Chapter02 Osc

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Digital Image Processing, 2nd ed.www.imageprocessingbook.com

2002 R. C. Gonzalez & R. E. Woods

Chapter 2: Digital Image Fundamentals

-Cornea(Gic mc)

- Sclera (Mng cng)

- Iris(Mng mt)

- Lens(Thu knh)

- Retina(Vng mc)

- Visual Axis


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- Cones: 6~7 millions are distributed around fovea. Highly sensitive to

color. Human resolve fine details with these.

- Rods: 75~150 millions are distributed over the retinal surface.

Several rods are connected to a single nerve end. Reduce the amount of

detail. Serve to give a general, overall picture of the field of view.

Sensitive to low levels of illumination.


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-Shape of the lens is controlled by the controlling muscles

- The muscles make the lens to be relatively flattened for

distant objects.


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Brightness Adaptation

The total range of intensity levels

that it can discriminate

simultaneously is rather small

compared with the total adaptation

range

Ba

is a brightness adaptation

level The short intersecting curve

represents the range of subjective

brightness that the eye can

perceive when adapted to this

level.


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Contrast Sensitivity

The ability of the eye to

discrimination between changes

in brightness at specific

adaptation level

I is uniform illumination on

a flat background area large

enough to occupy the entire

field of view

is the change in the

object brightness required to

just distinguish the object

from the background

Weber ratio: I/I

- Bad brightness discrimination

if Weber Ratio is large,


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Weber Ratio

Brightness discrimination is

poor (the Weber ratio is large) at

low levels of illumination and

improves significantly (the ratiodecreases) as background

illumination increases.

hard to distinguish the

discrimination when it is brightarea but easier when the

discrimination is on a dark area.


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Brightness vs. Function of intensity

Visual system tends toundershoot or overshoot around

the boundary of regions of

different intensities.


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Simultaneous Contrast

All the small squares have exactly the same intensity, butthey appear to the eye progressively darker as the background

becomes brighter.

Regions perceived brightness does not depend simply onits intensity.


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Optical Illusions


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Electromagnetic Spectrum


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Signal

A signal is a function that carries information.

Usually content of the signal changes over some set of

spatiotemporal dimensions.Time-Varying Signal: f(t)

Ex) audio signal


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Spatially-Varying Signal

Signals can vary over space as well.

An image can be thought of as being a function of 2

spatial dimensions:

f(x,y)for monochromatic images, the value of the function is the

amount of light at that point.

medical CAT and MRI scanners produce images that are

functions of 3 spatial dimensions:

f(x,y,z)

Spatiotemporal Signals:

f(x,y,t)

ex) a video signal, animation


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Analog and Digital Signal

Most naturally-occurring signals also have a real-

valued range in which values occur with infinite

precision.To store and manipulate signals by computer we

need to store these numbers with finite precision.

thus, these signals have a discrete range.

signal has continuous domain and range = analog

signal has discrete domain and range = digital


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Sampling

sampling = the spacing of discrete values in the domain ofa signal.

sampling-rate = how many samples are taken per unit ofeach dimension. e.g.,samples per second, frames per second


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Quantization

Quantization = spacing of discrete values in therange of a signal.

Usually thought of as the number of bits persample of the signal.

e.g., 1, 8, 24 bit images, 16-bit audio.

l d d


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Digital Image Representation

A digital image is an image f(x,y)

that has been digitized both in spatialcoordinates and brightness.

The value of f at any point (x,y) is

proportional to the brightness (or

gray level) of the image at that point.

Di i l I P i 2 d d


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2D Image Sensor

Di it l I P i 2 d d


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Coordinate Conversion used in this book


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Di it l I P i 2 d d


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Digital Image Acquisition Process

Di it l I P i 2 d d


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Sampling and Quantization

Di it l I P i 2 d d


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Example of Digital Image

Digital Image Processing 2nd ed


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Sampling Effect



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Sampling Effect



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Sampling Effect



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Quantization Effect



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Quantization Effect

if the gray scale is not

enough, the smooth area willbe affected.

False contouring can occur

on the smooth area which has

fine gray scales.



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Light-intensity function

image refers to a 2D light-intensityfunction, f(x,y)

the amplitude of f at spatial coordinates

(x,y) gives the intensity (brightness) of the

image at that point.

light is a form of energy thus f(x,y) mustbe nonzero and finite.

