iap chapter1 2012
DESCRIPTION
Image processingTRANSCRIPT
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Dept. of Telecomm. Eng. Faculty of EEE
DIP2012 DHT, HCMUT 1
Digital Image Processing
Dr.-Ing. Tuan Do-Hong
Department of Telecommunications Engineering Faculty of Electrical and Electronics Engineering
HoChiMinh City University of Technology
E-mail: [email protected]
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Dept. of Telecomm. Eng. Faculty of EEE
DIP2012 DHT, HCMUT 2
Outline
1. Digital Image Fundamentals
2. Image Enhancement and Restoration
3. Image Compression
4. Morphological Image Processing
5. Image Segmentation
6. Image Representation and Description
7. Introduction to Object (Pattern) Recognition
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Dept. of Telecomm. Eng. Faculty of EEE
DIP2012 DHT, HCMUT 3
References
[1] R. C. Gonzalez, R. E. Woods, Digital Image
Processing, Addison Wesley, 2nd edition (2002), 3rd edition (2008).
[2] R. C. Gonzalez, R. E. Woods, S. L. Eddins, Digital Image Processing Using Matlab, Gatesmark Publishing, 2nd edition (2009)
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DIP2012 DHT, HCMUT 4
Chapter 1: Digital Image Fundamentals
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DIP2012 DHT, HCMUT 5
1. Digital Image
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DIP2012 DHT, HCMUT 6
1. Analog to Digital (1)
Record
output Display
object observe
Imaging systems
digitize
Sample and quantize
store
Digital storage (disk)
process
Digital computer
Refresh/store
On-line buffer
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DIP2012 DHT, HCMUT 7
1. Analog to Digital (2)
Computers work with numerical (rather than pictorial) data.
An image must be converted to numerical form before processing by computer.
Picture elements or pixels.
Rectangular sampling grid.
(Intensity) Brightness of the image.
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Dept. of Telecomm. Eng. Faculty of EEE
DIP2012 DHT, HCMUT 8
1. Sampling (Digitization of Spatial Coordinates)
256256 6464
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DIP2012 DHT, HCMUT 9
1. Quantization (Intensity Digitization) (1)
0 0 0
0 0
0 0
0 0
0
0 0
0 0
0 0
0
255 255
255
255
255
255 255 255
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DIP2012 DHT, HCMUT 10
1. Quantization (2)
256256, 256 gray-levels 256256, 32 gray-levels
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DIP2012 DHT, HCMUT 11
1. Quantization (3)
256256, 2 gray-levels 256256, 256 gray-levels
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DIP2012 DHT, HCMUT 12
1. Colour Image
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DIP2012 DHT, HCMUT 13
1. Gray-level Image
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1. Binary Image
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DIP2012 DHT, HCMUT 15
1. Digital Image Processing
Manipulation of multidimensional signals Image (photo): Video: CT, MRI:
Coding/compression
Enhancement, restoration, reconstruction
Analysis, detection, recognition, understanding
Visualization
),( yxf),,( tyxf
),,,( tzyxf
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DIP2012 DHT, HCMUT 16
1. Image Transforms
Original Image Fourier Transform Magnitude Phase
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DIP2012 DHT, HCMUT 17
1. Image Enhancement
Original Image High Pass Filtering
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Dept. of Telecomm. Eng. Faculty of EEE
DIP2012 DHT, HCMUT 18
1. Image Compression
),( yxfH
),( yxg Compressed Representation
Decoder
1H),( yxf),( yxg
Encoder
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Dept. of Telecomm. Eng. Faculty of EEE
DIP2012 DHT, HCMUT 19
1. Image Analysis
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Dept. of Telecomm. Eng. Faculty of EEE
DIP2012 DHT, HCMUT 20
1. Applications
Image processing (medical image processing, satellite/astronomy image processing, radar image processing, etc.)
Image analysis - computer vision (character/face/hand/gesture recognitions, content-based browsing and retrieval, medical image analysis, industrial automation, remote sensing, forensics, robotics, radar imaging, cartography, etc.)
Virtual reality (applications in manufacturing, medicine, entertainment, etc.)
