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# Class Note for ECE 482 at UA-Comp Visn Dig Image Proc(6)

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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Alabama - Tuscaloosa taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

Computer Vision amp Digital Image Processing Image Restoration and Reconstruction Electrical amp Computer Engineering Dr D J Jackson Lecture 131 OrderStatistic filters Median filter Max and min filters Midpoint filter Alphatrimmed mean filter Electrical amp Computer Engineering Dr D J Jackson Lecture 132 Median filter Replaces the value of a pixel by the median of the pixel values in the neighborhood of that pixel my mediamgw mew The pixel at Xy is included in the calculation Works well for various noise types with less blurring than linear filters of similar size Odd sized neighborhoods and efficient sorts yield a computationally efficient implementation Most commonly used orderstatistic filter Ele nczl a Cnmrluler Enmneennu m n l lzcksnn Lecture 11 Median filter example lllllllll lll lllll I mung 39 m Lilli l iii m lllll Ele nczl a Cnmrluler Enmneenn Max and min filters The 100th percentile lter or max lter is given by x y max gum 52st Useful for nding the brightest points in an image Tends to reduce pepper noise ie dark pixel values The 0th percentile lter or min lter is given by my mimgm 52st Both lters require a data sort Electrical amp Computer Engineering Dr D J Jackson Lecture 135 Max and min filter examples ltering Fig 58a with a max filter of size 3 X 3 b Result I of filtering 58b with a min filtei of the same size ll ill ttttt I lit ttttt Electrical amp Computer Engineering Dr D J Jackson Lecture 136 Midpoint filter Replaces the value of a pixel by the midpoint between the maximum and minimum pixels in a neighborhood A 1 f xy maxgst m1ngst 2 masw masw Combines order statistics and averaging Works best for randomly distributed noise eg Gaussian or uniform Electrical amp Computer Engineering Dr D J Jackson Lecture 137 Alphatrimmed mean filter If we delete the d2 lowest and the d2 highest intensity values from a neighborhood gst of size mn and let gst represent the remaining mnd pixels the average of the remaining pixels is called an alphatrimmed mean filter and is given by fxy grst 7 d Loewa d can vary from O to mn l f d0 the filter becomes the arithmetic mean filter f dmn1 the filter reduces to a median filter Electrical amp Computer Engineering Dr D J Jackson Lecture 138 Alphatrimmed mean filter example llll ill lllllllll Milli 23 e f FIGURE 5 2 a Image corrupted by additive uniform noise b Image additionally corrupted by additive saltand peppei39 noise Image b ltered 39 with a 5 X 5 c aiithmetic 39 1 1 11 m l mean filter I l l l m lllll l l l l in All d 39 mean filter e median filter mm and f alpha g trimmed mean mquot lterwith d 5 Electrical amp Computer Engineering Dr D J Jackson Lecture 139 Adaptive filters All filters considered thus far are applied to an image without regard for how image characteristics may vary from one point to another in the image An adaptive filter is one whose behavior can change based on statistical characteristics of an area within the image This is typically the mn filter region in the 5ny window Generally provides superior performance at the cost of increased filter complexity Electrical amp Computer Engineering Dr D J Jackson Lecture 1310 Adaptive local noise reduction filter The mean and variance are reasonable parameters upon which to base a simple adaptive filter They are closely related to image properties The mean gives the average intensity over a region The variance gives a measure of the contrast in a region A simple lter will operate on a local region S with the response at any point Xy base on four quantities The value of the noisy image at xy gXy The variance ofthe noise corrupting fXy to form gxy lt52n The local mean of the pixels in SW mL The local variance ofthe pixels in SW 02L Electrical amp Computer Engineering Dr D J Jackson Lecture 1311 Adaptive local noise reduction filter algorithm If 02n0 return the value gXy This is the zeronoise case where gXy fXy If the local variance 02L is high relative to 32 return a value close to gXy A high local variance is generally associated with image features ie an edge etc and should be preserved If 02L 32 return the arithmetic mean ofthe pixels In Sny This occurs ifthe local area has the same properties as the overall image Local noise is reduced by averaging Electrical amp Computer Engineering Dr D J Jackson Lecture 1312 Adaptive local noise reduction filter equation An adaptive expression may be written as A 02 my gltxycG 2gxycmll L The only quantity that must be known is 62 Everything else can be computed from Sxyy An assumption here is that ngozL This is generally reasonable given that the noise we are considering is additive and position independent If this is not true then a simple test could set the ratio of the variances to one if G2ngt62L Electrical a Cnmrluler Enmneennn m n l Jacksnn Lecture 13713 Adaptive local noise reduction filter example l I ll lll lllll l l l m lllll mg l c Electrical a Cnmrluler Enmneennn m n l Jacksnn Lecture 13715 Adaptive median filter A median lter works well in the spectral density of the impulse noise is not large A Pa and Fquot1 less than 02 is a good general rule ofthumb An adaptive median lter can handle noise with probabilities greater than these An additional bene t is that the adaptive median lter attempts to preserve detail while smoothing the impulse n0se The adaptive median filter works in a rectangular window area S The size of SM is not fixed The output of the filter is a single value that will be used to replace the center value of S Electrical amp Computer Engineering Dr D J Jackson Lecture 1315 Adaptive median filter algorithm Consider the following Stage A1 notation A1 Zmed Zmin A2 Zmed Zmax 2mm minimum intensity value in SW If A1IgtO AND A2501 90K Stage B 2m maximum intensity value in SW Else Increase W39ndow Slze 2mm median intensity of values in SW lf WindOW Size Ssmax repeat Stage A zxy intensity value at xy Else output Zmed Smax maximum allowed size of SW Stage B o The algorithm works in two B1 zxyy z stages denoted A and B B2 zxyy 275X If B1 gt0 AND B2lt0 output 2 Else output zmed min Electrical amp Computer Engineering Dr D J Jackson Lecture 1316 Adaptive median filter example l ii iii l l I m ii39ii 39 7 l abc FIGURE 514 a Image corrupted by sallaudpepper noise with probabilities Pu Pb 025 b Result of ltering with a 7 gtlt 7 median like 2 Result of adaptive median filtering with sm 7 7 Electrical amp Computer Engineering Dr D J Jackson Lecture 1317

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