noise and filtering

Basis beeldverwerking (8D040)

dr. Andrea FusterProf.dr. Bart ter Haar Romenydr. 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

Periodic Noise

• Periodic noise can be generated during image acquisition due to electrical interference

Original Image Abs of Fourier Transform

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)