Chapter02.ppt of Image processing and Applications

Digital Image Processing, 2nd ed. www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 2
Digital Image Fundamentals

Elements of Visual Perception
中英名詞對照 :
Cornea: 角膜
Sclera: 鞏膜
Choroid: 脈絡膜
Retina: 視網膜
Iris: 虹彩
Lens: 晶體
Macula lutea: 黃斑
Fovea: 中央窩
Blind spot: 盲點
Rod: 桿狀細胞
Cone: 錐狀細胞

Structure of the Human Eye
• Pattern vision is afforded by the distribution of discrete light
receptors over the surface of the retina.
• There are two classes of receptors: cones and rods.
– The number of cones in each eye: 6 to 7 millions
– The number of rods in each eye: 75 to 150 millions
– The cones is concentrated in the central portion of the retina (fovea).
– The rods are distributed over the retinal surface.
• Photopic (bright-light) vision: vision with cones
– color receptors, high resolution in the fovea, less sensitive to light
• Scotopic (dim-light) vision: vision with rods
– color blind, much more sensitive to light (night vision), lower
resolution

Structure of the Human Eye

Image Formation in the Eye
• Focal length of the eye: 17 to 14 mm
• Let h be the height in mm of that object in the retinal image,
then
15/100 = h / 17 , h = 2.55mm
• The retinal image is reflected primarily in the area of the
fovea.

Brightness Adaptation and Discrimination
•The range of brightness that the eye can
adapt to is enormous, roughly around 1010
to 1.
•Photopic vision alone has a range of
around 106
to 1.
•Brightness adaptation: example “ Ba”
•mL: millilambert ( 亮度單位 )

Example: Mach bands

Example: Simultaneous Contrast

Examples for Human Perception Phenomena

Light and the Electromagnetic Spectrum

• Three basic quantities described the quality of
a chromatic ( 彩色的 ) light source:
– Radiance: the total amount energy that flow from
the light source (can be measured)
– Luminance: the amount of energy an observer
perceives from a light source (can be measured)
– Brightness: a subjective descriptor of light
perception; perceived quantity of light emitted
(cannot be measured)

• Relationship between frequency ( ) and wavelength ( )
, where c is the speed of light
• Energy of a photon
, where h is Planck’s constant




c


h
E 

Image Sensing and Acquisition
• Nowadays most visible and near IR electromagnetic imaging is done with
2-dimensional charged-coupled devices (CCDs).

A Simple Image Formation Model
• Binary images: images having only two possible brightness levels (black
and white)
• Gray scale images : “black and white” images
• Color images: can be described mathematically as three gray scale images
• Let f(x,y) be an image function, then
f(x,y) = i(x,y) r(x,y),
where i(x,y): the illumination function
r(x,y): the reflection function
Note: 0 < i(x,y)< ∞ and 0 <r(x,y)< 1.
• For digital images the minimum gray level is usually 0, but the maximum
depends on number of quantization levels used to digitize an image. The
most common is 256 levels, so that the maximum level is 255.

Image Sampling and Quantization

Image Sampling and Quantization
• Sampling: digitizing the 2-dimensional spatial coordinate values
• Quantization: digitizing the amplitude values (brightness level)

Representing Digital Images

Spatial and Gray-Level Resolution
Spatial Resolution

Spatial Resolution by Re-sampling

Gray-Level Resolution
2
4
8
16
128
32
64
256

How to Decide Spatial and Gray-Level Resolution?
• Figure 2.22 (a): The woman’s face; Image with low level of detail.
• Figure 2.22 (b): The cameraman; Image with medium level of detail.
• Figure 2.22 (c): The crowd picture; Image with a relatively large amount of
detail.

Aliasing and Moiré Pattern
• All signals (functions) can be shown to be made up of a linear
combination sinusoidal signals (sines and cosines) of different
frequencies. (Chapter 4)
• For physical reasons, there is a highest frequency component
in all real world signals.
• Theoretically,
– if a signal is sampled at more than twice its highest frequency
component, then it can be reconstructed exactly from its samples.
– But, if it is sampled at less than that frequency (called undersampling),
then aliasing ( 失真 ) will result.
– This causes frequencies to appear in the sampled signal that were not in
the original signal.
– The Moiré pattern shown in Figure 2.24 is an example. The vertical
low frequency pattern is a new frequency not in the original patterns.

Aliasing and Moiré Pattern
The effect of aliased frequencies

Zooming and Shrinking Digital Images
• Zooming: increasing the number of pixels in an
image so that the image appears larger
– Nearest neighbor interpolation
• For example: pixel replication--to repeat rows and
columns of an image
– Bilinear interpolation
• Smoother
– Higher order interpolation
• Image shrinking: subsampling

Zooming and Shrinking Digital Images
Nearest neighbor
Interpolation
(Pixel replication)
Bilinear
interpolation

Some Basic Relationships Between Pixels
• Neighbors of a pixel
– There are three kinds of neighbors of a pixel:
• N4(p) 4-neighbors: the set of horizontal and vertical neighbors
• ND(p) diagonal neighbors: the set of 4 diagonal neighbors
• N8(p) 8-neighbors: union of 4-neighbors and diagonal neighbors
O O O
O X O
O O O
O O
X
O O
O
O X O
O

• Adjacency:
– Two pixels that are neighbors and have the same grey-level
(or some other specified similarity criterion) are adjacent
– Pixels can be 4-adjacent, diagonally adjacent, 8-adjacent,
or m-adjacent.
• m-adjacency (mixed adjacency):
– Two pixels p and q of the same value (or specified
similarity) are m-adjacent if either
• (i) q and p are 4-adjacent, or
• (ii) p and q are diagonally adjacent and do not have any common
4-adjacent neighbors.
• They cannot be both (i) and (ii).

• An example of adjacency:

• Path:
– The length of the path
– Closed path
• Connectivity in a subset S of an image
– Two pixels are connected if there is a path between them that lies
completely within S.
• Connected component of S:
– The set of all pixels in S that are connected to a given pixel in S.
• Region of an image
• Boundary, border or contour of a region
• Edge: a path of one or more pixels that separate two regions
of significantly different gray levels.

• Distance measures
– Distance function: a function of two points, p and q, in space
that satisfies three criteria
– The Euclidean distance De(p, q)
– The city-block (Manhattan) distance D4(p, q)
– The chessboard distance D8(p, q)
)
,
(
)
,
(
)
,
(
)
(
and
),
,
(
)
,
(
)
(
0
)
,
(
)
(
z
q
D
q
p
D
z
p
D
c
p
q
D
q
p
D
b
q
p
D
a




2
2
)
(
)
(
)
,
( t
y
s
x
q
p
De 



|
|
|
|
)
,
(
4 t
y
s
x
q
p
D 



|)
|
|,
max(|
)
,
(
8 t
y
s
x
q
p
D 



Chapter02.ppt of Image processing and Applications

More Related Content

Similar to Chapter02.ppt of Image processing and Applications (20)

Recently uploaded (20)

Chapter02.ppt of Image processing and Applications