Christophoros Nikou Cnikou@cs.uoi
Digital Image ProcessingDigital Imaging FundamentalsChristophoros Nikoucnikou@cs.uoi.grImages taken from:R. Gonzalez and R. Woods. Digital Image Processing, Prentice Hall, 2008.Digital Image Processing course by Brian Mac Namee, Dublin Institute of Technology.University of Ioannina - Department of Computer Science
2Digital Image Fundamentals“Those who wish to succeed must ask theright preliminary questions”AristotleC. Nikou – Digital Image Processing (E12)
Contents3This lecture will cover:– The human visual system– Light and the electromagnetic spectrum– Image representation– Image sensing and acquisition– Sampling, quantisation and resolutionC. Nikou – Digital Image Processing (E12)
4Human Visual System The best vision model we have! Knowledge of how images form in the eyecan help us with processing digital images We will take just a whirlwind tour of thehuman visual systemC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)5Structure Of The Human Eye The lens focuses light from objects onto theretina The retina is covered withlight receptors calledcones (6-7 million) androds (75-150 million) Cones are concentratedaround the fovea and arevery sensitive to colour Rods are more spread outand are sensitive to low levelsof illuminationC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)6Structure Of The Human Eye (cont.)Density of cones and rods across a section of the right eyeC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)7Structure Of The Human Eye (cont.) Each cone is connectedto each own nerve end.– They can resolve finedetails.– Sensitive to color (photopicvision) Many rods are connectedto a single nerve end– Limited resolution withrespect to cones– Not sensitive to color– Sensitive to low levelillumination (scotopicvision)C. Nikou – Digital Image Processing (E12)
8Blind-Spot Experiment Draw an image similar to that below on a pieceof paper (the dot and cross are about 6 inchesapart) Close your right eye and focus on the cross withyour left eye Hold the image about 20 inches away from yourface and move it slowly towards you The dot should disappear!C. Nikou – Digital Image Processing (E12)
9Image Formation In The Eye Muscles within the eye can be used to changethe shape of the lens allowing us focus onobjects that are near or far away (in contrast witha camera where the distance between the lensand the focal plane varies) An image is focused onto the retina causing rodsand cones to become excited which ultimatelysend signals to the brainC. Nikou – Digital Image Processing (E12)
10Brightness Adaptation & Discrimination The human visual system can perceiveapproximately 1010 different light intensitylevels. At any time instance, we can onlydiscriminate between a much smallernumber – brightness adaptation. Similarly, the perceived intensity of aregion is related to the light intensities ofthe regions surrounding it.C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)11Brightness Adaptation & Discrimination(cont )Weber ratioC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)12Brightness Adaptation & Discrimination(cont )An example of Mach bandsC. Nikou – Digital Image Processing (E12)
Brightness Adaptation & Discrimination(cont )Images taken from Gonzalez & Woods, Digital Image Processing (2002)13C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)14Brightness Adaptation & Discrimination(cont )An example of simultaneous contrastC. Nikou – Digital Image Processing (E12)
Optical Illusions15 Our visual systemplays manyinteresting trickson usC. Nikou – Digital Image Processing (E12)
16Optical Illusions (cont )Stare at the crossin the middle ofthe image andthink circlesC. Nikou – Digital Image Processing (E12)
17Optical Illusions (cont )C. Nikou – Digital Image Processing (E12)
18Light And The ElectromagneticSpectrum Light is just a particular part of theelectromagnetic spectrum that can besensed by the human eye The electromagnetic spectrum is split upaccording to the wavelengths of differentforms of energyC. Nikou – Digital Image Processing (E12)
Reflected Light19 The colours that weperceive aredetermined by thenature of the lightreflected from anobject For example, if whitelight is shone onto agreen object mostwavelengths areabsorbed, while greenlight is reflected fromthe objectC. Nikou – Digital Image Processing (E12)ColoursAbsorbed
Images taken from Gonzalez & Woods, Digital Image Processing (2002)20Image AcquisitionImages are typically generated byilluminating a scene and absorbing theenergy reflected by the objects in that scene– Typical notions ofillumination andscene can be way off: X-rays of a skeleton Ultrasound of anunborn baby Electro-microscopicimages of moleculesC. Nikou – Digital Image Processing (E12)
21Image Sensing and Acquisition Sensors transform the incoming energyinto voltage and the output of the sensor isdigitized.Imaging SensorLine of Image SensorsArray of Image SensorsC. Nikou – Digital Image Processing (E12)
