This document provides an overview of digital image processing. It discusses key topics including digital image fundamentals, image transforms, image enhancement, image restoration, image compression, image segmentation, representation and description, and recognition and interpretation. The document outlines concepts and techniques within each of these topics at a high level over multiple sections and pages with headings, content lists, and explanatory diagrams.
7. SAMPLING AND QUANTIZATION
Quantization: limit of intensity resolution
Sampling: Limit of spatial and temp resolution
Uniform and non-uniform
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8. PIXEL’S RELATIONSHIPS
Two pixel are adjacent if
Neighbors as 4, 8, and m-connectivity
Gray levels satisfy a specified criterion
Connectivity
Existing a path between two pixels
Path
Path from p(x,y) to q(s,t) is
Where (x, y) = (x0, y0), (s, t) = (xn, yn)
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(x0, y0), (x1, x2), …, (xn, yn)
9. II. IMAGE ENHANCEMENT IN FREQ DOMAIN
Discrete Fourier Transform
Other Image Transform
Hotelling Transform
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10. THE DISCRETE FOURIER TRANSFORM
The Fourier transform
1-D
2-D
Properties
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11. THE DISCRETE FOURIER TRANSFORM
Discrete Fourier transform pair
One dimensional
Two dimensional
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13. THE DISCRETE FOURIER TRANSFORM
1. Multiply input image by −1 𝑥+𝑦
2. Compute 𝐹(𝑢, 𝑣), DFT
3. Multiply 𝐹(𝑢, 𝑣) by 𝐻 𝑢, 𝑣
4. Compute IDFT
5. Obtain the real part
6. Multiply the result by −1 𝑥+𝑦
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Fast Fourier transform
Efficient algorithm to compute DFT by reduce computation
burden: O(N2) – O(NlogN)
14. OTHER SEPARABLE IMAGE TRANSFORM
General relation ship
Several condition
Separable
Symmetric
Separable kernel can be compute in two step of 1D transf
For separable and symmetric kernel
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16. HOLTELLING TRANSFORM
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17. III. IMAGINE ENHANCEMENT
Basic intensity functions
Histogram processing
Spatial Filtering
Enhancement in the Frequency domain
Color image processing
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18. BASIC INTENSITY FUNCTIONS
Spatial domain process
Image negatives:
intensity level in the range [0, L-1]
s = L – 1 – r
Log trans
s = c log(1 + r)
Power law (gramma) trans
s = c r
Piecewise-Linear Trans
Contrast stretching
Intensity level slicing
Bit plane slicing
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21. SPATIAL FILTERING
Sharpening filter
Highpass spatial filtering
Emphasize fine details
High-boost filtering
Enhance high freq while keeping the low freq
Highboost = (A-1) original + Highpass
Derivative filters
First order: gradient
Second order
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22. ENHANCEMENT IN THE FREQUENCY DOMAIN
Spatial domain
Definition
Chang pixel position changes
in the scene
Distance is real
Processing
Directly process the input image
pixel array
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Frequency domain
Definition
Change in image position
changes in spatial frequency
Which image intensity values are
changing in the spatial domain
image
Processing
Transform the image to its
frequency representation
Perform image processing
compute
23. ENHANCEMENT IN THE FREQUENCY DOMAIN
Lowpass filter
Ideal
Butterword
Highpass filter
Ideal
Butterworth
Homomorphic
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24. COLOR IMAGE PROCESSING
Background
Human can perceive thousands of colors
Two major area: full color and pseudo color
Color quantization: 8-bit or 24bit
Color fundamental
Result of light in the rentina: 400-700nm
Characterization of light: monochromatic and gray level
Radiance: total amount of energy emitted by light source
Brightness: intensity
Luminance: amount of energy perceived by obervers, in lumens
Color characters
Hue
Saturation
Birghtness 24
25. IV. IMAGE RESTORATION
Degradation Model
Diagonalization of Circulant & Block-Circulant Matrices
Algebraic Approach
Inverse Filtering
Weiner Filter
Constrained LS Restoration
Interactive Restoration
Restoration at Spatial Domain
Geometric transform
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26. Noise models
Spatial and frequency properties
Noise PDF: Gaussian, Rayleigh, Erlang, Exponential, Uniform,
Impulse ..
