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)