Krita Gaussian Noise Reduction
- Krita Gaussian Noise Reduction Software
- Krita Gaussian Noise Reduction
- Krita Gaussian Noise Reduction Systems
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The noise reduction depends on the smooth width, the smooth type (e.g. Rectangular, triangular, etc), and the noise color, but the peak height reduction also depends on the peak width. The result is that the signal-to-noise (defined as the ratio of the peak height of the standard deviation of the noise) increases quickly at first, then reaches. Image processing for noise reduction Common types of noise:. Salt and pepper noise: contains random occurrences of black and white pixels. Impulse noise: contains random occurrences of white pixels. Gaussian noise: variations in intensity drawn from a Gaussian normal distribution Original Gaussian noise Salt and pepper noise Impulse noise. This one uses the gaussian algorithm to determine the fade. Out of the three auto brushes, this is the slowest. Krita is (mostly) compatible with the. Noise Image processing is useful for noise reduction. Common types of noise: Salt and pepper noise: contains random occurrences of black and white pixels Impulse noise: contains random occurrences of white pixels Gaussian noise: variations in intensity drawn from a Gaussian normal distribution Original Gaussian noise Salt and pepper noise. This one uses the gaussian algorithm to determine the fade. Out of the three auto brushes, this is the slowest. Krita is (mostly) compatible with the brush tip definitions files of these applications: abr. Gimp autobrush tip definitions. Gimp single bitmap brush tip. Can be black and white or colored.
The SUSAN Noise Filtering AlgorithmUp: SUSAN Structure Preserving Noise Reduction Previous: SUSAN Structure Preserving Noise ReductionIntroduction and Review
``Noise' can be introduced into a digitized image in many ways,starting with the lens of the imaging hardwareand ending at the digitization of the captured image. The reduction of noisewithout degradation of the underlying image has attracted muchattention in the past. However, whilst many ``structure preserving'filters have achieved some degree of success at preserving onedimensional image structure, very few have successfully preserved twodimensional image brightness structure, such as corners and junctions.
This section describes the SUSAN noise filteringalgorithm. This uses local measurements to obtain noise reductionwhilst preserving both one and two dimensional image structure. Themethod is based on image region determination using a non-rigid (infact, spatially undetermined) region model.
The simplest noise reduction method is the sliding mean or box filter (see [35]). Each pixel value is replaced bythe mean of its local neighbours. The Gaussian filter is similarto the box filter, except that the values of the neighbouring pixelsare given different weighting, that being defined by a spatialGaussian distribution. The Gaussian filter is probably the most widelyused noise reducing filter. It has been incorporated into the designof many algorithms such as the Canny edge detector (see[9]). The Gaussian filter is pleasing because Fourieranalysis shows that the Gaussian spatial distribution gives a Gaussianfrequency distribution, leading to a good (often described as``optimal') tradeoff between localization in the spatial and in thefrequency domains. The sharp cutoff of the box filter causes it togive a noisier output than the Gaussian (see the discussion in[9]) corresponding to a less well localized frequencyresponse.
More complicated ``optimal' statistical estimators have been derivedwhich use local means and autocorrelation functions to calculate theunderlying signal (for example Wiener filtering -- see[49]). However, these methods are usually very slow.
Linear filters such as the box and the Gaussian filters tend to createmore blurring of image details than do most non-linear filters. Anincrease in their ability to smooth noise corresponds to an increasein the blurring effect.
Many non-linear filters fall into the category of order statisticneighbour operators. This means that the local neighbours are sortedinto ascending order (according to their value) and this list isprocessed to give an estimate of the underlying image brightness. Thesimplest order statistic operator is the median (see[69]), where the central value in the ordered list is usedfor the new value of the brightness. The median filter is much betterat preserving straight edge structure than Gaussian smoothing, but ifthe edge is curved then image degradation occurs. At corners, othertwo dimensional features and thin lines the median does not performwell with regard to structure preservation. The median is good atreducing impulse noise (for example ``salt and pepper' noise) wherethe noisy pixels contain no information about their original values.
There have been several variations on the median filter, for examplethe weighted median filter (see [7]) selectivelygives the neighbouring pixels multiple entries to the ordered list,usually with the centre pixels of the neighbourhood contributing moreentries. The higher the weighting given to the central pixel, thebetter the filter is at preserving corners, but the less the smoothingeffect is. At corners, other pixels within the convex image regionincluding the centre pixel are not given any higher weighting thanthose outside, so this is an ineffective way of preserving the cornerstructure. Other methods include the contrast-dependentthresholded median (see [55]), adaptive decimatedmedian filtering (see [1]) and the midrangeestimator (see [2]), which places the brightness estimatehalfway between the maximum and minimum local brightness values.
Three similar filters, the first two of which are typical of morecomplicated order statistic operators, are the K-nearestneighbour operator (see [13]), the -trimmedmean (see [5]) and the sigma filter (see[30]). The K-nearest neighbour operator takes the mean ofthe K nearest neighbours from within the ordered list. The valuewhich K is usually set to (5 or 6 when a 3 by 3 mask is used) meansthat corners and thin lines are badly corrupted. The trimmed meanoperator takes the mean of the remaining entries in the ordered listonce the first and last entries in the list (originallycontaining N entries) have been thrown away. The sigma filter takesan average of only those neighbouring pixels whose values lie within of the central pixel value, where is found once forthe whole image. This attempts to average a pixel with only thoseneighbours which have values ``close' to it, compared with the imagenoise standard deviation.