Multimedia communication/storage (video processing, digital TV,
video over networks, etc.)
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DIP2012 DHT, HCMUT 21
1. Image Model Image: 2-D light-intensity function, f(x,y): value of f at spatial
coordinates (x,y) gives intensity of image at that point.
where i(x,y): illumination (amount of source light incident on the scene), r(x,y): reflectance (amount of light reflected by the objects in the scene).
0 (total absorption), 1 (total reflectance) In digital image processing, f called gray level G, Lmin < G < Lmax. Interval [Lmin, Lmax]: gray scale. In practice, shifting gray scale to [0, L], G = 0: black, G = L: white.
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1. Image Sampling & Quantization (1)
f(x,y) approximated by equally spaced samples in the form of (NM)-matrix:
Matrix A is called digital image, each element of A is called image element, pixel, or pel.
Sampling: partitioning xy-plane into grid, coordinates of center of each grid are (x,y); x,y: integer. Quantization: f is assigned a gray-level value G (real or integer numbers).
In practice, N = 2n, M = 2k, G = 2m. Total number of bits required to store a digital image: NMm
Resolution: degree of discernible detail (how good approximation in (2.4)), depending on the number of samples (spatial resolution) and gray-levels (intensity resolution).
A=
)1,1()1,1()0,1(
)1,1()1,1()0,1()1,0()1,0()0,0(
),(
MNfNfNf
MfffMfff
yxf
(2.4)
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DIP2012 DHT, HCMUT 23
1. Image Sampling & Quantization (2)
Digitizing the coordinate values
Digitizing the amplitude values
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1. Image Sampling & Quantization (3)
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DIP2012 DHT, HCMUT 25
1. Image Sampling & Quantization (4)
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1. Image Sampling & Quantization (5)
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DIP2012 DHT, HCMUT 27
1. Image Sampling & Quantization (6)
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1. Image Sampling & Quantization (7)
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1. Image Interpolation
Interpolation: Process of using known data to estimate unknown values. E.g., zooming, shrinking, rotating, and geometric correction.
Interpolation (sometimes called resampling): an imaging method to increase (or decrease) the number of pixels in a digital image.
Some digital cameras use interpolation to produce a larger image than the sensor captured or to create digital zoom
(http://www.dpreview.com/learn/?/key=interpolation)
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1. Relationships Between Pixels (1)
Neighbors of a pixel: consider a pixel p at (x,y)
o 4-neighbors of p, N4(p): neighbors at (x+1,y), (x-1,y), (x,y+1), (x,y-1).
o 4-diagonal neighbors of p, ND(p): (x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1).
o 8-neighbors of p, N8(p): N4(p) and ND(p).
p
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1. Relationships Between Pixels (2) Connectivity: Two pixels are connected if they are adjacent (e.g. 4-
neighbors) and their gray levels satisfy specified criterion of similarity (e.g. they are equal).
Let V set of gray levels used to define connectivity (e.g. V={1}: binary image; V={32,33,,63,64}: gray-scale image).
4-connectivity (4-adjacent): p and q are 4-connected if their values from V and q is in N4(p).
8-connectivity (8-adjacent): p and q are 8-connected if their values from V and q is in N8(p).
m-connectivity (m-adjacent, mixed connectivity): p and q are m-connected if their values from V and q is in N4(p), or q is in ND(p) and set S=N4(p) N4(q) is empty (pixels S
are 4-neighbors of both p and q, and whose values are from V).
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DIP2012 DHT, HCMUT 32
1. Relationships Between Pixels (3)
m-connectivity introduced to eliminate ambiguity in path connections (resulted from allowing 8-connectivity)
0 1 1 0 1 1 0 1 0 0 1 0
0 0 1 0 0 1 8-neighbors of center pixel m-neighbors of center pixel
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1. Relationships Between Pixels (4)
Path A (digital) path (or curve) from pixel p with coordinates (x0, y0) to
pixel q with coordinates (xn, yn) is a sequence of distinct pixels with coordinates:
(x0, y0), (x1, y1), , (xn, yn)
where (xi, yi) and (xi-1, yi-1) are adjacent for 1 i n. Here n is the length of the path.
