UNIVERSITY OF MEDICINE AND UNIVERSITY OF MEDICINE AND PHARMACY “Victor BabePHARMACY “Victor Babeş”ş” TIMISOARA TIMISOARA

MEDICAL INFORMATICS DEPARTMENTMEDICAL INFORMATICS DEPARTMENT

www.medinfo.umft.ro/dimwww.medinfo.umft.ro/dim

COURSE 10COURSE 10

DIGITAL IMAGE DIGITAL IMAGE PROCESSINGPROCESSING

1. 1. WHY IMAGE PROCESSINGWHY IMAGE PROCESSING??

• AAppplicaplicationstions::– (a) (a) improvement of pictorial information for human improvement of pictorial information for human

interpretationinterpretation;;– (b) (b) processing of scene data for autonomous machine processing of scene data for autonomous machine

perceptionperception..

  • LandmarksLandmarks::

          earlyearly 1920 1920ss – – pictures transmitted through cable pictures transmitted through cable between London and New York;between London and New York;

          1964 – 1964 – pictures from moon, transmitted bypictures from moon, transmitted by Ranger7Ranger7

• Application domainsApplication domains::• (a) (a) medicinemedicine, , geographygeography, , meteorologymeteorology, , physicsphysics, ,

astronomyastronomy, , defensedefense, , industryindustry• (b) (b) optical character recognitionoptical character recognition ( (OCROCR), ),

artificial imaging systems in industry, digital artificial imaging systems in industry, digital processing of fingerprints, weather prediction, processing of fingerprints, weather prediction, screening of blood samplesscreening of blood samples

• Human visual perception – superior Human visual perception – superior to all imaging methodsto all imaging methods

2. 2. FUNDAMENTALSFUNDAMENTALS IMAGING MODELIMAGING MODEL

• DefinitionDefinition: imag: imagee– Two-dimensional light intensity functionTwo-dimensional light intensity function, not, noteded f(x,y)f(x,y)

denoting the intensity (luminosity) of the denoting the intensity (luminosity) of the ““imagimagee” in ” in any any pointpoint (x,y)(x,y)

– The nature ofThe nature of f(x,y)f(x,y) may be characterised by two may be characterised by two componentscomponents::

– (1) (1) illumination illumination i(x,y)i(x,y)

– (2) (2) reflectancereflectance r(x,y)r(x,y)

• Definition:• The intensity of a monnochrome image f(x,y) =

the gray level – l of the image at the point (x,y)

• Lmin l Lmax

• Lmin=iminrmin si Lmax=imaxrmax

• [Lmin ,Lmax] - the gray scale

• in practice: [0,L]      l=0 is considered to be black      l=L is considered to be white

OutputInput

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. reconstruct. signal processing

signal

analysis

signal interpret.

vector

features

solid

graphics

vector-based graphics

display data processing

pattern recognition

0-D data

identity

modelling modelling

(2-D icon)

sketch

(1-D icon)

examples -

• Uniform sampling and quantization     Spatial coordinates (x,y) digitization =

image sampling     f(x,y) amplitude digitization = gray-

level quantization

IMAGE SAMPLING AND IMAGE SAMPLING AND QUANTIZATIONQUANTIZATION

SupposeSuppose::the continuous image the continuous image f(x,y)f(x,y) is approximated is approximated by equally spaced samples arranged by equally spaced samples arranged in the in the form of aform of a N*M N*M array – array – digitaldigital image image

pixel voxel

Digital image

f(x,y): f : ZZ R or f : ZZ ZIn digital image processing: N=2n M=2k

G=2m

 The bit number necessary to store a digital image:

b=NMmQuestion:How many samples and gray levels are required for

a good approximation?

• NotatNotationion::           f(x,y)f(x,y) – – imageimage           pp and and qq -pixel -pixelss           SS - subset - subset of of pixel pixelss fromfrom f(x,y)f(x,y)

• A pixel p at coordinates (x,y) hasA pixel p at coordinates (x,y) has– 4 horizontal and vertical neighbors4 horizontal and vertical neighbors

(x+1,y)(x+1,y) (x-1,y)(x-1,y) (x, y+1)(x, y+1) (x, y-1)(x, y-1)

NN44(p) – (p) – “4-neighbors of p”“4-neighbors of p”

– 4 diagonal neighbors4 diagonal neighbors

(x+1,y+1)(x+1,y+1) (x+1,y-1)(x+1,y-1) (x-1,y+1)(x-1,y+1) (x-1,y-1)(x-1,y-1)

NN88(p) – (p) – “8-neighbors of p”“8-neighbors of p”

0-East, 1-NE, 2-N, 3-NW, 4-W, 5-SW, 6-S, 7-SE0-East, 1-NE, 2-N, 3-NW, 4-W, 5-SW, 6-S, 7-SE

BASIC RELATIONSHIPS BETWEEN BASIC RELATIONSHIPS BETWEEN PIXELSPIXELS

3 2 1

4 p 0

5 6 7

CONNECTIVITYCONNECTIVITY      adjacent pixels      similarity criterion for the gray level lV   binary image V={1}   gray-level image V={32, 33, ........,63, 64}• We consider 3 connectivity types:• (a) 4-connectivity• p and q if lp, lq V and qN4(p)• (b) 8-connectivity• p and q if lp, lq V and q N8(p)• (c) m-connectivity (mixed connectivity)• p and q if lp, lq V and

• (1) q N4(p) or

• (2) q ND(p) and N4(p) N4(q) =

• DefinitiDefinitionsons::           AA pixel pixel pp isis adadjjacentacent to ato a pixel pixel qq if they are connectedif they are connected..

