Nguyễn Công Phương
DIGITAL IMAGE PROCESSING
Affine and Logical Operations, Distortions, and Noise in Images
Contents
Introduction to Image Processing & Matlab Image Acquisition, Types, & File I/O Image Arithmetic
Image Transform Spatial & Frequency Domain Filter Design Image Restoration & Blind Deconvolution
Binary Image Processing Image Encryption & Watermarking Image Classification & Segmentation
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I. II. III. IV. Affine & Logical Operations, Distortions, & Noise in Images V. VI. VII. VIII. Image Compression IX. Edge Detection X. XI. XII. XIII. Image – Based Object Tracking XIV. Face Recognition XV. Soft Computing in Image Processing
Image Arithmetic
1. Affine Operations
a) Translation b) Rotation c) Scaling
2. Logical Operators 3. Noise in Images 4. Distortions in Images
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Affine Operations
• An affine operation/transformation maps
variables into new variables by applying a linear combination of translation, rotation, and scaling (TRS) operations
x
A
B
2 y
2
x 1 y 1
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Translation
x
1 0 0 1
x 1 y 1
b 1 b 2
• Pixel movement by b1 in x & b2 in y direction. • Used to improve visualization of an image.
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2 y 2
Rotation
x
x 0 y
cos sin
sin cos
x 1 y 1
• Rotates all pixels by an angle of θ degrees
(counterclockwise for positive angle)
• Used to improve the visual appearance of an
image.
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2 y 0 2
Scaling
x
0
a
a 11 0
x 1 y 1
0 0
• Performs a geometric transformation that can be
used to shrink or zoom the size of an image.
• Image reduction/subsampling: replacement (of a group of pixel values by one arbitrarily chosen pixel, a11 or a22, value from within this group), or by interpolating between pixel values.
• Image zooming: achieved by pixel replication or
by interpolation
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2 y 2 22
Image Arithmetic
1. Affine Operations 2. Logical Operators a) AND & NAND b) OR & NOR c) XOR & XNOR d) NOT
3. Noise in Images 4. Distortions in Images
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AND & NAND
• Used to:
– Compute the intersection of two images, – Extract a portion of an image.
A B AND NAND
AND
AB
0 0 0 1
AB
NAND (
)
0 1 0 1
1 0 0 1
Binary operator
Grayscale operator
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1 1 1 0
OR & NOR
A B OR NOR
OR
A B
0 0 0 1
NOR (
)
A B
0 1 1 0
1 0 1 0
Binary operator
Grayscale operator
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1 1 1 0
Image Arithmetic
1. Affine Operations 2. Logical Operators a) AND & NAND b) OR & NOR c) XOR & XNOR d) NOT
3. Noise in Images 4. Distortions in Images
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XOR & XNOR
A B XOR XNOR
XOR
AB
0 0 0 1
AB
A B A B
XNOR (
)
0 1 1 0
1 0 1 0
Binary operator
Grayscale operator
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1 1 0 1
NOT
A A’
A
2
1b
A
0 1
Binary operator
Grayscale operator
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1 0
Image Arithmetic
1. Affine Operations 2. Logical Operators 3. Noise in Images 4. Distortions in Images
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Noises in Images
• Photon noise: due to the stochastic nature of
photon generation.
• Thermal noise: electrons are released due to
thermal activity & get trapped in the CCD wells.
• On – chip electronic noise: originates in the process of reading the signal from the sensor. • KTC noise: associated with the gate capacitor of
an FET.
• Amplifier noise: in modern well – designed
electronics, it is generally negligible.
• Quantization noise: occurs in the analog – to –
digital converter (ADC).
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Distortions in Images
• Commonly called blur. • Linear motion blur: due to relative motion
between the recording device and the object.
• Uniform out – of – focus blur: when a camera on a 2D imaging plane images a 3D object, some parts of the object are in focus whereas other parts are not.
• Atmospheric turbulence blur: due to a long – term
exposure case.
• Scatter blur: the incident imaging quanta are
reflected by the system structure or other incident quanta.
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