a real convex cost function, is a set of evaluation points and is the 8-neighbor set of the location in the raw image
11Quadratic programming problem If a quadratic penalty function, , is chosen, the optimization problem is equivalent to the following quadratic program (QP)where
12Solution of the QPA solution that generalizes well to the full image should be sparse because only the dark frames that were taking under similar conditions as the noisy image should be used for denoising; this is enforced by the constraints and , implying= 1Our method also allows to estimate in an indirect way the exposure time, temperature and ISO of a photograph
13Evaluation pointsAs evaluation points, we use points that have high variance between dark frames and,The selection of evaluation points is done only once for a specific camera and a relatively low number of evaluation points (~1000) is enoughThe complexity does not depend on the size of the images but the # of dark framesAs the solution is usually sparse, we only need to load a few full dark frames to denoise
14EvaluationThe same evaluation metric in the training set S and the test set T to numerically evaluate the performance; however S and T are disjoint → True generalization performanceDark frames taken with a Canon EOS 1Ds with,ISO of 800, 1000, 1250Exposure times 1, 2, 4, 8,… 128 seconds, and 21 secondsVarious temperature conditionshave been used for the analysis
15EvaluationThree problem instances in increasing order of difficulty are proposed to validate our method,TemperatureExposure time1st problemConstant and matching the noisy imageVariable, including the same exposure time as the noisy image2nd problemVariable3rd problemVariable, not including the same exposure time as the noisy image
16Evaluation: 1st caseLight frame with ISO 800, 16 seconds of exposure time18 dark frames: constant temperature, variable exposure timeCorrect exposure time!Not used!
17Evaluation: 2nd caseLight frame: ISO 1000, 16 seconds of exposure time175 dark frames: variable temperature, variable exposure timeNot used!Correct exposure time!
18Evaluation: 3rd caseLight frame: ISO 1000, 21 seconds of exposure time175 dark frames: variable temperature, variable exposure time (not inc. 21 sec)200 evaluation points!
19Noisy imageOur methodHorsehead nebula Barnard 33 in nebula IC 434, flame nebula NGC 2024, Canon EOS 5D with 300mm f/2.8 lens
20Bilateral filter Our method Horsehead nebula Barnard 33 in nebula IC 434, flame nebula NGC 2024, Canon EOS 5D with 300mm f/2.8 lens
21Wavelet denoising Our method Horsehead nebula Barnard 33 in nebula IC 434, flame nebula NGC 2024, Canon EOS 5D with 300mm f/2.8 lens
22Our method + wavelet denoising Horsehead nebula Barnard 33 in nebula IC 434, flame nebula NGC 2024, Canon EOS 5D with 300mm f/2.8 lens
23Part of Orion constellation. Combination of ca Part of Orion constellation. Combination of ca. 10 R, G, and B images, denoised using the proposed method. Canon 200mm lens, SBIG CCD camera using Kodak KAF CCD chip
25ConclusionsA relatively simple method with low complexity can help denoise long exposure images in raw formatOur method can beneficially be combined with image-based noise reduction methodsIf available, our method could use evaluation points from the "optical black” (an area around the main image portion of the sensor which does not get light).We believe that the proposed method can become a practical tool for digital photography