          TwoTwo subset subsetss S S11 andand SS22 of the imageof the image areare adjacentadjacent if at least if at least

one one pixel pixel fromfrom SS11 is is adadjjacent acent to another fromto another from SS22..

          AA pathpath fromfrom pixel pixel pp ofof coord. coord. (x,y) (x,y) to ato a pixel pixel qq ofof coord. coord. (s,t)(s,t) is a sequence of distinctis a sequence of distinct pixel pixelss withwith coord coordinatesinates

• (x(x00,y,y00), (x), (x11,y,y11), ......, (x), ......, (xnn,y,ynn))

• (x(x00,y,y00)= (x,y))= (x,y) andand (x(xnn,y,ynn)= (s,t))= (s,t)

• (x(xii,y,yii) ) is adjacentis adjacent (x(xi-1i-1,y,yi-1i-1)), , withwith 0 0 i i n n..

• nn = = length of the pathlength of the path betweenbetween pp andand qq..           If If pp andand qq areare pixel pixelss of a of a subset subset SS of the imageof the image, , then then pp isis

connectedconnected toto qq in in SS if there is a path fromif there is a path from pp toto qq withwithin in SS..           For any For any pixel pixel pp in in SS, , the set of pixels inthe set of pixels in SS connected toconnected to pp isis

the connected componentthe connected component ofof SS..

DISTANCE MEASURESFor 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) 0 D(p,q)=0 if p=q(2) D(p,q) = d(q,p)(3) D(p,z) D(p,q) + D(q,z)Euclidean distanceDe(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|)D42 from (x,y) D82 from (x,y)2

2 1 2

2 1 0 1 2

2 1 2

2

2 2 2 2 2

2 1 1 1 2

2 1 0 1 2

2 1 1 1 2

2 2 2 2 2

ARITHMETIC AND LOGIC ARITHMETIC AND LOGIC OPERATIONSOPERATIONS

• Arithmetic operationsArithmetic operations between two pixels between two pixels pp and and qq• addition:addition: p+qp+q• subtraction:subtraction: p-qp-q• multiplication:multiplication: p*qp*q (or (or pq pq oror p pqq))• division:division: ppqq•   • Logic operationsLogic operations • AND:AND: p AND qp AND q (or (or ppqq))• OR:OR: p OR qp OR q (or (or p+qp+q))• COMPLEMENT:COMPLEMENT: NOT pNOT p (or (or ~p~p))

Neighborhood-oriented operations

Mask – template, window, filter

New value for z5

IMAGING GEOMETRYIMAGING GEOMETRY

• NotationNotation::           (X,Y,Z)(X,Y,Z) in 3-D in 3-D           (x,y)(x,y) in 2-D in 2-D

• TranslatiTranslationon• ScalScalinging• RotRotationation• Concatenating transformationsConcatenating transformations• Inverse transformationsInverse transformations

IMAGE ENHANCEMENTIMAGE ENHANCEMENT

     the techniques discussed are problem-oriented

     Spatial domain techniques      Frequency domain techniques      combinations of the two techniques

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)

ENHANCEMENT BY POINT PROCESSINGENHANCEMENT BY POINT PROCESSING SIMPLE INTENSITY TRANSFORMATIONSSIMPLE INTENSITY TRANSFORMATIONS

s=T(r)s=T(r) Image negative

Contrast stretching Bit-plane slicing

HISTOGRAM PROCESSINGHISTOGRAM PROCESSING

• The histogram of a digital imageThe histogram of a digital image with L gray with L gray levels in the range [0,L-1], is a discrete function:levels in the range [0,L-1], is a discrete function:

• rrk k - - the the kkthth gray level gray level, , kk=0, 1,2, ...., L-1=0, 1,2, ...., L-1

• nnkk – the number of pixels with the – the number of pixels with the kkthth gray level n gray level n

– the total number of pixels in the image– the total number of pixels in the image

Histogram equalization

SPATIAL FILTERINGSPATIAL FILTERING

       fog effect + imprecise edges (fog effect + imprecise edges (blurringblurring))              smoothing filters=”integrative filterssmoothing filters=”integrative filters”

Linear filters – using a “mask”

Nonlinear filters

Example:

Smoothing filters

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.

DICOM DICOM standardDigital Imaging and Communications in Digital Imaging and Communications in

MedicineMedicine • DICOMDICOM standard facilitates medical imaging standard facilitates medical imaging

equipment interoperability, by :equipment interoperability, by :              a set of mandatory protocols for all the a set of mandatory protocols for all the

equipments which are conform to the standard equipments which are conform to the standard        syntax and semantic of the commands and        syntax and semantic of the commands and information associated to these protocols information associated to these protocols

• Informations provided by the equipment Informations provided by the equipment conforming to the standardconforming to the standard

• 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)

• DICOM v.3 standard DICOM v.3 standard

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

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