The peak noise filter is specifically designed to remove impulseor peak noise. A pixel's value is compared with the local mean. If itis close then the value remains unchanged. If it is very differentthen the pixel's value is replaced by the local mean. A more advancedversion of this takes a weighted mean of the central value and thelocal mean, the weighting depending on the difference between thesetwo quantities and also on the local brightness variance. This issimilar to the contrast-dependent thresholded median filter, andagain, is not very good at structure preservation.
In [47] Perona and Malik use local image gradient tocontrol anisotropic diffusion; smoothing is prevented fromcrossing edges. This is, in a sense, an opposite approach to theK-nearest neighbour, sigma and SUSAN filters, which work out whichneighbours to include in smoothing; anisotropic diffusion works outwhich neighbours to exclude. In [54] Saint-Marc et al. ``refine and generalize' the approach of Perona and Malik,using many iterations of a 3 by 3 mask which weights a mean of theneighbours' values according to the edge gradient found at eachneighbours' position. This method shall be referred to as the SMCMfilter. Because pixels both sides of an edge have high gradientassociated with them, thin lines and corners are degraded by thisprocess. This problem is also true with Perona and Malik's method. Biased Anisotropic Diffusion (see [44]) usesphysical diffusion models to inhibit smoothing across boundaries,according to a cost functional which attempts to minimize acombination of desired components. These individual costs are imagesmoothness and quality of fit between original and smoothed image.This type of approach is similar to the weak membrane model (see[6]) which fits a membrane to the image surface, allowingit to ``break' at significant discontinuities, incurring a cost,which is balanced against the ``badness of fit' cost. This methodtends to be very computationally expensive.
Specific surface model fitting techniques have been developed;for example, in [59] a two stage surface fitting method isused. In the first stage a moving least median of squares of errors ofa fit to planar facets is used. This is similar to a least meansquares fit to a plane, but uses the median of the errors instead ofthe mean so that discontinuities are correctly fitted. However,corners are rounded, as with the standard median smoothing; this isexpected, and can be clearly seen in the results presented. The secondstage fits a weighted bicubic spline to the output of the first stage.As with this approach in general, the success is limited by the modelused; image structure not conforming to the model will not be wellpreserved.
Morphological noise suppression, using mathematical morphology,is related to order statistic neighbour operators. In [43]this type of operator is discussed and compared with other filters.Noble reports that morphological filters perform worse than the movingaverage and median filters for Gaussian type noise and slightly betterthan these for ``salt and pepper' noise.
Krita Gaussian Noise Reduction Software
The hysteresis smoothing approach (see [17]) followspositive and negative gradients in the image, only allowing changes inthe gradient when the change is significant, i.e., the new gradientcontinues further on in the image. The results of using this approach,tested in [24], were not very encouraging, showing a decrease in the signal to noise ratio with each of four differenttypes of noise.
The selected-neighbourhood averaging (e.g., see [40])method chooses a local neighbourhood to smooth over based on a varietyof criteria. Each pixel can be part of several different ``windows';the one chosen to smooth over is the most homogeneous window whichcontains the pixel in question as part of its homogeneity. Variouswindow shapes have been tried. These methods are limited to succeedingonly on those parts of the image which obey the model used. Sharpcorners, for example, will not be correctly dealt with by a squarewindow. A variation on these algorithms is the use of a thin windowwhich is perpendicular to the direction of maximum gradient. Clearlythe structure preserving success of this is limited to relativelystraight edges.
The symmetric nearest neighbours (see [27]) approachtakes each symmetric pair of neighbouring pixels and uses the closervalue to the centre pixel from each pair to form a mean output value.Again this is not well suited to preserving corners.
In [31] three methods of noise reduction using different localimage measurements to avoid destroying image structure are presented,all based on the assumption that image regions bounded by edges have constant value. In the first method, image edges are found, andfor each image position the local edge structure is matched to a listof binary templates which attempt to cover all possible straight edgeconfigurations. Each template has a corresponding weight matrix whichdetermines which elements of the local neighbourhood should be usedfor smoothing. The system attempts to cope with junctions by taking aconvex combination of the different matrix outputs, each weightedaccording to the quality of the match between the actual local edgeconfiguration and the template. This process is applied iteratively.Although edge structures are well preserved, corners are rounded andramps are flattened. In the second method the local image gradient iscalculated in several different directions, and the results of thisare combined to give a smoothing matrix which attempts to smooth onlyover the bounded constant image region which includes the centralpixel. Again, this is applied iteratively. The second method suffersfrom the same problems as the first method. The third method uses probabilistic relaxation where each pixel has a probabilitydistribution amongst the entire set of possible values, thus vastlyincreasing the data set. The initial distribution is assumed to beGaussian. Relaxation is then used to allow the pixels' distributionsto interact to find a stable best estimate of the underlying signal.The results given suggest that this method does not in general work aswell as the first two.
Krita Gaussian Noise Reduction
The gradient inverse weighted operator (see [73]) formsa weighted mean of the local pixels, with the weights depending on thedifference between the central pixel's value and the value of thelocal pixels;
where is the original image, is the smoothed image,and the summation is taken over a 3 by 3 square neighbourhood. Thefilter is applied iteratively, typically five times. No presetthreshold is needed. This method reduces Gaussian noise well whilstpreserving image structure. Impulse noise would be much better dealtwith if the central pixel were excluded from the two sums inEquation 34, for obvious reasons, but this was not includedin the method.
Finally, image averaging using many images of the same scene (takenquickly one after another) has been used to reduce image noise. Forexample, see [57]. However, for many image processingapplications this approach is impractical; the camera may be moving,the scene may be changing, and it may be necessary to use every imagein its own right.
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