If (x0, y0) = (xn, yn), the path is closed path.
We can define 4-, 8-, and m-paths based on the type of connectivity used.
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DIP2012 DHT, HCMUT 34
1. Relationships Between Pixels (5)
Examples: Connectivity and Path, V = {1, 2}
01,1 11,2 11,3 0 1 1 0 1 1 02,1 22,2 02,3 0 2 0 0 2 0 03,1 03,2 13,3 0 0 1 0 0 1 8-adjacent m-adjacent
The 8-path from (1,3) to (3,3): (i) (1,3), (1,2), (2,2), (3,3) (ii) (1,3), (2,2), (3,3)
The m-path from (1,3) to (3,3): (1,3), (1,2), (2,2), (3,3)
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1. Relationships Between Pixels (6)
Connected in S Let S represent a subset of pixels in an image. Two pixels p with
coordinates (x0, y0) and q with coordinates (xn, yn) are said to be connected in S if there exists a path:
(x0, y0), (x1, y1), , (xn, yn) where
Let S represent a subset of pixels in an image For every pixel p in S, the set of pixels in S that are connected to p
is called a connected component of S. If S has only one connected component, then S is called
connected set. We call R a region of the image if R is a connected set. Two regions, Ri and Rj are said to be adjacent if their union forms
a connected set. Regions that are not to be adjacent are said to be disjoint.
,0 , ( , )i ii i n x y S
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1. Relationships Between Pixels (7)
Boundary (or border) The boundary of the region R is the set of pixels in the region that
have one or more neighbors that are not in R. If R happens to be an entire image, then its boundary is defined as
the set of pixels in the first and last rows and columns of the image.
Foreground and background An image contains K disjoint regions, Rk, k = 1, 2, , K. Let Ru denote
the union of all the K regions, and let (Ru)c denote its complement. All the points in Ru is called foreground; All the points in (Ru)c is called background.
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1. Relationships Between Pixels (8)
Distance measures Given pixels p, q and z with coordinates (x, y), (s, t), (u, v)
respectively, the distance function D has following properties: 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)
The following are the different distance measures: a. Euclidean distance: De(p, q) = [(x - s)2 + (y - t)2]1/2 b. City block distance: D4(p, q) = |x - s| + |y - t| c. Chess board distance: D8(p, q) = max(|x - s|, |y - t|)
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1. Relationships Between Pixels (9)
Array vs. Matrix operation
11 12
21 22
b bB
b b
=
11 12
21 22
a aA
a a
=
11 11 12 21 11 12 12 22
21 11 22 21 21 12 22 22
* a b a b a b a b
A Ba b a b a b a b
+ + = + +
11 11 12 12
21 21 22 22
.* a b a b
A Ba b a b
=
Array product
Matrix product
Array product operator
Matrix product operator
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1. Relationships Between Pixels (10)
Linear vs. Nonlinear operation
[ ]( , ) ( , )H f x y g x y=
[ ][ ]
( , ) ( , )
( , ) ( , )
( , ) ( , )
( , ) ( , )
i i j j
i i j j
i i j j
i i j j
H a f x y a f x y
H a f x y H a f x y
a H f x y a H f x y
a g x y a g x y
+ = + = +
= +
Additivity
Homogeneity
H is said to be a linear operator; H is said to be a nonlinear operator if it does not meet the above qualification.
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1. Relationships Between Pixels (11)
Arithmetic operation Arithmetic operations between 2 pixels p and q: addition,
subtraction, multiplication, division (carry out pixel by pixel). Mask (window) operation:
with proper selection of coefficients, the operation is used for noise reduction, region thinning, edge detection.
p7
p4
p1 p6
p3
p8
p5
p2
p9 w7
w4
w1 w6
w3
w8
w5
w2
w9
5
9
1ppwp
iii =
=
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1. Relationships Between Pixels (12) Example of average window:
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1. Relationships Between Pixels (13)
Set and Logical operations Let A be the elements of a gray-scale image. The elements of A are triplets of the form (x, y, z), where x and y are
spatial coordinates and z denotes the intensity at the point (x, y). The complement of A is denoted Ac The union of two gray-scale images (sets) A and B is defined as the set:
{( , , ) | ( , )}A x y z z f x y= =
{( , , ) | ( , , ) }2 1; is the number of intensity bits used to represent
c
k
A x y K z x y z AK k z
=
=
{max( , ) | , }z
A B a b a A b B =
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1. Relationships Between Pixels (14)
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1. Relationships Between Pixels (15)
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1. Relationships Between Pixels (16) Logic operations: used for feature detection, shape analysis, binary image processing.