0 < f(x,y)<



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Illumination and Reflectance

The basic nature of f(x,y) may becharacterized by 2 components:

the amount of source light incident

on the scene being viewed

Illumination, i(x,y)

the amount of light reflected by the

objects in the scene

Reflectance, r(x,y)



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Illumination and Reflectance

f(x,y) = i(x,y)r(x,y)

i(x,y):

determined by the nature of the light sourcebounded by

0 < i(x,y)<

r(x,y) :

determined by the nature of the objectsbounded by

0 < r(x,y)< 1



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Gray Level

we call the intensity of a monochrome image f at

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

that point.thus, l lies in the range Lmin l Lmax

Lminand Lmaxare positive and finite.

gray scale = [Lmin, Lmax]

common practice, shift the interval to [0, L ]0 = black , L = white



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Resolution

Resolution (how much you can see the detail of

the image) depends on sampling and gray levels.

the bigger the sampling rate (n) and the gray scale(g), the better the approximation of the digitized

image from the original. But the size of the image

gets bigger



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Non-uniform Sampling

For a fixed value of spatial resolution, the

appearance of the image can be improved by

using adaptive sampling rates.Fine sampling

Required in the neighborhood of sharp

gray-level transitions.Coarse sampling

Utilized in relatively smooth regions.

Digital Image Processing, 2nd ed.


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For the images with a

large amount of detail

only a few gray levelsmay be needed.



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Non-uniform Quantization

unequally spaced levels in quantization process

influences on the decreasing the number of gray

level.use few gray levels in the neighborhood of

boundaries.

use more gray levels on smooth area in order to

avoid the false contouring.



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igital mage rocessing, nd ed.www.imageprocessingbook.com


Basic Relationship amongpixels

Neighbors of a pixelConnectivity

Labeling of Connected ComponentsDistance Measures

Arithmetic/Logic Operations

Digital Image Processing, 2nd ed.i i b k


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g g g,www.imageprocessingbook.com


Neighbors of a Pixels



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Connectivity

Let V be the set of gray-level values used to defined connectivity4-connectivity :

2 pixels p and q with values from V are 4-connected if q is in the

set N4(p)

8-connectivity :

2 pixels p and q with values from V are 8-connected if q is in the set

N8(p)

m-connectivity (mixed connectivity):

2 pixels p and q with values from V are m-connected if

q is in the set N4(p) orq is in the set ND(p) and the set N4(p)N4(q) is empty.(the set of pixels that are 4-neighbors of both p and q whose

values are from V )



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Example of Connectivity

Path 8 neighbors m neighbors

m-connectivity eliminates the multiple pathconnections that arise in 8-connectivity.

Digital Image Processing, 2nd ed.www imageprocessingbook com


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Path

a path from pixel p with coordinates (x,y) to pixel

q with coordinates (s,t) is a sequence of distinct

pixels with coordinates(x0,y0),(x1,y1),(xn,yn)

, where (x0,y0) = (x,y) , (xn,yn) = (s,t) and (xi,yi) is

adjacent to (xi-1,yi-1)

n is the length of the pathwe can define 4-,8-, or m-paths depending on

type of adjacency specified.



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Adjacent

A pixel p is adjacent to a pixel q if they are

connected.

Two image area subsets S1 and S2 areadjacent if some pixel in S1 is adjacent to

some pixel S2.



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Labeling 1

Scan the image from left to right

Let p denote the pixel at any step in the scanning

process.

Let r denote the upper neighbor of p.Let t denote the left-hand neighbors of p,

respectively.

When we get to p, points r and t have already

been encountered and labeled if they were 1s.r

t p



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Labeling 2

if the value of p = 0, move on.

if the value of p = 1, examine r and t.

if they are both 0, assign a new label to p.

if only one of them is 1, assign its label to p.if they are both 1

if they have the same label, assign that label to p.

if not, assign one of the labels to p and make a note that

the two labels are equivalent. (r and t are connected

through p).At the end of the scan, all points with value 1 have been

labeled.

Do a second scan, assign a new label for each equivalent

labels.



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Labeling with 8 connected components

do the same way but examine also the upper

diagonal neighbors of p.

if p is 0, move on.

if p is 1

if all four neighbors are 0, assign a new label to p.if only one of the neighbors is 1, assign its label to p.

if two or more neighbors are 1, assign one of the

label to p and make a note of equivalent classes.

after complete the scan, do the second round and

introduce a unique label to each equivalent class.



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Distance Measures

for pixel p, q and z with coordinates (x,y),

(s,t) and (u,v) respectively,

D is a distance 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)



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Euclidean Distance



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g p g


City-Block Distance



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g p g


Chessboard Distance



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g p g


M-connectivity distances

distances of m-connectivity of the pathbetween 2 pixels depends on values of pixelsalong the path.

e.g., if only connectivity of pixels valued 1 isallowed. find the m-distance between p and p4

p3 p4 0 1 1 1 1 1

p1 p2 0 1 0 1 1 1

p 1 1 1

d = 2 d=3 d=4



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Linear and Nonlinear Operations

An operator H is said to be alinearoperatorif it satisfy the following conditions.

H(af - bg) = aH(f) + bH(g)

where f and g are images and a and b are scalarsThe sum of two images is identical to applyingthe operator to the image individually, muliplyingthe results by the constants, and adding those

results.An operator that fails the test of aboveequation is nonlinear. Ex) |afbg|

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