Lie Gonzalez Ch2

8/3/2019 Lie Gonzalez Ch2

1/26

CCU, Taiwan

Wen-Nung Lie

Chapter 2 : Digital Image

Fundamentals


2/26

2-1CCU, Taiwan

Wen-Nung Lie

Image formation in the eye

Components : lens, retina Focal length varies (17 ~14 mm) as the refractive

power increases from minimum to maximum or the

focused object locates from far to near


3/26

2-2CCU, Taiwan

Wen-Nung Lie

Human visual perception

Weber ratio Mach bands

Simultaneous contrast Optical illusion


4/262-3CCU, Taiwan

Wen-Nung Lie

Brightness discrimination of

the eye Weber ratio

The ability of the eye to discriminate betweenchanges in light intensity at any specific

adaptation level is different

Weber ratio : , is the increment ofillumination discriminable 50% of the time with

background illuminationI

Small : good brightness discrimination

Large : poor brightness discrimination

I

I

I

I

I

I

I


5/262-4CCU, Taiwan

Wen-Nung Lie

Typical Weber ratio as a

function of intensity

Brightness discrimination is poor at low levels of

illumination

At low levels of illumination, vision is carried out by

activity of rods, at high levels, it is by cones


6/262-5

CCU, Taiwan

Wen-Nung Lie

Simultaneous contrast

A regions perceived brightness does not dependsimply on its intensity

In the figure below, all the center squares have exactly

the same intensity


7/262-6

CCU, Taiwan

Wen-Nung Lie

Optical illusion

The eye fills in nonexisting information or wrongly

perceives geometrical properties of objects


8/262-7

CCU, Taiwan

Wen-Nung Lie

Quantities to describe quality

of chromatic light source

Radiance Total amount of energy that flows from the light

source (Watts, W)

Luminance A measure of the amount of energy an observer

perceives from a light source (lumens, lm)

Brightness A subjective descriptor of light perception

Light emitted from a far infrared source have high radiance,but almost no luminance for a sensor in visible band


9/26

2-8CCU, Taiwan

Wen-Nung Lie

Image sensing & acquisition

The illumination source emits energy which isreflected or absorbed by the element of the scene

being imaged

The wavelength of an EM wave required to see anobject must be of the same size as or smaller than the

object

The physical properties of the sensor materials alsolimits the capability of imaging sensors (cf. CCD &

CMOS, CCD & IRCCD)


10/26

2-9CCU, Taiwan

Wen-Nung Lie

Image scanning architectures

Single sensor

Sensor strip, the motion of stripcompletes the other dimensionsimaging

Need algorithm


11/26

2-10CCU, Taiwan

Wen-Nung Lie

2-D sensor array, up to 4000x4000

noise reduction is achieved by long

integration time


12/26

2-11CCU, Taiwan

Wen-Nung Lie

Image formation model

Intensity=illumination*(reflectance ortransmissivity)

),(),(),( yxryxiyxf =


13/26

2-12CCU, Taiwan

Wen-Nung Lie

Image sampling &

quantization

Digitalizing the coordinate values is calledsampling. Digitalizing the amplitude values is

called quantization

Sampling for 2-D sensor array is needless image content is a consideration in choosing parameters

in sampling and quantization


14/26

2-13CCU, Taiwan

Wen-Nung Lie

Representing digital images Definition of coordinate system

Dynamic range of an image

the range of values spanned by the gray levels of existing pixels

Spatial resolution (e.g., dpi, or 1024x1024)

Gray-level resolution (8 (often visual), 10, 12 (e.g.,

thermal), or 16 bits/sample)


15/26

2-14CCU, Taiwan

Wen-Nung Lie

Different spatial resolution, but with the same display size


16/26

2-15CCU, Taiwan

Wen-Nung Lie

False contouring effect False contouring effect is quite visible in images displayed

using 16 or less gray levels


17/26

2-16CCU, Taiwan

Wen-Nung Lie

Isopreference curve InNkplane (N: spatial resolution, k: graylevel resolution)

Points on the same curve represent equal subjective quality

The isopreference curve tends to shift right and upward

For images with a large amount of detail(e.g., crowd), only a few gray level maybe needed (see the vertical behaviorwhich is graylevel-independent)


18/26

2-17CCU, Taiwan

Wen-Nung Lie

Zooming and shrinking digital

images Zooming : oversampling

shrinking : undersampling

Methods

Nearest neighbor interpolation Pixel replication

Bilinear interpolation

Use more neighbors for interpolation (e.g., cubicinterpolation)

Blur an image slightly before shrinking it (according to

sampling theory)


19/26


20/26

2-19CCU, Taiwan

Wen-Nung Lie

Cubic interpolation)]1,(),()1,()2,([({),( +++++++=+ ykxfykxfykxfykxfdydydyykxh

)])1,(2),(2)2,()1,([ ++++++++ ykxfykxfykxfykxf

2,1,0,1for),()]}1,()1,([ =++++++ kykxfykxfykxf

)],1(),(),1(),2([({),( yxhyxhyxhyxhdxdxdxyxg +++=

)]),1(2),(2),2(),1([ yxhyxhyxhyxh ++++

),()]},1(),1([ yxhyxhyxh +++

xR

xdx =

yR

ydy =

),(),(

=

R

y

R

xyx

By 16 neighborhoods

g(x,y)f x y( $, $)


21/26

2-20CCU, Taiwan

Wen-Nung Lie

Comparisons for zooming

techniques Duplication

Bilinear interpolation

Cubic interpolation

Edge preserving zooming (to be discussed)

4Xzooming

duplicate bilinear cubic


22/26

2-21CCU, Taiwan

Wen-Nung Lie

Image resampling (non-

integer zooming or shrinking) For non-integer zooming or shrinking

Steps :

For each point in G(x,y), compute its non-grid correspondence in

F(x,y) by the ratioR

Obtain the assigned graylevel by bilinear interpolation technique(by using the four nearest neighbors)

ZR

(4,4)(2.7, 2.7)

F(x,y) G(x,y)

R =1.5


23/26

2-22CCU, Taiwan

Wen-Nung Lie

Some basic concepts in DIP

4-neighborhoods and 8-neighborhoods

4, 8-connected

Adjacency

Connected and graylevels are similar (in an allowed set)

4, 8, or m-adjacency (mixed)

Two pixels are not 8-connected if they can bechained together via 4-connected


24/26

2-23CCU, Taiwan

Wen-Nung Lie

Connected component

Any two pixelsp and q in a region S are connected via

4 or 8 neighborhoods in S (exists a path)

Distance measures Euclidean distance

D4 distance (city-block distance)

2:2 yxnorm

=

=N

n

nnyxyxnorm

11

:1tysxqpD +=),(4

2

21012

2

212

212Equal-distance map


25/26

2-24CCU, Taiwan

Wen-Nung Lie

D8 distance (chessboard distance)

Dm distance (the shortest m-path between the points)

depends on the pixels along the path

),max(),(8

tysxqpD =

21112

21012

21112

22222

22222

P1

P4

P2

P3

P

The m-path between p and p4 isdependent on the value (0 or 1) of p1and p3 -- 2 or 3 or 4

nnNn

yxyx == ,1

supTchebyshev (supermum ormaximum) norm


26/26

2-25CCU, Taiwan

Wen-Nung Lie

Linear and nonlinear operation on images

)()()( gnHfaHbgafH +=+

Documents

Lie Gonzalez Ch2