Estimate noise parameters:
Spectrum inspection: periodic noise
Test image: mean, variance and histogram shape, if imaging system is
available
De-noising
Spatial filtering ( for additive noise)
Mean filters
Order-statistics filters
Adaptive filters:
Frequency domain filtering (for periodic noise)
DEGRADATION MODEL
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27. V. IMAGE COMPRESSION
Fundamentals
Image Compression Models
Elements of Information Theory
Error-Free Compression
Lossy Compression
Image Compression standard
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28. VI. IMAGE SEGMENTATION
Detection of Discontiuties
Edge Linking and Boundary Detection
Thresholding
Region-Oriented Segmentation
Motion in Segmentation
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29. VII. REPRESENTATION AND DESCRIPTION
Representation Scheme
Boundary Descriptors
Regional Descriptors
Morphology
Relational Descriptors
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30. VIII. RECOGNITION AND INTERPRETATION
Elements of Image Analysis
Patterns and Pattern Classes
Decision-Theoretic Methods
Structural Methods
Interpretation
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Hinweis der Redaktion
Image acquisition: acquire digital image by using sampling and quantization (lossy-compress)
Preprocessing: enhancing contrast, remove noise…
Segmentation: partition an image to its objects
Rep & Des: Representation of image for suitable processing and select the interest of features.
Recog & Interp: assign a label to an object and meaning to an ensemble of recognized object
Knowledge: knowledge of problem domain is coded into an DIP
Image acquisition: acquire digital image by using sampling and quantization (lossy-compress)
Preprocessing: no-longer called, but use Image enhancement instead. The simplest technique of DIP
Bring out the detail(which is obscured), highlight the certain features of interest
subjective area (chu quan),
Image restoration: improve the appearance of an image, unlike enhancement, it restoration based on image degradation
Color image processing: every application now require color image: print, advertising, computer displays…
Wavelets and multi-resolution processing: recent trans for easier compress, transmit and alyze
Compression: reduce storage required to save an image.
Morphological processing: extracting image component
Segmentation: partition an image into its constituent parts or
Rep & Des: Representation of image for suitable processing and select the interest of features.
Knowledge: knowledge of problem domain is coded into an DIP
- Aliasing: under-sampling, poor reconstruction (spatial aliasing, temporal aliasing)
Gray level: 2^n, n is a positive integer
To establish boundaries, components
4-adjacency: Two pixels p and q with values from V are 4-adjacent if q is in the set N4(p).
8-adjacency: Two pixels p and q with values from V are 8-adjacent if q is in the set N8(p).
m-adjacency: Two pixels p and q with values from V are m-adjacent if,
q is in N4(P).
q is in ND(p) and the set of { N4(p) giao voi N4(q)} is emplty.
Connectivity: To determine whether the pixels are adjacent in some sense. (N4, N8… )
With finite area under the curve can be expressed as the integral of sines and/pr cosines multiplied by a weight function
Requirement
F(x) is piecewise continuous on every finite interval
Fx is integrable
H(u,v) is transfer function
Application:
Noise removal
Pattern or texture recognition
T is the transform of f and g is the forward trans kernel
H is the inverse transformation kernel
Separable kernel can be computed in two steps, each requiring 1D transform
Parameters:
F^ is apprxomated imgae,
B is inverse transformation matrix
A is NxN transformation matrix
F is NxN image matrix
For example
Calculation of Fourier transform of 2 pixel by 2 pixel 2 D
Wash transform Hadamard transform was used because of its simplicity of implementation and faster than fft.
For measuring randomess of a finite sequence
Testing number sequences
Solving first order partial differential equation, and integral equations
Astronomical image processing, coding and filtering operation
Discrete Cosine Transform: widely use in image compression, use in JPEC< MPECG< H261…
Notice that the DCT is a real transform.
The DCT has excellent energy compaction properties.
There are fast algorithms to compute the DCT similar to the FFT.
The rows of matrix A are the eigen vectors of the covarience matrix arranged in descending order (The first row corresponds to the eigen vector
corresponding to the largest eigen value of C, ...)
- f(x, y) denotes the input image and g(x,y) presents the processed image. T is an operator on f which defined over some neighborhood of (x,y).
