![Page 1: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/1.jpg)
Image Analysis
Digital Image Fundamentals
Raul Queiroz Feitosa
Gilson A. O. P. Costa
![Page 2: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/2.jpg)
8/14/2019 Digital Image Fundamentals 2
Digital Image Fundamentals
Objective
“The purpose of this chapter is to introduce some
basic concepts related to digital images…”
![Page 3: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/3.jpg)
8/14/2019 Digital Image Fundamentals 3
Digital Image Fundamentals
Contents: Elements of Visual Perception
Image Sensing and Acquisition
Image Sampling and Quantization
Image Interpolation
Color
Relationships Between Pixels
![Page 4: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/4.jpg)
8/14/2019 Digital Image Fundamentals 4
Elements of Visual Perception
Structure of the Human Eye
Eye diameter ~ 20mm Fovea diameter ~ 1.5mm
![Page 5: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/5.jpg)
8/14/2019 Digital Image Fundamentals 5
Elements of Visual Perception
Structure of the Human Eye
Light receptors in the retina: Rods and Cones
![Page 6: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/6.jpg)
8/14/2019 Digital Image Fundamentals 6
Elements of Visual Perception
Structure of the Human Eye
Cones
• Highly sensitive to color
• Photopic (bright light) vision
• 3 types: S(blue); M(green); L(red)
• 6 to 7 mio, located primarily
in the fovea
100
80
60
40
20
400 450 500 550 600 650 700
ab
sorp
tion
wavelength
![Page 7: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/7.jpg)
8/14/2019 Digital Image Fundamentals 7
Elements of Visual Perception
Structure of the Human Eye
Cones
• Highly sensitive to color
• Photopic (bright light) vision
• 3 types: S(blue); M(green); L(red)
• 6 to 7 mio, located primarily in the fovea
Rods
• Sensitive to low levels of illumination
• Scotopic (dim-light) vision
• 75 to 150 mio, distributed over the retina
![Page 8: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/8.jpg)
8/14/2019 Digital Image Fundamentals 8
Elements of Visual Perception
Structure of the Human Eye
![Page 9: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/9.jpg)
8/14/2019 Digital Image Fundamentals 9
Elements of Visual Perception
Cone density in fovea area: 150000/mm2 (comparable to artificial sensors)
![Page 10: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/10.jpg)
8/14/2019 Digital Image Fundamentals 10
Elements of Visual Perception
Image Formation in the Eye
![Page 11: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/11.jpg)
8/14/2019 Digital Image Fundamentals 11
Image Sensing and Acquisition
Sensing
sensor array
single sensor
line sensor
![Page 12: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/12.jpg)
8/14/2019 Digital Image Fundamentals 12
Image Sensing and Acquisition
Single Sensor
![Page 13: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/13.jpg)
8/14/2019 Digital Image Fundamentals 13
Image Sensing and Acquisition
Line Sensor
![Page 14: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/14.jpg)
8/14/2019 Digital Image Fundamentals 14
Image Sensing and Acquisition
Sensor Array
![Page 15: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/15.jpg)
8/14/2019 Digital Image Fundamentals 15
Image Sensing and Acquisition
Image Formation Model
In this part of the course images will be denoted by a
function of the form
f(x,y):R2→(0,∞)
with two components: illumination and reflectance
f(x,y) = i(x,y) r(x,y)
where
0< i(x,y) <∞ and 0< r(x,y) <1
![Page 16: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/16.jpg)
8/14/2019 Digital Image Fundamentals 16
Image Sensing and Acquisition
Image Formation Model
The intensity i of a monochrome image at any coordinate (x ,y) is called the gray level of the image at that point. That is
i(x,y):R2→(0,∞)
Intensity lies in a range
0< Lmin≤ i(x,y) ≤ Lmax <∞
The interval [Lmin, Lmax ] is called gray scale
Common practice is to shift the interval to [0, L-1] where f(x,y)=0 is considered black and f(x,y)=L-1 is considered white.
![Page 17: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/17.jpg)
8/14/2019 Digital Image Fundamentals 17
Image Sampling and Quantization
Sampling: digitizing in space
M colums
N r
ow
s
f(N,M)f(N,2)f(N,1)
f(2,M)f(2,2)f(2,1)
f(1,M)f(1,2)f(1,1)
yxf
),(
Matrix N M
pixel
![Page 18: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/18.jpg)
8/14/2019 Digital Image Fundamentals 18
Image Sampling and Quantization
Quantization: digitizing the amplitude - 2m-1
- 0 - 1
•
•
•
![Page 19: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/19.jpg)
8/14/2019 Digital Image Fundamentals 19
Image Sampling and Quantization
Sampling and quantization
![Page 20: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/20.jpg)
8/14/2019 Digital Image Fundamentals 20
Image Sampling and Quantization
Result of sampling and quantization
![Page 21: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/21.jpg)
8/14/2019 Digital Image Fundamentals 21
Image Sampling and Quantization
400x304 200x152 100x76 50x38
16 gray levels 8 gray levels 4 gray levels 2 gray levels
![Page 22: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/22.jpg)
8/14/2019 Digital Image Fundamentals 22
Image Sampling and Quantization
Spatial resolution
pixels per unit distance
dots per inch (dpi)
pixels per inch (ppi)
Remote Sensing
ground sampling distance (GSD)
pixel resolution, e.g., pixel = 1x1m
Intensity resolution
number of bits used to quantize intensity (= gray levels)
pixel depth, e.g., 8 bits, 11bits, 16bits, etc.
