Chapter 02

Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.

www.ImageProcessingPlace.com

19922008 R. C. Gonzalez & R. E. Woods

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Chapter 2 Digital Image FundamentalsChapter 2 Digital Image Fundamentals

Element of Visual Perception

Structure of the human eye (~20 mm)3 membranes ():

Sclera () Choroid () Retina()2 chambers ():

Anterior chamber()Posterior chamber()Six Ciliary, body, fiber and muscle (

)Control the lens and protect the

human eye ()




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Receiver of Retina ()Cone ( ): 6~7 million

Photopic vision, Bright-light visionRod ( ): 75~150 million :

Scotopic vision, Dim-light vision




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Lens shape controlled by the tension of ciliary fiberFocal length: 17 mm ~ 14mm




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Range of light intensity that humancan adapt

1010 Transition from scotopic to photopic

vision is gradualFrom 0.001 to 0.1 millilambert

(-3 to -1 in log) Vision system cannot operate over

such a range simultaneously Brightness adaptation level: current

sensitivity level of the visual system




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Uniformly illuminated background, occupying entire field of view. Add a short duration of flashI. I c: the increment of illumination discriminable 50% of the time

with background illumination I. I c/ I : Weber ratio




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Rod vision (photopic vision): Weber ration largerbrightness discrimination poor

Cone vision (scotopic vision): Weber ration smallerbrightness discrimination better




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Human Vision Phenomenon: Mach Band

Ernst Mach first describedthe phenomenon in 1865.

The visual system tends to undershootor overshoot around the boundary ofregions of different intensities.




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Human Vision Phenomenon: Simultaneous Contrast




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Human Vision Phenomenon: Optical Illusion

The outline of a squareis seen clearly.

A few lines are sufficient togive the illusion of a circle.




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Light and EM Spectrum

vc

hvE




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Visible band: 0.43 um (violet)~0.79 um (red)

Achromatic or monochromatic lightGray level, intensity Radiance (watts): total energy from light source Luminance (lumens): energy that an observer perceives Brightness : subjective descriptor of light perception

hard to measureEx. The light emitted from a source operating in the far infrared region of

the spectrum could have significant energy, but an observer wouldhardly perceived it.




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Image sensing and acquisition




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Image acquisition using a single sensor




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Image acquisition using sensor strips

1. OA: scanner.2. Airborne: the imaging system is

mounted on an aircraft that flies at aconstant speed over the geographicalarea to be imaged.




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A simple image formation model f(x, y) = i(x, y) r(x, y) i(x, y) : the amount of illumination incident on the scene r(x, y) : the reflectivity function (or transmissivity function)

yxf ,0

yxi ,0 1,0 yxr




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Image Sampling and Quantization




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Sampling and Quantization with a Sensing Array




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Representing Digital Images




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Representing Digital Images

1,11,10,1

1,11,10,11,01,00,0

,

NMfMfMf

NfffNfff

yxf

1,11,10,1

1,11,10,1

1,01,00,0

NMMM

N

N

aaa

aaaaaa

A




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Representing Digital Images maxmin , LLDynamic range/ Image contrast

max

minL

L




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Image SizeThe number of gray levels: L = 2k

The number of bits required to store a digitalized image:b = M * N * kWhen M=N:

b = N2 * k




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Spatial and Gray-Level Resolution




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Zoom in to show the effect of subsampling

Blocking effect




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False contouring




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Detail increased




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Isopreference curves tend to become more vertical in theNk-plane as the detail in the image increases.For images with a large amount of detail only a few gray

levels may be needed.




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Aliasing and Moire Pattern




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A moir pattern formed by incorrectly downsamplingthe image left.




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Zooming and Shrinking Digital Images

Zooming: oversamplingNeed interpolationSuperresolutionShrinking: undersampling

Better to apply LPF (blurring of digital image) beforesubssampling to avoid aliasingNeed interpolation for non-interger factor




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Image Interpolation Nearest Neighbor Interpolation Bilinear Interpolation Bicubic Interpolation etc

Application Image Scaling/Resize Image Rotation Image Warping Image Morphing etc

Image Morphing




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Nearest-neighborInterpolation

BilinearInterpolation




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Neighbors of a pixel

A pixel p at coordinate (x, y)N4(p): 4-neighbors of p

(x+1, y), (x-1, y), (x, y+1), (x, y-1)ND(p): 4 diagonal neighbors of p

(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1)N8(p): N4(p) together with ND(p)




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AdjacencyLet V be the set of gray-level values used to define adjacency4- adjacency

Two pixels p and q with values from V are 4- adjacency if q is in theset N4(p).

8- adjacencyTwo pixels p and q with values from V are 8- adjacency if q is in the

set N8(p).

m- adjacency (mixed adjacency)Two pixels p and q with values from V are m- adjacency if

(i) q is in N4(p), or(ii) q is in ND(p) and the set N4(p) N4(q) has no pixels whose values

are from V.




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m- adjacency is a modification of 8-adjacency

V={1} Multiple 8-adjacency ambiguousAmbiguity is removed bym-adjacency




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A digital path from pixel p(x, y) to pixel q(s, t)

S: a subset of pixels in an imageTwo pixels p and q are said to be connected in S if there exists a path

between them consisting entirely of pixels in S.The set of pixels that are connected to it in S is called a connected

component of S.If it is only one connected component, then S is called a connected set.

(x0, y0), (x1, y1), ,(xn, yn)(x0, y0)= (x, y), (xn, yn)=(s, t)(xi, yi) and (xi+1, yi+1) are adjacentn is the length of the pathIf (x0, y0)= (xn, yn), the path is a closed path.

Connectivity




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Regions and BoundariesR: subset of pixels in an imageWe call R a region of image if R is a connected set. Two pixels p and

Boundary of R:The set of pixels have one or more neighbors that are not in R.

Edge : intensity discontinuities (local concept)Boundary : closed paths (global concept)




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For pixels p, q, and z, with coordinates (x, y), (s, t), and (v, w)D is a distance function or metric if(a) D(p, q)0(b) D(p, q)= D(q, p), and(c) D(p, z)D(p, q)+ D(q, z)

Distance Measures

Euclidean distance between p and q:

2/122, tysxqpDe




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D4 distance between p and q:

tysxqpD4 ,D8 distance between p and q:

tysxqpD8 ,max,

2212

21012212

2

2222221112210122111222222




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Let H be an operator whose input and output are images.H is said to be a linear operator if

Linear and Nonlinear Operations

gbHfaHbgafH Where f, g are two images, a and b are two scalars

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Chapter 02