COURSE 10 DIGITAL IMAGE PROCESSING

1. UNIVERSITY OF MEDICINE AND PHARMACY “Victor Babeş” TIMISOARAMEDICAL INFORMATICS DEPARTMENTwww.medinfo.umft.ro/dim

2. COURSE 10DIGITAL IMAGE PROCESSING

3. 1. WHY IMAGE PROCESSING? • Applications: • (a) improvement of pictorial information for human interpretation; • (b) processing of scene data for autonomous machine perception. • Landmarks: • ·early 1920s – pictures transmitted through cable between London and New York; • ·     1964 – pictures from moon, transmitted byRanger7

4. Application domains: • (a) medicine, geography, meteorology, physics, astronomy, defense, industry • (b) optical character recognition (OCR), artificial imaging systems in industry, digital processing of fingerprints, weather prediction, screening of blood samples • Human visual perception – superior to all imaging methods

5. 2. FUNDAMENTALS IMAGING MODEL • Definition: image • Two-dimensional light intensity function, notedf(x,y)denoting the intensity (luminosity) of the “image” in any point(x,y) • The nature off(x,y)may be characterised by two components: • (1) illumination i(x,y) • (2) reflectancer(x,y)

6. Definition: • The intensity of a monnochrome imagef(x,y) = the gray level – lof the image at the point (x,y) • Lmin  l  Lmax • Lmin=iminrmin si Lmax=imaxrmax • [Lmin ,Lmax] - the gray scale • in practice: [0,L] • ·l=0 is considered to be black • ·l=L is considered to be white

8. IMAGE SAMPLING AND QUANTIZATION • Uniform sampling and quantization • ·Spatial coordinates(x,y)digitization = image sampling • ·f(x,y) amplitude digitization = gray-level quantization

9. Suppose:the continuous image f(x,y)is approximated by equally spaced samples arranged in the form of a N*M array – digital image

10. pixel voxel

11. Digital image f(x,y): f : ZZ  Rorf : ZZ  Z In digital image processing: N=2n M=2k G=2m The bit number necessary to store a digital image: b=NMm Question: How many samples and gray levels are required for a good approximation?

13. BASIC RELATIONSHIPS BETWEEN PIXELS • Notation: • ·f(x,y) – image·pand q -pixels • ·S - subset of pixelsfromf(x,y) • A pixel p at coordinates (x,y) has • 4 horizontal and vertical neighbors (x+1,y) (x-1,y) (x, y+1) (x, y-1) N4(p) – “4-neighbors of p” • 4 diagonal neighbors (x+1,y+1) (x+1,y-1) (x-1,y+1) (x-1,y-1) N8(p) – “8-neighbors of p” 0-East, 1-NE, 2-N, 3-NW, 4-W, 5-SW, 6-S, 7-SE

14. CONNECTIVITY • ·adjacent pixels • ·similarity criterion for the gray levellV • ¨binary image V={1} • ¨gray-level image V={32, 33, ........,63, 64} • We consider 3 connectivity types: • (a) 4-connectivity • pand qif lp, lq Vand qN4(p) • (b) 8-connectivity • pand qif lp, lq Vand q N8(p) • (c) m-connectivity(mixed connectivity) • pand qif lp, lq V and • (1) q N4(p)or • (2) q ND(p) andN4(p) N4(q) = 

16. Definitions: • ·A pixel pisadjacentto a pixel qif they are connected. • ·Two subsets S1andS2of the imageareadjacentif at least one pixel fromS1is adjacent to another fromS2. • ·Apathfrom pixel pof coord. (x,y) to a pixel qof coord. (s,t)is a sequence of distinct pixelswith coordinates • (x0,y0), (x1,y1), ......, (xn,yn) • (x0,y0)= (x,y)and(xn,yn)= (s,t) • (xi,yi) is adjacent(xi-1,yi-1), with0  i  n. • n = length of the pathbetweenpandq. • ·If pandqare pixelsof a subset Sof the image, then pisconnectedtoq in Sif there is a path fromptoqwithin S. • ·For any pixel p in S, the set of pixels inSconnected topisthe connected componentofS.

17. DISTANCE MEASURES • For pixels p, q and z of coord. (x,y), (s,t) and (u,v) • D is a distance function or metric if: • D(p,q)  0 D(p,q)=0 if p=q • D(p,q) = d(q,p) • D(p,z)  D(p,q) + D(q,z) • Euclidean distance • De(p,q)=[(x-s)2+(y-t)2]1/2 • D4 Distance (city block D8 Distance • distance) (chessboard distance) • D4(p+q)=|x-s|+|y-t| D8(p,q)=max(|x-s|,|y-t|) • D42 from (x,y) D82 from (x,y)

18. ARITHMETIC AND LOGIC OPERATIONS • Arithmetic operations between two pixels p and q • addition: p+q • subtraction: p-q • multiplication: p*q (or pq or pq) • division: pq • Logic operations • AND: p AND q (or pq) • OR: p OR q (or p+q) • COMPLEMENT: NOT p (or ~p)

20. Neighborhood-oriented operations Mask – template, window, filter New value for z5

21. IMAGING GEOMETRY • Notation: • ·(X,Y,Z) in 3-D • ·(x,y) in 2-D • Translation • Scaling • Rotation • Concatenating transformations • Inverse transformations

22. IMAGE ENHANCEMENT • ·the techniques discussed are problem-oriented • ·Spatial domain techniques • ·Frequency domain techniques • ·combinations of the two techniques

23. SPATIAL DOMAIN METHODS g(x,y)=T[f(x,y)] where f(x,y) – input image, g(x,y) – processed image, T – an operator on f,defined over some neighborhood of (x,y)

24. ENHANCEMENT BY POINT PROCESSINGSIMPLE INTENSITY TRANSFORMATIONSs=T(r) Image negative Contrast stretching Bit-plane slicing

26. HISTOGRAM PROCESSING • The histogram of a digital image with L gray levels in the range [0,L-1], is a discrete function: • rk - the kth gray level, k=0, 1,2, ...., L-1 • nk – the number of pixels with the kth gray level n – the total number of pixels in the image

28. Histogram equalization

29. SPATIAL FILTERING Linear filters – using a “mask” Nonlinear filters Example: §fog effect + imprecise edges (blurring) §smoothing filters=”integrative filters”

30. Smoothing filters

31. Derivative filters Gradient filter Laplace filter “Derivative filters” – emphasize the areas of sudden gray level transition (1st and 2nd derivative of the image function)Used to identify edges and delimiting contours.

32. DICOM standardDigital Imaging and Communications in Medicine • DICOM standard facilitates medical imaging equipment interoperability, by : • §       a set of mandatory protocols for all the equipments which are conform to the standard §       syntax and semantic of the commands and information associated to these protocols • Informations provided by the equipment conforming to the standard

33. Short history • 1970s  computerized tomography, followed by development of other imagistic investigation techniques  need of standards for image and associated information transfer between the equipment manufactured by various companies • §       1983 American College of Radiology (ACR) and National Electrical Manufacturers Association (NEMA)  committee developing DICOM standard (developed and publlished according to NEMA and ISO/IEC guidelines) • Ø    the standard was developed together with other international standardization organizations • CEN TC251 – Europa • JIRA Japonia • IEEE • HL7 • ANSI - SUA • §       1988 – DICOM version 2 • 2001 – DICOM version 3 (published by NEMA)

34. DICOM v.3 standard

35. Modular structure – can add new facilitiesIntroducing “information objects” not only for images and graphics (studies, reports etc)Sets the method for identifying relationships between “information objects” in a network

36. BREAK