UNIVERSITY OF MEDICINE AND PHARMACY

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UNIVERSITY OF MEDICINE AND PHARMACY Victor
Babes TIMISOARAMEDICAL INFORMATICS
DEPARTMENTwww.medinfo.umft.ro/dim
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COURSE 11DIGITAL IMAGE PROCESSING
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1. WHY IMAGE PROCESSING?

• Applications
• (a) improvement of pictorial information for
  human interpretation
• (b) processing of scene data for autonomous
  machine perception.
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• Landmarks
•      early 1920s pictures transmitted through
  cable between London and New York
•      1964 pictures from moon, transmitted by
  Ranger7

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• 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

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2. FUNDAMENTALS

• IMAGING MODEL
• Definition 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) reflectance r(x,y)

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• 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
• Lminimin?rmin si Lmaximax?rmax
• Lmin ,Lmax - the gray scale
• in practice 0,L
•      l0 is considered to be black
•      lL is considered to be white

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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 -
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IMAGE SAMPLING AND QUANTIZATION

• Uniform sampling and quantization
•      Spatial coordinates (x,y) digitization
  image sampling
•      f(x,y) amplitude digitization gray-level
  quantization

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Supposethe continuous image f(x,y) is
approximated by equally spaced samples arranged
in the form of a NM array digital image
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pixel voxel
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Digital image

• f(x,y) f Z?Z ? R or f Z?Z ? Z
• In digital image processing N2n M2k G2m
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• The bit number necessary to store a digital
  image
• bN?M?m
• Question
• How many samples and gray levels are required for
  a good approximation?

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BASIC RELATIONSHIPS BETWEEN PIXELS

• Notation
•      f(x,y) image      p and q -pixels
•      S - subset of pixels from f(x,y)
• A pixel p at coordinates (x,y) has
• 4 horizontal and vertical neighbors
• (x1,y) (x-1,y) (x, y1) (x, y-1)
• N4(p) 4-neighbors of p
• 4 diagonal neighbors
• (x1,y1) (x1,y-1) (x-1,y1) (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

3 2 1
4 p 0
5 6 7
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CONNECTIVITY

•      adjacent pixels
•      similarity criterion for the gray level
  l?V
•   binary image V1
•   gray-level image V32, 33, ........,63, 64
• We consider 3 connectivity types
• (a) 4-connectivity
• p and q if lp, lq? V and q?N4(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) ?

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• Definitions
•      A pixel p is adjacent to a pixel q if they
  are connected.
•      Two subsets S1 and S2 of the image are
  adjacent if at least one pixel from S1 is
  adjacent to another from S2.
•      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
• (x0,y0), (x1,y1), ......, (xn,yn)
• (x0,y0) (x,y) and (xn,yn) (s,t)
• (xi,yi) is adjacent (xi-1,yi-1), with 0 ? i ?
  n.
• 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.

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• 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 pq
• 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)21/2
• D4 Distance (city block D8 Distance
• distance) (chessboard distance)
• D4(pq)x-sy-t D8(p,q)max(x-s,y-t)
• D4?2 from (x,y) D8?2 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
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ARITHMETIC AND LOGIC OPERATIONS

• Arithmetic operations between two pixels p and q
• addition pq
• subtraction p-q
• multiplication pq (or pq or p?q)
• division p?q
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• Logic operations
• AND p AND q (or p?q)
• OR p OR q (or pq)
• COMPLEMENT NOT p (or p)

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Neighborhood-oriented operations Mask template,
window, filter
New value for z5
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IMAGING GEOMETRY

• Notation
•      (X,Y,Z) in 3-D
•      (x,y) in 2-D
• Translation
• Scaling
• Rotation
• Concatenating transformations
• Inverse transformations

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IMAGE ENHANCEMENT

•      the techniques discussed are
  problem-oriented
•      Spatial domain techniques
•      Frequency domain techniques
•      combinations of the two techniques

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SPATIAL DOMAIN METHODS g(x,y)Tf(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)
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ENHANCEMENT BY POINT PROCESSING SIMPLE INTENSITY
TRANSFORMATIONSsT(r)
Image negative
Contrast stretching
Bit-plane slicing
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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, k0, 1,2, ...., L-1
• nk the number of pixels with the kth gray level
  n the total number of pixels in the image

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Histogram equalization
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SPATIAL FILTERING
Linear filters using a mask
Nonlinear filters Example
       fog effect imprecise edges
(blurring)        smoothing filtersintegrative
filters
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Smoothing filters
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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.
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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

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• 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)

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• DICOM v.3 standard

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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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