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1. Imaging Geometry (1) Translation: A point (x, y, z) is shifted to new position at (x, y, z) by
using displacements (x0, y0, z0):
Matrix form: v=Tv.
Scaling: by factors Sx, Sy, Sz along the x, y, z axes given by
0
0
0
'''
zzzyyyxxx
+=+=+=
=
1100010001
'''
0
0
0
zyx
zyx
zyx
=
11000100010001
1'''
0
0
0
zyx
zyx
zyx
=
1000000000000
z
y
x
SS
S
S
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1. Imaging Geometry (2)
Rotation: Rotation of a point about z-coordinate by an angle :
Rotation of a point about x-coordinate by an angle :
=
1000010000cossin00sincos
R
=
10000cossin00sincos00001
R
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1. Imaging Geometry (3)
Rotation of a point about y-coordinate by an angle :
=
10000cos0sin00100sin0cos
R
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1. Image Transforms: General Form
1
0( , ) ( , , , ) ( , )
M
xT u v r x y u v f x y
=
=
1 1
0 0( , ) ( , , , ) [ ( , )]
M N
u vg x y s x y u v R T u v
= =
=
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1. Image Transforms: 2-D Fourier Transform (1) Definition:
Properties: Separability:
for u, v = 0, 1., N-1.
for x, y = 0, 1., N-1.
=
=
+=1
0
1
0
)//(2),(1),(M
x
N
y
NvyMuxjeyxfMN
vuF
=
=
+=1
0
1
0
)//(2),(),(M
u
N
v
NvyMuxjevuFyxf
( ) ( )
=
=
=1
0
/21
0
/2 ),(1),(N
y
NvyjN
x
Nuxj eyxfeN
vuF
( ) ( )
=
=
=1
0
/21
0
/2 ),(1),(N
v
NvyjN
u
Nuxj evuFeN
yxf
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1. Image Transforms: 2-D Fourier Transform (2)
Advantage of separability property: F(u,v) or f(x,y) can be obtained in 2 steps by successive applications of the 1-D Fourier transform or its inverse:
with Others: translation, periodicity and conjugate symmetry, rotation,
scaling.
( )
=
=1
0
/2),(1),(N
x
NuxjevxFN
vuF
( )
=
=
1
0
/2),(1),(N
y
NvyjeyxfN
NvxF
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1. Image Transforms: 2-D Fourier Transform (3)
Examples of 2-D Fourier transform:
Original Image Magnitude of Fourier transform
Phase of Fourier transform
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1. Image Transforms: 2-D Fourier Transform (4)
Original image
Magnitude of Fourier transform
Low pass filter used
Reconstructed image
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1. Image Transforms: 2-D Fourier Transform (5)
High pass filter used
Reconstructed image
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1. Image Transforms: 2-D Fourier Transform (6)
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1. Image Transforms: 2-D DCT (1)
DCT (Discrete Cosine Transform):
for u, v = 0, 1., N-1, and
for x, y = 0, 1., N-1. where
+
+=
=
= Nvy
NuxyxfvuvuC
N
x
N
y 2)12(cos
2)12(cos),()()(),(
1
0
1
0
+
+=
=
= Nvy
NuxvuCvuyxf
N
u
N
v 2)12(cos
2)12(cos),()()(),(
1
0
1
0
=
==
1,...,2,1,2
0,1
)(Nu
N
uNu
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1. Image Transforms: 2-D DCT (2)
2-D general transform:
where T(x,y,u,v) and I(x,y,u,v) are forward and inverse transform kernel (basis functions), respectively. The basis function depends only on the indexes u, v, x, y, not on the values of image or its transform.
