where f(x, y): input image, g(x, y): processed image, and T: operator Or: s = T(r), where r: input pixel, and s: output pixel

Transcription

1 3 Intenit Tanfomation and Spatial Filteing - Intenit tanfomation Change the intenit of each piel in ode to enhance the image: g, T[f, ], whee f, : input image, g, : poceed image, and T: opeato O: T, whee : input piel, and : output piel a Hitogam - Hitogam: occuence of piel h k n k k : ga level, 0,, G, k,,, MATAB: G 55 fo uint8, 65,536 fo uint6, and.0 fo double n k : numbe of piel of ga level k Nomalize: 3-

2 p k n k /n n: total numbe of piel Ma conide p a the piel pobabilit: 0 p E.g., Tiffan: Eample of hitogam: Piel concentate at the high ga level, low contat p Dak Bight object, dak backgound 3-

3 Bight Good epoal - MATAB imhit function imhitim: Dipla hitogam h imhitim, b: h: hitogam, b: numbe of hitogam bin b Enhancing image uing point poceing - No change on piel value T : output piel value : input piel value 0 T 3-3

4 - Contat eveal: negative T T 0 Tiffan - Contat tetching: enhance contat though hitogam tetching Undeepoed T, if <, othewie. Oveepoed 3-4

5 3-5 <, othewie. if 0, T ow-contat, mid-ga-level < < othewie., if, if 0, T

6 3-6 Mot image: < < othewie., if, if, T Non-linea tetching A B C A B C,,

7 - MATAB imadjut function Snta: g imadjutf, [low_in high_in] [low_out high_out], gamma Map input ga level ange [low_in high_in] to ange [low_out high_out] gamma: a eal numbe indicating the mapping cuve high_out low_out low_in gamma < high_in gamma gamma > * E.g.: Fig. 3.3a # g imadjutf, [0 ], [ 0]: Fig. 3.3b contat eveal # g imadjutf, [ ], [0 ]: Fig. 3.3c # g imadjutf, [ ], [ ], : Fig. 3.3d 3-7

8 Fig. 3.3a: Oiginal digital mammogam Fig. 3.3b: Negative image Fig. 3.3c: Epending intenit Fig. 3.3d: gamma c Hitogam equalization - Hitogam equalization Stetch hitogam uch that piel value cove entie ga level ange Continuou quantitie * Aume ga level ae continuou quantitie nomalized to ange [0, ] * Intenit tanfomation: T * Pobabilit of input piel: p n /N 3-8

9 * Pobabilit of output piel: q n /N * Accumulated numbe of piel fom ga level 0 to : N N 0 pw dw w: dumm vaiable * Define cumulative ditibution function: cdf 0 pw dw * To geneate an output image whoe ga level ae equall likel, q hould be a contant Q, and 0 Q dw ; hence Q / p q / N N 0 / dw N / N T/ N N T N /N N /N 0 pw dw cdf 3-9

10 Dicete quantitie * Pobabilit of output piel i not a contant Howeve, in tem of egion, the numbe of piel in a unit egion can be contant Σ0 Q, Q / T cdf * E.g.: an image with 00 piel and ga level: 0 ~ 7 Input ga level Numbe of Output ga Ga p cdf piel level level Numbe of piel 3-0

11 MATAB hiteq function im hiteqim, e.g., ca: 3-

12 - Advantage of hitogam equalization Optimal contat Full automated adaptive, no human intevention Image nomalization: ea to compae two image taken unde diffeent lighting condition d Image aveaging - Thee i alwa noie in natual image Aume noie i added into eve piel of an ideal image: g, f, η, g: eulting image, f: ideal image, η: noie - Image aveaging: eveal image ae taken fo the ame cene, and then take thei aveage Aume Gauian noie: η ~ N0, n Totall M image: g i, f, η i,, i,,, M 3-

13 g g i i, M * Aveage:, * Epected value: E i M M { } E f, E{ η } i i i, M M { g, } E g, E [ f, η, ] M i i i i * E{ f, } f,, independent noie: E{ η, } 0 i i i * Hence, g, f, ideal image g η g η M M Inceaing M will educe the vaiance of noie e Spatial filteing - Spatial filteing Uing a mak filte to poce the image 3-3

14 Mak opeation: output piel value ome algoithm pefomed on all the piel in the neighbohood of the coeponding input piel * Size of neighbohood ize of mak * Mak lide fom left to ight, top to bottom * Same opeation i pefomed on eve piel * Neighbohood eceed image bounda: zeo padding o eplication of bode piel 3-4

15 * Eample: * Smoothing filte Spatial domain: piel aveaging, bluing Fequenc domain: attenuate high fequenc component * Smooth aea: low fequenc * Noie and edge: high fequenc owpa patial filteing Image bluing, noie eduction * 3 3 and5 5 mean filte:

16 * Gauian moothing: G, e π 5 5 Gauian mak 0.5: MATAB * w fpecial'gauian', 3, 0.5, im imfilteim, w Geneate a 3 3 Gauian filte with 0.5 and filte the image * Filte: 'gauian', 'obel', 'pewitt', 'laplacian', 'log', 'aveage', 'unhap' 3-6

17 Oiginal image Reult of moothing - Shapening filte Enhance detail and edge Spatial domain: diffeentiation; fequenc domain: attenuate low-fequenc component highpa Gadient filte * Gadient: diffeence between two neighboing point diection: f, f, f, diection: f, f, f, 3-7

18 * Gadient vecto: f f f, magnitude: f mag f f f / * Robet co-gadient opeato * Pewitt opeato G G G G 0 G * Sobel opeato G G G G 0 G g, f, f, f, f, 3-8

19 * Shapening: g, f, G, # Eample of Robet opeation: Input image F: G: Output image F G G: G:

20 * E.g.: aplacian filte G G G f, f, f, [f, f, f, ] [f, f, f, ] f, f, f, f, 4f, * aplacian mak:

21 * Shapening: g, f, f, * Shapening mak: * Eample of aplacian opeation: Input image F: G:

22 Output image F G: * ena: a ena b Reult of aplacian filteing c Reult: a b 3-

23 3-3 * aplacian filte i ve enitive to noie # Impovement: educe noie uing Gauian filte befoe aplacian filteing aplacian of Gauian filte, OG [ ],, G G G OG ; π π e e G 4 π π e e e ; π π e e G 4 π π e e e ;

24 OG, π * Matlab: w fpecial'log' e mak: MATAB: Fig. 3.7 * w fpecial'laplacian', 0, im imfilteim, w, 'eplicate'; im im - im, imhowim; Median filteing Odeing the piel unde the mak, and eplace the output cente piel with the median one emove eteme value Bet fo filteing the alt-and-peppe noie: g imnoief, 'alt & 3-4

25 peppe' Salt-and-peppe noie Reult of median filteing MATAB, e.g.: * im medfiltim Default: 3 3 mak * im medfiltim, [5 5], 'zeo' 5 5 median filte, padded with zeo * im odfiltim, 5, one3 3 3 odeed filte median: 5 th element * im odfiltim, median[:m*n], one[m n] m n odeed filte 3-5