Transcript Min filter
Basis beeldverwerking (8D040) dr. Andrea Fuster Prof.dr. Bart ter Haar Romeny 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 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 9 Mean Filters • Blurring used to smooth images by e.g. convolution with smoothing kernel • Can be used to suppress noise 10 Arithmetic Mean Filter • Arithmetic mean filter replaces the current pixel with a uniform weighted average of the neighbourhood 11 Geometric Mean Filter • Like arithmetic mean filter, but loses less detail 12 Harmonic Mean Filter • Works well for Gaussian noise • Works well for salt noise, but fails for pepper noise 13 Contraharmonic Mean Filter • Is very effective in eliminating Salt-and-Pepper noise Q is the order of the filter 14 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 15 Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed 16 Order-statistic filters • Result is based on ordering pixel values in the neighbourhood • Examples: median, max, min filters min median max 17 Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed 18 Median Filter • Replaces value of a pixel by the median of its neighbourhood 19 Median filter • Can be used to reduce random noise • Less blurring than linear smoothing filter • Very effective for impulse noise (salt-and-pepper noise) Mean filtering Median filtering9x9 3x3 3x3 9x9 20 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) 21 rd st Max filtered Original Salt-and-Pepper filtered 3Midpoint quartile filtered noise 1 Median quartile Min filtered filtered filtered 22 Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed 23 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 24 • Alpha-trimmed mean filter works good for combination of S&P noise and Gaussian noise Alpha-trimmed image (5x5, d=6) noise Image with Median S&Pfiltered noise and image Gaussian (5x5) 25