Image SensingImages taken from Gonzalez & Woods, Digital Image Processing (2002)22Using Sensor Strips and RingsC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)23Image Representation A digital image iscomposed of M rowsand N columns of pixelseach storing a value Pixel values are in therange 0-255 (blackwhite) Images can easilybe represented asmatricescolf (row, col)rowC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)24Colour imagesC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)25Colour imagesC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)26Image Sampling And Quantisation A digital sensor can only measure a limitednumber of samples at a discrete set ofenergy levels Quantisation is the process of converting acontinuous analogue signal into a digitalrepresentation of this signalC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)27Image Sampling And Quantisation(cont ) Remember that a digital image is alwaysonly an approximation of a real worldsceneC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)28Image RepresentationC. Nikou – Digital Image Processing (E12)
Saturation & NoiseImages taken from Gonzalez & Woods, Digital Image Processing (2002)29 Dynamic range: Theratio of the maximum(saturation) to theminimum (noise)detectable intensity ofthe imaging system. Noise generally appearas a grainy texturepattern in the darkerregions and masks thelowest detectable trueintensity levelC. Nikou – Digital Image Processing (E12)
Spatial Resolution30 The spatial resolution of an image isdetermined by how sampling was carried out Spatial resolution simply refers to thesmallest discernable detail in an image– Vision specialists willoften talk about pixelsize– Graphic designers willtalk about dots perinch (DPI)C. Nikou – Digital Image Processing (E12)
Spatial Resolution (cont )Images taken from Gonzalez & Woods, Digital Image Processing (2002)31C. Nikou – Digital Image Processing (E12)
Spatial Resolution (cont )Images taken from Gonzalez & Woods, Digital Image Processing (2002)321024 * 1024512 * 512256 * 256128 * 12864 * 6432 * 32C. Nikou – Digital Image Processing (E12)
Spatial Resolution (cont )Images taken from Gonzalez & Woods, Digital Image Processing (2002)33C. Nikou – Digital Image Processing (E12)
Intensity Level Resolution34 Intensity level resolution refers to the number ofintensity levels used to represent the image– The more intensity levels used, the finer the level ofdetail discernable in an image– Intensity level resolution is usually given in terms of thenumber of bits used to store each intensity levelNumber of BitsNumber of IntensityLevelsExamples120, 12400, 01, 10, 114160000, 0101, 1111825600110011, 010101011665,5361010101010101010C. Nikou – Digital Image Processing (E12)
35Intensity Level Resolution (cont )128 grey levels (7 bpp)16 grey levels (4 bpp)8 grey levels (3 bpp)64 grey levels (6 bpp)32 grey levels (5 bpp)Images taken from Gonzalez & Woods, Digital Image Processing (2002)256 grey levels (8 bits per pixel)4 grey levels(E12)(2 bpp)C. Nikou – Digital Image Processing2 grey levels (1 bpp)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)36Intensity Level Resolution (cont )Low DetailMedium DetailC. Nikou – Digital Image Processing (E12)High Detail
Images taken from Gonzalez & Woods, Digital Image Processing (2002)37Intensity Level Resolution (cont ) Isopreference curvesrepresent the dependencebetween intensity andspatial resolutions.– Points lying on a curverepresent images of “equal”quality as described byobservers.– The curves become morevertical as the degree ofdetail increases (a lot ofdetail need less intensitylevels).C. Nikou – Digital Image Processing (E12)
38Resolution: How Much Is Enough?The big question with resolution is alwayshow much is enough?– This all depends on what is in the image andwhat you would like to do with it– Key questions include Does the image look aesthetically pleasing? Can you see what you need to see within theimage?C. Nikou – Digital Image Processing (E12)
39Resolution: How Much Is Enough?(cont )The picture on the right is fine for countingthe number of cars, but not for reading thenumber plateC. Nikou – Digital Image Processing (E12)
Interpolation40 The process of using known data to estimatevalues at unknown locations Basic operation for shrinking, zooming, rotationand translation– e.g. a 500x500 image has to be enlarged by 1.5 to750x750 pixels– Create an imaginary 750x750 grid with the same pixelspacing as the original and then shrink it to 500x500– The 750x750 shrunk pixel spacing will be less thanthe spacing in the original image.– Pixel values have to be determined in between theoriginal pixel locationsC. Nikou – Digital Image Processing (E12)
Interpolation (cont.)41 How to determine pixel values– Nearest neighbour– Bilinear– Bicubic– 2D sincabY1-bC. Nikou – Digital Image Processing (E12)1-a
Images taken from Gonzalez & Woods, Digital Image Processing (2002)42Interpolation (cont.)C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)43Distances between pixels For pixels p(x,y), q(s,t) and z(v,w), D is adistance function or metric if:a) D( p, q) 0 ( D( p, q) 0 iff p q),b) D( p, q) D(q, p),c) D( p, z ) D( p, q) D(q, z ). The Euclidean distance between p and q isdefined as:De ( p, q) ( x s) 2 ( y t ) 2 C. Nikou – Digital Image Processing (E12)12
