Topic -3 Image Enhancement
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- Archibald Edwards
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1 Topic -3 Image Enhancement (Pat 1) DIP: Details Digital Image Pocessing Digital Image Chaacteistics Spatial Spectal Gay-level Histogam DFT DCT Pe-Pocessing Enhancement Restoation Point Pocessing Masking Filteing Degadation Models Invese Filteing Wiene Filteing Compession Infomation Theoy Lossless Lossy LZW (gif) Tansfom-based (jpeg) Segmentation Edge Detection Desciption Shape Desciptos Textue Mophology 1
2 Why Image Enhancement? To pocess an image so that the esult is suitable fo specific application. Selection of technique is vital Noise emoval, Smoothing, Highlighting edges, Shapening, Impoving contast, Poblem of poo lighting. IE in two domains Spatial domain, Fequency domain. Oveview of Spatial domain. Domain efes to aggegate of pixels Opeate diect on the pixels. g ( x, y) = T[ f ( x, y)] f(x,y) input image g(x,y) Output image T is opeato on define ove neighbohood of (x,y) 2
3 3
4 Schematic epesentation f(x,y) g(x,y) f(x,y) g(x,y) Point pocessing Global pocessing (x,y) f(x,y) g(x,y) Neighbohood pocessing. Pixel Neighbouhoods - eview A neighbouhood is a egion adjacent to a given pixel 4-neighbous 2 hoizontal plus 2 vetical D-neighbous - 4 diagonal 8-neighbous - 4 diagonal plus 4 neighbous 4-neighbous D-neighbous 8-neighbous 4
5 Initial mask position Opeation Diection of movement of the mask is top left to bottom ight of the image Image Final mask position Gay level tansfomation functions fo contast enhancement If neighbohood = 1x1 Simple point pocessing s = T () Contast Stetching Thesholding function 5
6 Oveview of Fequency domain Convolution theoem is the foundation g ( x, y) = h( x, y) * f ( x, y) G( u,v ) = g( x, y ) = H( u,v )F( u,v ) f 1 [ H( u,v )F( u,v )] H(u,v) Tansfe function, Optical tansfe function, Modulation tansfe function - Pope choice of H(u,v) is necessay to achieve g(x,y) with desied featues Quality Testing afte enhancement Human Peception Machine Peception 6
7 Enhancement by Point Pocessing Image Negatives Applied in Medical application, Photogaphing with monochome film slide pepaation L-1 To obtain the negative of an image with gay levels in the ange of [0, L-1], use the negative tansfomation: s L-1 s = (L 1) whee, L = gay levels s = gay value of the output = gay value fom the input image Example Negative image is useful fo enhancing white o gay detail embedded in dak egions of an image (especially when the black aeas ae dominant in size) 7
8 Contast Stetching Low contast poo lighting, lack of ange of imaging senso M: imadjust Contast Stetching Result ( 1, s 1 ) = ( min, 0) ( 2, s 2 ) = ( max, L-1) 1 = 2 = mean gay level in the image s 1 = 0 and s 2 = L - 1 Thesholding Result 8
9 Compession of Dynamic ange Dynamic ange of pocessed image may exceed the capacity of display device Log tansfomation: s = c log( 1+ Use to expand the values of dak pixels in an image while compessing the highe-level values ) Gay level slicing To highlight specific ange of gay level in an image Example enhancing flaws in a x-ay image. 2 appoaches: Appoach 1: Fig. 3.11(a): highlight the desied ange esult: binay image shown in Fig. 3.11(d) Appoach 2: Fig. 3.11(b): Bightens the desied ange of gay levels but peseved the backgound and othe gay levels 9
10 Bit Plane Slicing Instead of highlighting ange gay-level anges, contibution made to image by specific bits may consideed. Highe ode bits contain the majoity of the visually significant data 10
11 Histogam Pocessing Histogam of a digital image with gay-levels in the ange [0, L-1] is a discete function: h( k ) = n k whee, k = kth gay level and n k = numbe of pixels in the image having gay level k Common pactice to nomalize a histogam: p( k ) = n k /n whee, n = total numbe of pixels in the image and k = 0,1,2,3.., L-1 o [0, L-1] In othe wods, p( k ) gives an estimate of the pobability of occuence of gay level k # Plot of this function gives global desciption of the image # But does not specify about the content of the image # Shape histogam give useful infomation fo enhancement h( k ) = n k k p( k ) = n k /n k An image whose pixels: occupy the entie ange + distibuted unifomly high-contast appeaance and lage vaiety of gay tones 11
12 Histogam Equalization Let be the vaiable fo gay levels of the image to be enhanced; Assumed has been nomalized to [0 1], with = 0 (black) and = 1 (white) Tansfomation: s = T() 0 1 poduces a level s fo evey pixel value in the oiginal image and the tansfomation function T() satisfies: (1) T() is single valued function (2) T() is in ange [0 1] fo [0 1] = T -1 (s) -- invese tansfom (both condition satisfied) Gay level in an image may be viewed as andom quantities in the inteval [0 1] that can be descibed using Pobability Density Function (PDF) If gay level is continuous chaacteized by PDF, p () and p s (s) Fom pobability theoy if p () and T() ae known and T -1 (s) satisfies condition (1), the pobability density function of the tansfomed gay: d ps ( s) = p ( ) ds 1 = T ( s) Enhancement tech is based on modifying the appeaance of an image by contolling PDF Conside the following tansfomation function: s = T( ) = p ( w) dw whee, - w is the dummy vaiable of integation - Right-hand Side (RHS) is the cumulative distibution function (CDF) of andom vaiable - Since PDF ae always positive and integal of a function is the aea unde the function, conditions (1) and (2) ae satisfied -- A (3.3-4) 12
13 13 Deivative of A w..t s () p d ds = --B Sub B in ) ( 1 ) ( ) ( s T s ds d p s p = = [1] ) ( 1 ) ( ) ( ) ( 1 1 ) ( = = = = = s p p s p s T s T s Becomes unifom density function Eqn. (3.3-8): a discete vesion of Eqn. (3.3-4) (Eqn. (A)) and is mapping called histogam equalization/histogam lineaization
14 Histogam Specification Histogam Equalization: poduce an output image that has a unifom histogam Histogam specification/histogam Matching: poduce an output image with a specified histogam o PDF Steps to implement histogam specification: (1)Equalize the image (2)Specify the desied PDF, obtain the tansfomation (3)Apply the invese tansfom on PDF in (1) 14
15 Image contains a lot of Dak colos Results of Image Equalization: Light, appeaance white-washed Oiginal Histogam 15
16 Local Enhancement Enhancement based on local Statistics Let, (x,y) = coodinates of a pixel in an image and S xy = subimage of specified size centeed at (x,y) 16
17 17
18 Enhancement using Aithmetic/Logic Opeations Image Subtaction Image subtaction is useful fo enhancement of diffeences between images 18
19 Mask mode adiogaphy The spinal cod in bight colo in Fig (a) becomes quite dak in Fig (b) X-ay image of the top of a patient s head 19
20 Image Aveaging Conside a noisy image fomed by addition of noise to an oiginal image: Image Aveaging 20
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