Negative
Reversing the intensity level of an image
Expand value of dark pixels, compressing higer level value
Power law: the Same as log trans
Piece wise: advantage – arbitrarily complex, disadvantage – require more user input.
Contrast stretching: spans the range of intensity levels in an image to full intensity range. HOW – just scale with upper and lower limit
Intensity level slicing: highlighting a specific range of intensities in an image.
Bit plane slicing: high order bit give almost information
Histogram: rk is the kth gray level and nk is number of pixels wich have the nk gray level
Histogram Equalization: map from r to s, from poor dynamic rang to wider, but give only one result
Histogram Matching: specify a particular histogram shape. Equalize levels of original image, then specify desired density fucntion to get G(z), and finally applu inverse trans to find z
Local histogram: devise trans functions based on gray-level of distribution by using previous techniques and define a square or rectangular location
The two properties call intensity mean and variance are frequently used ---
Image Subtraction: the difference between the two image
Image averaging : by consider the average of a set of image
The word “filtering” has been borrowed from the frequency domain, defined by:
(1) A neighborhood and (2)
An operation that is performed on the pixels inside the neighborhood
A filtered image is generated as the center of the mask moves to every pixel in the input image Handling Pixels Close to Boundaries by zero padding or some other method
Mask mxn, where m and. n is an odd positive integer. And the gray level in (x,y) pixel are replicated by R
Smoothing filter: for blur and noise reduction, because of always got “snow” on the image
Lowpass filter: averages out rapid changes in intensity
Simplest low-pass: calculate the average of a pixel and all of its 8 immediate neighbors then replace the original pixel
Replete for every pixel in the image. ( about the pixel in the edge?)
Meadian filter
Processing: sort differential value of one pixel and its nearest 8 pixels by ascending order.
Pickup the middle value from sorted 9 values and replace value on the middle with the new value.
d
Sharpening filter: Enhance the edges of objects and adjust the contrast and the shade characteristics. Being detectors with threshold, sensitive to shut noise
Highpass filter: make image appear sharper, emphasize fine details in the image but amplifies noise.
Positive coefficients near its center, and negative in other which satisfy the sum of the coefficients is zero.- constant intensity
Results may negative need scale or cutting
Don’t take the absolute value of the response
Not overdoing this, make degrade image quality, look grainy and unnatural, get a dark donuts around every points.
High-boot filtering
allows some of the low-frequencies back in result looks more like the original with accents on the highpass
Derivative filters:enhance contrast, detect edges and boundaries and also measure feature orientation. Can be taken by using the gradient
First order: require the sum of the coefficient is equal zero
Second order:
Center pixel coefficient be positive
Outercoefficient be negative
Sum of coefficients be zero
Frequencies means:
High frequency - pixel values that change rapidly across the image (e.g: text, texture, leaves…)
Strong low frequency large scale feature in the image( e.g: single object that dominates the image)
Any spatial or temporal signal has an equivalent frequency representation
Low-pass filtering smooths a signal or image: low freq– gradual transitions and high freq = rapid transition
Smoothing helps remove noise
High pass filter only the brightest parts of the image – where SNR is highest
Color fundamental
Radiance: including spectral power distribution
Brightness: visual sensation, which area appers to meit more or less light and cannot be meased quantitatively
Lumiance: more tractable of brightness, mangniture of luminance propotional to physical power, b
Color characters
Hue: Dominant color as perceived by an observer (red, orange, or yellow)
Saturation: Relative purity of color; pure spectrum colors are fully saturated, inversely proportional to amount of light
Brightness: Achromatic notion of intensity
Application:
Scientific exploration, investigation, film making, image and video code/decoding
Consumer photography
Image enhancement: “improve” an image subjectively and Image restoration: remove distortion from image, to go back to the “original” -- objective process, degradation is the degrade of image quality by some affect of noise.
Noise
Spatial and freq properties: define spatial characteristics of noise,
There are several noise like:
Periodic noise: made by electrical or electromechanical interference during the acquisition time.
Reduced significantly via frequency domain filtering.
Estimate noise: by fourier spectrum
Spectrum inspection
Test image
Denoising
Mean filters: arithmetic, geometric
Order statistics filter: based on the ranking ò the pixels