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DIGITAL IMAGE PROCESSINGPART IThuong Nguyen

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CONTENT

Digital image fundamentals Image transform Image enhancement Image restoration Image compression

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I. DIGITAL FUNDAMENTAL

Digital Image Processing System Sampling and Quantization Relationships between pixels

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DIP SYSTEM

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DIP SYSTEM

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DIP SYSTEM

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SAMPLING AND QUANTIZATION

Quantization: limit of intensity resolution Sampling: Limit of spatial and temp resolution

Uniform and non-uniform

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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)(x0, y0), (x1, x2), …, (xn, yn)

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II. IMAGE ENHANCEMENT IN FREQ DOMAIN

Discrete Fourier Transform Other Image Transform Hotelling Transform

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THE DISCRETE FOURIER TRANSFORM

The Fourier transform 1-D 2-D

Properties

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THE DISCRETE FOURIER TRANSFORM Discrete Fourier transform pair

One dimensional

Two dimensional

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THE DISCRETE FOURIER TRANSFORM

2D FFT and Image Processing

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THE DISCRETE FOURIER TRANSFORM

1. Multiply input image by 2. Compute , DFT3. Multiply by

4. Compute IDFT5. Obtain the real part6. Multiply the result by

Fast Fourier transform Efficient algorithm to compute DFT by reduce computation

burden: O(N2) – O(NlogN)

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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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OTHER SEPARABLE IMAGE TRANSFORM

Walsh Transform

Hadamard transform

Discrete cosine transform

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HOLTELLING TRANSFORM

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2

.

.

n

x

x

x

x

1

1{ }

M

x kk

m E x xM

x,........,

M data points

1 M

1

1{( )( ) }

MT TT

x x x k k k kk

C E x m x m x x m mM

Mean:

Covariance:

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III. IMAGINE ENHANCEMENT

Basic intensity functions Histogram processing Spatial Filtering Enhancement in the Frequency domain Color image processing

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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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HISTOGRAM PROCESSING

Histogram Histogram equalization: Histogram matching Local histogram processing

Image subtraction Image averaging

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SPATIAL FILTERING Fundamental: using spatial masks for Image Processing

Smoothing Filter Lowpass spatial filtering Meadian filtering

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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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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

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

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ENHANCEMENT IN THE FREQUENCY DOMAIN

Lowpass filter Ideal

Butterword

Highpass filter Ideal

Butterworth

Homomorphic

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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

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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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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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V. IMAGE COMPRESSION

Fundamentals Image Compression Models Elements of Information Theory Error-Free Compression Lossy Compression Image Compression standard

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VI. IMAGE SEGMENTATION

Detection of Discontiuties Edge Linking and Boundary Detection Thresholding Region-Oriented Segmentation Motion in Segmentation

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VII. REPRESENTATION AND DESCRIPTION

Representation Scheme Boundary Descriptors Regional Descriptors Morphology Relational Descriptors

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VIII. RECOGNITION AND INTERPRETATION

Elements of Image Analysis Patterns and Pattern Classes Decision-Theoretic Methods Structural Methods Interpretation