Thresholding
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Thresholding
Introduction
Intensity histogram h(i ): occurrences of pixel intensity value i e.g., h(i = 3) = 100: there are 100 pixels having intensity value i = 3 For an image f (x , y ) having light object and dark backgroun
Edge Linking
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Edge Linking
Edge Linking
Problem Edge points/pixels/segments seldom characterize an edge completely (e.g., noise, breaks in the edge from non-uniform illumination)
Edge points are linked to become a boundary by using either l
Detection of Discontinuities
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Detection of Discontinuities
Image Segmentation
Segmentation subdivides an image into its constituent regions or objects
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Detection of Discontinuities
Image Segmentation.
Segmentation accuracy determines
Some Basic Morphological Algorithms
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Some Basic Morphological Algorithms
Boundary Extraction
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Some Basic Morphological Algorithms
Boundary Extraction.
Boundary of a set A dierence between the object and the eroded object (A) = A (A B
Opening and Closing
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Opening and Closing
Morphological Image Processing
Opening and Closing Boundary Extraction Region Filling Connected Components Skeletons
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Opening and Closing
Opening
A B = (A B) B
erosion of A by B , followed by
Preliminaries
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Preliminaries
Morphological Image Processing
It is a tool for extracting image components that are useful in the representation and description of region shape, such as boundaries, skeletons etc We use the language in set the
Geometric Transformations
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Geometric Transformations
Geometric Transformations
Also called rubber-sheet transformations Useful for image distortion correction Example X-ray image distortion
distorted image g (x , y )
corrected image f (x ,
Restoration Based on Degradation Function H
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Restoration Based on Degradation Function H
Restoration based on Degradation Function H
Estimating the degradation function Inverse ltering Minimum mean square error (Wiener) ltering Geometric me
Periodic Noise Reduction by Frequency Domain Filtering
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Periodic Noise Reduction by Frequency Domain Filtering
Motivating Example
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Periodic Noise Reduction by Frequency Domain Filtering
Motivating Example.
masked power spectrum
noise
Restoration in the Presence of Noise Only Spatial Filtering
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Restoration in the Presence of Noise Only Spatial Filtering
Restoration in the Presence of Noise Only
g (x , y ) = h(x , y ) f (x , y ) + (x , y ) When noise is the only image deg
Noise Models
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Noise Models
Probability Density Functions
The statistical behavior of the gray-level values in the noise component can be described by some probability density functions
p (x ) 0 for all x p (x ) dx = 1 (the total area under
Image Restoration
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Image Restoration
Motivation: CCD
CCD: converts photons into electrons which are then stored in each pixel well The number of electrons stored in each pixel well is proportional to the number of photons that struck that p
Sharpening Frequency-Domain Filters
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Sharpening Frequency-Domain Filters
Concepts
Edges and other abrupt changes in grey levels are associated with high-frequency components
image sharpening can be achieved by using the high-pass frequency
Smoothing Frequency-Domain Filters
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Smoothing Frequency-Domain Filters
Example
Edges, noise contribute signicantly to the high-frequency content of the FT of an image
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Smoothing Frequency-Domain Filters
Lowpass Filtering in the Frequ
Frequency-Domain Filters
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Frequency-Domain Filters
Filtering in Frequency Domain
One image, two representations f (x , y ): spatial (a collection of pixels) F (u , v ): frequency (rate of change of intensity values or grey level)
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Fr
Discrete Fourier Transform
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Discrete Fourier Transform
Discrete Signals
Discretize a continuous function f (x ) into a sequence
cfw_f (x0 ), f (x0 + x ), f (x0 +2x ), f (x0 +3x ) . . . f (x0 +[N 1]x ) N samples, x units apart Sequence f (0)
Fourier Transform
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Fourier Transform
What is Frequency Domain Analysis?
analyze the image in the frequency domain involves interpreting the frequency spectrum
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Fourier Transform
Example: Signal Corrupted by Noise
Question What is the
Enhancement using Arithmetic/Logic Operations
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Enhancement using Arithmetic/Logic Operations
Motivating Example
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Enhancement using Arithmetic/Logic Operations
Image Operations
Arithmetic operations (p and q are images) p+q pq p q (al
Sharpening Spatial Filters
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Sharpening Spatial Filters
Sharpening
Objectives of sharpening highlight ne detail in an image enhance detail that has been blurred
COMP344 Sharpening Spatial Filters
Sharpening.
We can think of this as high-pass
Histogram Processing
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Histogram Processing
Image Histogram
Digital image with gray level [0, L 1] nk = number of pixels with k th gray level (k = 0, 1, 2, . . . , L 1) N : total number of pixels rk : k th gray level p (rk ) = nk /N : probab
Introduction and Some Basic Gray Level Transformations
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Introduction and Some Basic Gray Level Transformations
Enhancement
Objectives makes an image more suitable than original for specic and problem-oriented applications is often for human