This document provides an overview of digital image processing and is divided into multiple parts. Part I discusses digital image fundamentals, image transforms, image enhancement, image restoration, image compression, and image segmentation. It introduces key concepts such as digital image systems, sampling and quantization, pixel relationships, and image transforms in both the spatial and frequency domains. Image processing techniques like filtering, histogram processing, and frequency domain filtering are also summarized.
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
(x0, y0), (x1, x2), …, (xn, yn)
Where (x, y) = (x0, y0), (s, t) = (xn, yn)
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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
Fast Fourier transform
Efficient algorithm to compute DFT by reduce computation 13
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
Mean:
M
1
x1 mx E{x} xk
x2 M k 1
x1 . ,........, x M Covariance:
M
. T 1 T T
xn Cx E{( x mx )( x mx ) } xk xk mk mk
M k 1
M data points
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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=cr
Piecewise-Linear Trans
Contrast stretching
Intensity level slicing 18
Bit plane slicing
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 Frequency domain
Definition Definition
Chang pixel position changes Change in image position
changes in spatial frequency
in the scene
Which image intensity values are
Distance is real
changing in the spatial domain
image
Processing Processing
Directly process the input image Transform the image to its
pixel array frequency representation
Perform image processing
compute
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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. DEGRADATION MODEL
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:
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Frequency domain filtering (for periodic noise)
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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Notas del editor
Image acquisition: acquire digital image by using sampling and quantization (lossy-compress)Preprocessing: enhancing contrast, remove noise…Segmentation: partition an image to its objectsRep & 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 objectKnowledge: 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 (chuquan), Image restoration: improve the appearance of an image, unlike enhancement, it restoration based on image degradationColor image processing: every application now require color image: print, advertising, computer displays… Wavelets and multi-resolution processing: recent trans for easier compress, transmit and alyzeCompression: reduce storage required to save an image.Morphological processing: extracting image componentSegmentation: 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, components4-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) giaovoi 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 functionRequirementF(x) is piecewise continuous on every finite intervalFx is integrable
H(u,v) is transfer functionApplication:Noise removalPattern or texture recognition
T is the transform of f and g is the forward trans kernelH is the inverse transformation kernelSeparable kernel can be computed in two steps, each requiring 1D transformParameters:F^ is apprxomatedimgae, B is inverse transformation matrixA is NxN transformation matrixF is NxN image matrixFor exampleCalculation 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 sequenceTesting number sequencesSolving first order partial differential equation, and integral equationsAstronomical image processing, coding and filtering operationDiscrete 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 matrixarranged 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).NegativeReversing the intensity level of an imageExpand value of dark pixels, compressing higer level valuePower law: the Same as log transPiece 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 limitIntensity 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 levelHistogram Equalization: map from r to s, from poor dynamic rang to wider, but give only one resultHistogram 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 zLocal histogram: devise trans functions based on gray-level of distribution by using previous techniques and define a square or rectangular locationThe two properties call intensity mean and variance are frequently used --- Image Subtraction: the difference between the two imageImage 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 neighborhoodA filtered image is generated as the center of the mask moves to every pixel in the input image Handling Pixels Close to Boundaries byzero padding or some other methodMaskmxn, where m and. n is an odd positive integer. And the gray level in (x,y) pixel are replicated by RSmoothing filter: for blur and noise reduction, because of always got “snow” on the imageLowpass filter: averages out rapid changes in intensitySimplest low-pass: calculate the average of a pixel and all of its 8 immediate neighbors then replace the original pixelReplete for every pixel in the image. ( about the pixel in the edge?)Meadian filterProcessing: 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 noiseHighpass 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 intensityResults may negative need scale or cuttingDon’t take the absolute value of the responseNot overdoing this, make degrade image quality, look grainy and unnatural, get a dark donuts around every points. High-boot filteringallows some of the low-frequencies back in result looks more like the original with accents on the highpassDerivative filters:enhance contrast, detect edges and boundaries and also measure feature orientation. Can be taken by using the gradientFirst order: require the sum of the coefficient is equal zeroSecond order:Center pixel coefficient be positiveOutercoefficient be negativeSum 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 transitionSmoothing helps remove noiseHigh pass filter only the brightest parts of the image – where SNR is highest
Color fundamentalRadiance: including spectral power distributionBrightness: visual sensation, which area appers to meit more or less light and cannot be meased quantitativelyLumiance: more tractable of brightness, mangniture of luminance propotional to physical power, bColor charactersHue: 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 lightBrightness: Achromatic notion of intensity
Application:Scientific exploration, investigation, film making, image and video code/decodingConsumer 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.NoiseSpatial 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 spectrumSpectrum inspection Test imageDenoisingMean filters: arithmetic, geometricOrder statistics filter: based on the ranking ò the pixels