=
=
=1
0
1
0),(),,,(),(
M
x
N
yyxfvuyxTvuF
=
=
=1
0
1
0),(),,,(),(
M
u
N
vvuFvuyxIyxf
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1. Image Transforms: 2-D DCT (3) Example of basis functions of 2-D DCT, N=4:
0
1
2
3
0 1 2 3
u
v
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1. Image Transforms: 2-D DCT (4) Example of basis functions of 2-D DCT, N=8:
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1. Image Transforms: 2-D DCT (5)
DCT is a real transform. There are fast algorithms to compute the DCT similar to the FFT. DCT has excellent energy compaction properties.
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1. Image Transforms: 2-D DCT (6)
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1. Image Transforms: 2-D DCT (7)
DCT FFT
Original
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1. Image Transforms: 2-D DCT (8)
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1. Image Transforms: 2-D DCT (9)
Original Reconstructed from IDCT, (J < 5)
Reconstructed from IDCT, (J < 10) Reconstructed from IDCT, (J < 20)
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1. Probabilistic Methods (1) Let , 0, 1, 2, ..., -1, denote the values of all possible intensitiesin an digital image. The probability, ( ), of intensity level
occurring in a given image is estimated as
i
k
k
z i LM N p z
z
=
( ) ,
where is the number of times that intensity occurs in the image.
kk
k k
np zMN
n z
=
1
0( ) 1
L
kk
p z
=
=
1
0
The mean (average) intensity is given by
= ( )L
k kk
m z p z
=
12 2
0
The variance of the intensities is given by
= ( ) ( )L
k kk
z m p z
=
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1. Probabilistic Methods (2)
14.3 =
th
1
0
The moment of the intensity variable is
( ) = ( ) ( )L
nn k k
k
n z
u z z m p z
=
31.6 =
Example: Comparison of standard deviation values
49.2 =31.6 =
Slide Number 1OutlineReferencesSlide Number 41. Digital Image1. Analog to Digital (1)1. Analog to Digital (2)1. Sampling (Digitization of Spatial Coordinates)1. Quantization (Intensity Digitization) (1)1. Quantization (2)1. Quantization (3)1. Colour Image1. Gray-level Image1. Binary Image1. Digital Image Processing1. Image Transforms1. Image Enhancement1. Image Compression1. Image Analysis1. Applications1. Image Model1. Image Sampling & Quantization (1)1. Image Sampling & Quantization (2)1. Image Sampling & Quantization (3)1. Image Sampling & Quantization (4)1. Image Sampling & Quantization (5)1. Image Sampling & Quantization (6)1. Image Sampling & Quantization (7)1. Image Interpolation1. Relationships Between Pixels (1)1. Relationships Between Pixels (2)1. Relationships Between Pixels (3)1. Relationships Between Pixels (4)1. Relationships Between Pixels (5)1. Relationships Between Pixels (6)1. Relationships Between Pixels (7)1. Relationships Between Pixels (8)1. Relationships Between Pixels (9)1. Relationships Between Pixels (10)1. Relationships Between Pixels (11)1. Relationships Between Pixels (12)1. Relationships Between Pixels (13)1. Relationships Between Pixels (14)1. Relationships Between Pixels (15)1. Relationships Between Pixels (16)1. Imaging Geometry (1)1. Imaging Geometry (2)1. Imaging Geometry (3)1. Image Transforms: General Form1. Image Transforms: 2-D Fourier Transform (1)1. Image Transforms: 2-D Fourier Transform (2)1. Image Transforms: 2-D Fourier Transform (3)1. Image Transforms: 2-D Fourier Transform (4)1. Image Transforms: 2-D Fourier Transform (5)1. Image Transforms: 2-D Fourier Transform (6)1. Image Transforms: 2-D DCT (1)1. Image Transforms: 2-D DCT (2)1. Image Transforms: 2-D DCT (3)1. Image Transforms: 2-D DCT (4)1. Image Transforms: 2-D DCT (5)1. Image Transforms: 2-D DCT (6)1. Image Transforms: 2-D DCT (7)1. Image Transforms: 2-D DCT (8)1. Image Transforms: 2-D DCT (9)1. Probabilistic Methods (1)1. Probabilistic Methods (2)