![Page 23: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/23.jpg)
8/14/2019 Digital Image Fundamentals 23
Image Interpolation
What is the intensity at a non-integer pixel coordinate?
(x1 ,y1) (x2 ,y1)
(x1 ,y2) (x2 ,y2)
(x ,y)
I(x ,y) = ax + by + cxy + d
I(x1,y1) = ax1 + by1 + cx1y1 + d
I(x2,y1) = ax2 + by1 + cx2y1 + d
I(x1,y2) = ax1 + by2 + cx1y2 + d
I(x2,y2) = ax2 + by2 + cx2y2 + d
4 unknowns
4
equations
Bilinear interpolation Bicubic interpolation
3
0
3
0
,
i j
ji
ijyxayxI
16 coefficients
16 equations
on 16 nearest neighbors
![Page 24: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/24.jpg)
Image Interpolation
What is the intensity at a non-integer pixel coordinate?
(x2 ,y1) Bilinear interpolation Bicubic interpolation
![Page 25: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/25.jpg)
8/14/2019 Digital Image Fundamentals 25
Image Interpolation
1250 dpi (3692×2812)
↓↑
72 dpi (213×162)
1250 dpi (3692×2812)
↓↑
150 dpi (443×337)
nearest neighbor bilinear bicubic
![Page 26: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/26.jpg)
8/14/2019 Digital Image Fundamentals 26
Image Interpolation
Geometric Transformations (T)
y
x x´
y´
+
+
(xi´,yi´)=T(xi,yi)
(xj,yj)=T-1 (xj´,yj´) +
+
original image transformed image
pixels of the output image
are visited and their values
are estimated upon their
corresponding locations in
the input image
![Page 27: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/27.jpg)
Image Interpolation
Application: image co-registration Fitting of the coordinate system of an image to that of a second image
reference image (orthophoto) unregistered image
![Page 28: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/28.jpg)
Image Interpolation
Application: image co-registration Fitting of the coordinate system of an image to that of a second image
reference image (orthophoto) coregistered image
![Page 29: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/29.jpg)
8/14/2019 Digital Image Fundamentals 29
Color
Multispectral Images are acquired by sensors sensitive to a
limited range of the electromagnetic spectrum
c =
where c = ~3x108m/s
![Page 30: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/30.jpg)
8/14/2019 Digital Image Fundamentals 30
Color
Multispectral Images are acquired by sensors sensitive to a
limited range of the electromagnetic spectrum
cosmic rays gamma
rays
X
rays UV visibel
light
infra
red
termal
radiation
10-5nm 10-3nm 1 nm 0,3 m 0,4 m 0,75 m 3 m 15 m wavelength
Visible range
BLUE GREEN RED
Spectrum in bands
Remote Sensing
![Page 31: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/31.jpg)
8/14/2019 Digital Image Fundamentals 31
Color
RGB and CYM Models
Primary colors
• red
• green
• blue
Secondary colors
• cyan
• yellow
• magenta
A secondary color subtracts or
absorbs a primary color and reflects
or transmits the others.
Any color can be expressed as
additive combinations of the
primary colors.
B
G
R
Y
M
C
1
1
1
Convertion operation
cyan
yellow
magenta
red green
blue
![Page 32: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/32.jpg)
8/14/2019 Digital Image Fundamentals 32
Color
HSV Model Any color is defined by three values: • Hue (H): associated with the dominant
wavelength.
• Saturation (S): refers to the purity, or the
amount of white light mixed with a hue.
• Value (V): associated to brightness.
Advantages: • Brightness is expressed by intensity,
while chromaticity by hue and
saturation.
• Intimately related to the human
perception of colors.
Conversion Operation See text book
![Page 33: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/33.jpg)
8/14/2019 Digital Image Fundamentals 33
Color
CIE Lab Model Any color is defined by three values: • L: associated with the brightness.
• a : - green / + magenta .
• b : - blue / + yellow.
Advantages: • Perceptually uniform: equal
distances on the CIELab space
correspond to equal perceived color
differences.
