Outline for ECE 482 at UA-Comp Visn Dig Image Proc(2)
Outline for ECE 482 at UA-Comp Visn Dig Image Proc(2)
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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 14 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 121 Outline Periodic noise Estimation of noise parameters Restoration in the presence of noise only spatia e ng Electrical amp Computer Engineering Dr D J Jackson Lecture 122 Periodic noise Periodic noise typically arises from interference during image acquisition Spatially dependent noise type a h FIGURE 55 zl Imugc corrupted by sinusoidal noise r b Spectrum 39 each pair of conjugal 39 Can be impulses e eCtively corresponds to reduced via one sine wave frequency rial image domain filtering 39 b 1 Electrical amp cirrnnuler Engineering Dr D l Jedrsnn Le ure1273 Sample periodic imaes and their spectra Electrical amp cirrnnuler Engineering Dr D l Jedrsnn Lecture 124 Sample periodic images and their spectra Eiectrrczi a Cnmrluler Enmneerme Dr D l Jamsnn Lecture 1275 Estimation of noise parameters Noise parameters can often be estimated by observing the Fourier spectrum of the image Periodic noise tends to produce frequency spikes Parameters of noise PDFs may be known partially from sensor specification Can still estimate them for a particular imaging setup One method Capture a set of at images from a known setup Le a uniform gray surface under uniform illumination Study characteristics of resulting images to develop an indicator of system noise Eiectrrczi a Cnmrluler Enmneerme Dr D l Jamsnn Lecture 12 s Estimation of noise parameters continued If only a set of images already generated by a sensor are available estimate the PDF function ofthe noise from small strips of reasonably constant background intensity Consider a subimage S and let psz i012L1 denote the probability estimates ofthe intensities of the pixels in S o L is the number of possible intensities in the image The mean and the variance ofthe pixels in S are given by L71 L71 2 Zzipszi and 0 2 2zi Z2pszi i0 i0 Electrical amp Computer Engineering Dr D J Jackson Lecture 127 Estimation of noise parameters continued The shape ofthe noise histogram identifies the closest PDF match lfthe shape is Gaussian then the mean and variance are all that is needed to construct a model for the noise ie the mean and the variance completely de ne the Gaussian PDF lfthe shape is Rayleigh then the Rayleigh shape parameters a and b can be calculated using the mean and variance lfthe noise is impulse then a constant with the exception ofthe noise area of the image is needed to calculate Pa and Pb probabilities forthe impulse PDF Electrical amp Computer Engineering Dr D J Jackson Lecture 128 Histograms from noisy strips of an area of an image ahc FIGURE 56 Histograms computed using small strips shown as insens from a the Gaussian b the Rayleigh and c the uniform noisy images in Fig 54 Electrical amp Computer Engineering Dr D J Jackson Lecture 128 Restoration in the presence of noise only spatial filtering When only additive random noise is present spatial ltering is commonly used to restore images Common types Mean filters OrderStatistic filters Adaptive lters Electrical amp Computer Engineering Dr D J Jackson Lecture 1210 Mean filters arithmetic Arithmetic mean filter Computes the average value ofa corrupted image gXy in the area de ned by a window neighborhood fxyi Zgw mn LOSSW The operation is generally implemented using a spatial lter of size mn in which all coef cients have value 1mn A mean filter smoothes local variations in an image Noise is reduced as a result of blurring Electrical amp Computer Engineering Dr D J Jackson Lecture 1211 Mean filters geometric Geometric mean filter A restored pixel is given by the product ofthe pixels in an area de ned by a window neighborhood raised to the power 1mn 1 fxy Hawk 506 Achieves smoothing comparable to the arithmetic mean lter but tends to loose less detail in the process Electrical amp Computer Engineering Dr D J Jackson Lecture 1212 Arithmetic and geometric mean filter examples ill Lilli i ii Ele rlczl a CnmnulerEnmneennn ur212713 Mean filters harmonic Harmonic mean filter A restored pixel is given by the expression mn fxy 1 Elev 090 Works well for salt noise fails for pepper noise Works well for Gaussian noise also Ele rlczl a cumrmer Enmneennu m n l Jamsnn Le ure 12715 Mean filters contraharmonic Contraharmonic mean filter A restored pier is given by the expression 2 gs I 21 c 7 506 fx 0 a Z my 506 Q is the order ofthe lter Works well for salt and pepper noise cannot do both simultaneously Q eliminates pepper noise Q eliminates salt noise Q0 gt arithmetic mean lter Q1 gt harmonic mean lter Elemnezl a Cnmrluler Enmneennu m n l Jamsnn Lecture 12715 Contraharmonic mean filter examples le I l I u m lllll m m lllll I iif lg Elemnezl a Cnmrluler Enmneennu m n l Jamsnn Lecture 1271s Contraharmonic mean filter examples ab FIGURE 59 Results of select ing the wrong Sign in Contraharmonic ltering a Result of ltering Fig 5321 with a con mhm monic lter ofsize 3 X 3 and Q 715 b Result of ltering 58b with Q 15 Electrical amp ComputerEngineering Dr D J Jackson Lecture 1217
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