Basis beeldverwerking (8D040)
dr. Andrea Fusterdr. Anna VilanovaProf.dr. Marcel Breeuwer
Noise and Filtering
Contents
• Noise• Mean Filters• Order-statistic filters
• Median• Alpha-trimmed
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Gaussian Noise
• Gaussian noise follows a Gaussian distribution
Average =
Standard deviation =
• Good approximation of noise that occurs in practical cases.
Additive Gaussian Noise Example
Impulse Noise Model
• Bipolar impulse noise follows the following distribution
If or is zero, we have unipolar impulse noiseIf both are nonzero, and almost equal, this is also called salt-and-pepper noise
Impulse Noise
• Impulses • can be positive and negative• are often very large• can go out of the range of the image• appear as black and white dots, saturated peaks
Impulse Noise Example
Contents
• Noise• Mean Filters• Order-statistic filters
• Median• Alpha-trimmed
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Mean Filters
• Blurring used to smooth images by e.g. convolution with smoothing kernel
• Can be used to suppress noise
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Arithmetic Mean Filter
• Arithmetic mean filter replaces the current pixel with a uniform weighted average of the neighbourhood
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Geometric Mean Filter
• Like arithmetic mean filter, but loses less detail
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Harmonic Mean Filter
• Works well for Gaussian noise• Works well for salt noise, but fails for pepper noise
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Contraharmonic Mean Filter
• Is very effective in eliminating Salt-and-Pepper noise
Q is the order of the filter
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Contraharmonic Mean Filter
• If Q=0, this is the arithmetic mean filter• If Q=-1, this is the harmonic mean filter• If Q<0, salt noise is eliminated• If Q>0, pepper noise is eliminated
• For examples, see book page 324-325
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Contents
• Noise• Mean Filters• Order-statistic filters
• Median• Alpha-trimmed
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Order-statistic filters
• Result is based on ordering pixel values in the
neighbourhood• Examples: median, max, min filters
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medianmin
max
Contents
• Noise• Mean Filters• Order-statistic filters
• Median• Alpha-trimmed
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Median Filter
• Replaces value of a pixel by the median of its neighbourhood
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Median filter
• Can be used to reduce random noise• Less blurring than linear smoothing filter• Very effective for impulse noise (salt-and-pepper
noise)
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Mean filtering 3x3Mean filtering 9x9Median filtering 3x3Median filtering 9x9
Max and min filters
• Max filter:− Take maximum of ordered pixel values− Find brightest points of an image (so: filters pepper
noise)
• Min filter:− Take minimum of ordered pixel values− Find darkest points of an image (filters salt noise)
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Original Salt-and-Pepper noiseMedian filteredMin filteredMax filtered1st quartile filtered3rd quartile filteredMidpoint filtered
Contents
• Noise• Mean Filters• Order-statistic filters
• Median• Alpha-trimmed
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Alpha-trimmed mean filter
• Delete d/2 lowest and d/2 highest values of from neighbourhood
• remains• d=0 arithmetic mean filter• d=mn-1 median filter
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• Alpha-trimmed mean filter works good for combination of S&P noise and Gaussian noise
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Image with S&P noise and Gaussian noiseAlpha-trimmed image (5x5, d=6)Median filtered image (5x5)