• Larger gamut (the number of
colors that can be accurately
represented).
Conversion Operation See text books
![Page 34: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/34.jpg)
8/14/2019 Digital Image Fundamentals 34
Relationships Between Pixels
Neighbors of a Pixel
Neighborhood N4 Neighborhood ND Neighborhood N8
N8 = N4 ND
(x,y-1)
(x,y +1)
(x+1,y) (x-1,y) (x,y)
pixel p (x-1,y-1) (x+1,y-1)
(x+1,y+1) (x-1,y+1)
(x,y)
(x+1,y-1)
(x+1,y+1)
(x+1,y)
(x-1,y-1)
(x-1,y+1)
(x,y -1)
(x-1,y)
(x,y+1)
(x,y)
pixel p
![Page 35: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/35.jpg)
8/14/2019 Digital Image Fundamentals 35
Relationships Between Pixels
Adjacency
Let V be the set of gray-levels used to define adjacency.
Two pixels p and q with values in V are adjacent if:
4-adjacency : q N4 (p),
8-adjacency : q N8 (p),
m-adjacency : (i) q N4 (p), OR
(ii) q ND (p) AND N4 (p) N4 (q) = .
q
p q p
q
p
q
p
q
p
adjacent adjacent adjacent non adjacent non adjacent
![Page 36: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/36.jpg)
8/14/2019 Digital Image Fundamentals 36
Relationships Between Pixels
Why is this important?
How many objects are there in this picture?
![Page 37: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/37.jpg)
8/14/2019 Digital Image Fundamentals 37
Relationships Between Pixels
Why is this important?
Are the object borders connected?
No if 4-adjacency is considered Yes for all adjacency types
![Page 38: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/38.jpg)
8/14/2019 Digital Image Fundamentals 38
Relationships Between Pixels
Adjacency
Two image subsets S1 and S2 are adjacent if some pixel in S1 is adjacent to some pixel in S2.
Path
A (digital) path (or curve) 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) and (xi-1,yi-1) are adjacent for 1≤ i ≤ n.
![Page 39: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/39.jpg)
8/14/2019 Digital Image Fundamentals 39
Relationships Between Pixels
Connectivity between pixel sets
Two pixels p and q are said to be connected in a subset S
of pixels in an image, if there exists a path between them
consisting entirely of pixels in S.
pixels in S
p q
p and q are connected in S ?
![Page 40: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/40.jpg)
8/14/2019 Digital Image Fundamentals 40
Relationships Between Pixels
Connected components
For any pixel p in S, the set of pixels that are connected
to it in S is called a connected component of S.
Pixels in S are colored white
How many connected components in S ?
![Page 41: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/41.jpg)
8/14/2019 Digital Image Fundamentals 41
Relationships Between Pixels
Connected components
If it only has one connected component, then the set S is
called a connected set.
Pixels in S are colored white
Is S a connected set?
![Page 42: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/42.jpg)
8/14/2019 Digital Image Fundamentals 42
Relationships Between Pixels
Region
A subset of pixels R in an image is called a region if it
is a connected set.
How many regions (objects) in this image?
![Page 43: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/43.jpg)
8/14/2019 Digital Image Fundamentals 43
Relationships Between Pixels
Boundary (border or contour)
The boundary of a region R is the set of pixels in the
region that have one or more neighbors that are not in
R.
![Page 44: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/44.jpg)
8/14/2019 Digital Image Fundamentals 44
Relationships Between Pixels
Distance Measures
For pixels 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 ), and
(c) D(p,z) D(p,q ) + D(q,z ).
![Page 45: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/45.jpg)
8/14/2019 Digital Image Fundamentals 45
Relationships Between Pixels
Commonly used distance functions:
Euclidean distance:
De(p,q) = [( x - s )2 + ( y - t )2]1/2
City-block (Manhatan) distance:
D4(p,q) = |( x - s )| + |( y - t )|
Chessboard distance:
D8(p,q) = max( |( x - s )| ,|( y - t )| )
D4
De D8
p
q
4 3 2 3 4
3 2 1 2 3
2 1 0 1 2
3 2 1 2 3
4 3 2 3 4
2 2 2 2 2
2 1 1 1 2
2 1 0 1 2
2 1 1 1 2
2 2 2 2 2
![Page 46: Image Analysis Digital Image Fundamentalsraul/ImageAnalysis/Fundamentals.pdfImage Sensing and Acquisition Image Formation Model The intensity i of a monochrome image at any coordinate](https://reader030.vdocuments.site/reader030/viewer/2022040416/5f3768e73b740b2b58290b42/html5/thumbnails/46.jpg)
8/14/2019 Digital Image Fundamentals 46
Next Topic
Image
Enhancement in the
Spatial Domain