Images taken from Gonzalez & Woods, Digital Image Processing (2002)44Distances between pixels (cont.) The city-block or D4 distance between p and q isdefined as:D4 ( p, q) x s y t Pixels having the city-block distance from a pixel(x,y) less than or equal to some value T form adiamond centered at (x,y) . For example, for T 2:2221210121222C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)45Distances between pixels (cont.) The chessboard or D8 distance between p and q isdefined as:D8 ( p, q) max( x s , y t ) Pixels having the city-block distance from a pixel(x,y) less than or equal to some value T form asquare centered at (x,y). For example, for T 2:2222221112210122111222222C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)46Mathematical operations used indigital image processing Arithmetic operations (e.g image subtraction pixelby pixel) Matrix and vector operations Linear (e.g. sum) and nonlinear operations (e.g.min and max) Set and logical operations Spatial and neighbourhood operations (e.g. localaverage) Geometric spatial transformations (e.g. rotation)C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)47Image subtractionC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)48Image multiplicationC. Nikou – Digital Image Processing (E12)
Image multiplication (cont.)Images taken from Gonzalez & Woods, Digital Image Processing (2002)49C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)50Logical operatorC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)51Neighbourhood operationC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)52A note on arithmetic operations Most images are displayed at 8 bits (0-255). When images are saved in standard formatslike TIFF or JPEG the conversion to this rangeis automatic. However, the approach used for the conversiondepends on the software package.– The difference of two images is in the range [-255,255] and the sum is in the range [0, 510].– Many packages simply set all negative values to 0and all values exceeding 255 to 255 which isundesirable.C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)53A note on arithmetic operations(cont.) An approach that guarantees that the full rangeis captured into a fixed number of bits is thefollowing: At first, make the minimum value of the imageequal to zero:f m f min f Then perform intensity scaling to [0, K]fmfs Kmax f m C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)54Geometric spatial transformations A common geometric transformation is the affinetransform x t11 t11y 1 u v 1 T u v 1 t21 t12 t31 t130 0 1 It may translate, rotate, scale and sheer an imagedepending on the value of the elements of T To avoid empty pixels we implement the inversemapping Interpolation is essentialC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)55Geometric spatial transformations(cont.)C. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)56Geometric spatial transformations(cont.) The effects and importance of interpolation inimage transformationsC. Nikou – Digital Image Processing (E12)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)57Image Registration Estimate the transformation parametersbetween two images. Very important application of digital imageprocessing. Single and multimodal Temporal evolution and quantitative analysis(medicine, satellite images) A basic approach is to use control points (userdefined or automatically detected) and estimatethe elements of the transformation matrix bysolving a linear system.C. Nikou – Digital Image Processing (E12)
Image Registration (cont.)Images taken from Gonzalez & Woods, Digital Image Processing (2002)58Manually selectedlandmarksC. Nikou – Digital Image Processing (E12)
Digital Imaging Fundamentals Christophoros Nikou cnikou@cs.uoi.gr Digital Image Processing Images taken from: R. Gonzalez and R. Woods. Digital Image Processing, Prentice Hall, 2008. Digital Image Processing course by Brian Mac Namee, Dublin Institute of Technology.
L. Chandra Kumar v. UOI [AIR 1997 SC 1125]1 General background- For a long time search was going
9 The space of all face images Insight into principal componentlit analysis (PCA). We want to construct a low-dimensional linear subspace that C. Nikou – Image Analysis (T-14) linear subspace that best explains the variation in the set of face images. 10 Principal Component Analysis Given: N data points x1, ,xN in Rd
2 UNIVERSITÉ NATIONALE ET CAPODISTRIENNE D’ATHÈNES DÉPARTEMENT DE LANGUE ET LITTÉRATURE FRANÇAISES Section de Langue française et de Linguistique Révision, mise en page et 1re mise à jour (septembre 2018) : Maro PATÉLI et Christos NIKOU La Presse
14/2/2011 3 5 Preliminaries (cont.) Adjacency of pixels Let V be the set of intensity values used tobe the set of intensity values used to define the adjacency (e.g. V {1} for binary images). 4-adjacency.Two pixels p and q with values in V are 4-adjacent if q is in N4(p). C. Nikou – Image Analysis (T-14) 8-adjacency.Two pixels p and q with values in V are 8-adjacent if q is in N8(p).
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Level 4 IS Business Analyst Minimum Standards and Grading Criteria This paper defines the minimum requirements for the knowledge, skills and behaviours defined in the standard, which are required for a pass. It also defines the criteria to be used for awarding the grade for merit or distinction. This paper should be read in conjunction with the Standard and Assessment Plan for the Level 4 IS .
