Basis beeldverwerking (8D040) dr. Andrea Fuster dr. Anna Vilanova Prof.dr. Marcel Breeuwer Noise and Filtering

Contents Noise Mean Filters Order-statistic filters Median Alpha-trimmed 2

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 noise If 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 8

Mean Filters Blurring used to smooth images by e.g. convolution with smoothing kernel Can be used to suppress noise 9

Arithmetic Mean Filter Arithmetic mean filter replaces the current pixel with a uniform weighted average of the neighbourhood 10

Geometric Mean Filter Like arithmetic mean filter, but loses less detail 11

Harmonic Mean Filter Works well for Gaussian noise Works well for salt noise, but fails for pepper noise 12

Contraharmonic Mean Filter Is very effective in eliminating Salt-and-Pepper noise Q is the order of the filter 13

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

Contents Noise Mean Filters Order-statistic filters Median Alpha-trimmed 15

Order-statistic filters Result is based on ordering pixel values in the neighbourhood Examples: median, max, min filters 16 median min max

Contents Noise Mean Filters Order-statistic filters Median Alpha-trimmed 17

Median Filter Replaces value of a pixel by the median of its neighbourhood 18

Median filter Can be used to reduce random noise Less blurring than linear smoothing filter Very effective for impulse noise (salt-and-pepper noise) 19 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) 20

21 Original Salt-and-Pepper noise Median filteredMin filtered Max filtered 1 st quartile filtered 3 rd quartile filtered Midpoint filtered

Contents Noise Mean Filters Order-statistic filters Median Alpha-trimmed 22

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 23

Alpha-trimmed mean filter works good for combination of S&P noise and Gaussian noise 24 Image with S&P noise and Gaussian noise Alpha-trimmed image (5x5, d=6) Median filtered image (5x5)