1. UNIVERSITY OF MEDICINE AND PHARMACY “Victor Babeş” TIMISOARA MEDICAL INFORMATICS DEPARTMENT www.medinfo.umft.ro/dim

2. COURSE 10 DIGITAL IMAGE PROCESSING

3. 1. WHY IMAGE PROCESSING? Applications:Applications: –(a) improvement of pictorial information for human interpretation; –(b) processing of scene data for autonomous machine perception. Landmarks:Landmarks: –  early 1920s – pictures transmitted through cable between London and New York; –  1964 – pictures from moon, transmitted by Ranger7

4. Application domains:Application domains: (a) medicine, geography, meteorology, physics, astronomy, defense, industry(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(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 methodsHuman visual perception – superior to all imaging methods

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

6. Definition: The intensity of a monnochrome image f(x,y) = the gray level – l of the image at the point (x,y) L min  l  L max L min =i min  r min si L max =i max  r max [L min,L max ] - the gray scale in practice: [0,L]  l=0 is considered to be black  l=L is considered to be white

7. Output Input 3-D data 3-D image 2-D data picture 1-D data signal vector features 0-D data identity 3-D data 3-D image restoration enhancement boundary detection line detection image analysis image interpret. 2-D data picture reconstruct.restoration enhancement boundary detection image analysis image interpret. 1-D data signal reconstruct. signal processing signal analysis signal interpret. vector features solid graphics vector-based graphics displaydata processing pattern recognition 0-D data identity modelling (2-D icon) sketch (1-D icon) examples-

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

11. Digital image f(x,y): f : Z  Z  R or f : Z  Z  Z In digital image processing: N=2 n M=2 k G=2 m 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. Notation:Notation:  f(x,y) – image  p and q -pixels  S - subset of pixels from f(x,y) A pixel p at coordinates (x,y) hasA pixel p at coordinates (x,y) has –4 horizontal and vertical neighbors (x+1,y)(x-1,y)(x, y+1)(x, y-1) N 4 (p) – “4-neighbors of p” –4 diagonal neighbors (x+1,y+1)(x+1,y-1)(x-1,y+1)(x-1,y-1) N 8 (p) – “8-neighbors of p” 0-East, 1-NE, 2-N, 3-NW, 4-W, 5-SW, 6-S, 7-SE BASIC RELATIONSHIPS BETWEEN PIXELS 321 4p0 567

14. CONNECTIVITY  adjacent pixels  similarity criterion for the gray level l  V  binary image V={1}  gray-level image V={32, 33,........,63, 64} We consider 3 connectivity types: (a) 4-connectivity p and q if l p, l q  V and q  N 4 (p) (b) 8-connectivity p and q if l p, l q  V and q  N 8 (p) (c) m-connectivity (mixed connectivity) p and q if l p, l q  V and (1) q  N 4 (p)or (2) q  N D (p) and N 4 (p)  N 4 (q) = 

16. Definitions:Definitions:  A pixel p is adjacent to a pixel q if they are connected.  Two subsets S 1 and S 2 of the image are adjacent if at least one pixel from S 1 is adjacent to another from S 2.  A path from pixel p of coord. (x,y) to a pixel q of coord. (s,t) is a sequence of distinct pixels with coordinates (x 0,y 0 ), (x 1,y 1 ),......, (x n,y n )(x 0,y 0 ), (x 1,y 1 ),......, (x n,y n ) (x 0,y 0 )= (x,y) and (x n,y n )= (s,t)(x 0,y 0 )= (x,y) and (x n,y n )= (s,t) (x i,y i ) is adjacent (x i-1,y i-1 ), with 0  i  n.(x i,y i ) is adjacent (x i-1,y i-1 ), with 0  i  n. n = length of the path between p and q.n = length of the path between p and q.  If p and q are pixels of a subset S of the image, then p is connected to q in S if there is a path from p to q within S.  For any pixel p in S, the set of pixels in S connected to p is the connected component of S.

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: (1)D(p,q)  0D(p,q)=0 if p=q (2)D(p,q) = d(q,p) (3)D(p,z)  D(p,q) + D(q,z) Euclidean distance De(p,q)=[(x-s) 2 +(y-t) 2 ] 1/2 D 4 Distance (city blockD 8 Distance distance)(chessboard distance) D 4 (p+q)=|x-s|+|y-t| D 8 (p,q)=max(|x-s|,|y-t|) D 4  2 from (x,y)D 8  2 from (x,y) 2 212 21012 212 2 22222 21112 21012 21112 22222

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

20. Neighborhood-oriented operations Mask – template, window, filter New value for z 5

21. IMAGING GEOMETRY Notation:Notation:  (X,Y,Z) in 3-D  (x,y) in 2-D TranslationTranslation ScalingScaling RotationRotation Concatenating transformationsConcatenating transformations Inverse transformationsInverse 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 PROCESSING SIMPLE INTENSITY TRANSFORMATIONS s=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:The histogram of a digital image with L gray levels in the range [0,L-1], is a discrete function: r k - the k th gray level, k=0, 1,2,...., L-1r k - the k th gray level, k=0, 1,2,...., L-1 n k – the number of pixels with the k th gray level n – the total number of pixels in the imagen k – the number of pixels with the k th gray level n – the total number of pixels in the image

28. Histogram equalization

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

30. Smoothing filters

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

32. DICOM Digital Imaging and Communications in Medicine DICOM standard Digital Imaging and Communications in Medicine DICOM standard facilitates medical imaging equipment interoperability, by :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 standardInformations 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)  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 standardDICOM v.3 standard

35. Modular structure – can add new facilities Introducing “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