5th Intensive Course on Soil Micromorphology Naples 2001 12th - 14th September Image Analysis Lecture 10 Advanced Image Restoration Other Methods - Batch.
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5th Intensive Course on Soil Micromorphology
Naples 2001
12th - 14th September
Image Analysis
Lecture 10
Advanced Image Restoration
Other Methods
- Batch Processing
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
All Imaging involves imperfection
- no matter how good the optics are
•Non-standard illumination [ lecture 5]
•Blurring from defects in lenses
•Specimen Beam interactions in SEM
Image Restoration.
Other Methods
•Optical Diffraction and Convolution
•Photogrammetry
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Image Restoration
Example from Lecture 5
Though not perfect, the background illumination has been suppress making thresholding much easier.
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
SEM
•electron beam hits specimen and spreads through specimen
•information about specimen comes from an area larger than beam
Problem
•Sharp edges will become blurred
•loss of resolution
Image Restoration.
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Specimen Beam interaction in SEM
Specimen Beam Spreads within specimen.
Two different areas are represented by blue and green areas.
The idealised output is degraded as information comes from both parts of the specimen.
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
•If the intensity at the point x,y is a function f(x,y)
•and the spreading function is similarly defined as h(x,y)
•Then the actual image obtained g(x,y) is given by
Image Restoration.
),(),(),( yxhyxfyxg Where represents the convolution operation
),(.),(),( vuHvuFvuG In Fourier Space the equivalent relationship is:-
),(
),(),(
vuH
vuGvuF Thus we can recover the Fourier
Transform of the unblurred image from:
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image Restoration.
Image 1: Rosette Diagram: Diffraction Pattern (Fourier Transform)
Note: high frequency peaks at large Fourier Spacings
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
In reality, there will always be noise present.
i.e.
),(),(),(),( yxnyxhyxfyxg
2
2
*
1),mod
,,
SNRvuH
vuHvuY
An estimate of the point Spread function in Fourier Space is given by:-
vuYvuGvuF ,.,,
So even with noise, we can estimate what the image would have looked like in the absence of blurring.
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Batch Processing
Determination of Point Spread Function in SEM
• use an object with a sharp edge - of comparable BSE reflectivity to objects to be viewed and in similar matrix.
e.g. glass / resin boundary
•capture image (preferably several)
•determine the distance that the intensity takes to go from say 90% to 10% across the boundary and this indicates the spreading.
•Ideally, several different images at different orientation should be taken.
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Batch Processing
Some Results of consolidated
Kaolin and Silt/Clay Mixtures
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 1 Note that though the contrast is less, the detail and resolution is much better in restored image.
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 2
Image 3
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 4
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 5
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 6
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 7 - Consolidated Silt (Quartz) / Kaolin
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 8 - Consolidated Silt (Quartz) / Kaolin
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
Image 9 - Consolidated Silt (Quartz) / Kaolin
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Advanced Image Restoration
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
•best possible that can be achieved.•No OPERATOR involvement (no subjectivity).
Objective Thresholding:
For objective segmentation - the peaks must be identified and these are used to set threshold level.
Case with Several Phases:
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
Thesholding:
Interactive selection of threshold will be unreliable and may well differ significantly from one person to another.
Data from 2nd and 3rd Intensive Courses:
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
Binary Segmentation with and without image reconstruction.
Porosity is approximately the same in both cases.
But Void Size / Particle Size distribution is very different
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
•Original Image
•Restored Image
•Objective Threshold
•Combination with Domain-Segmentation
Stages in Analysis
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
Domain area porosity(%) (%)
vertical (|) 38.13 45.16inclined (/) 5.95 42.06horizontal (-) 4.74 34.23inclined (\) 42.96 45.92random (O) 8.01 46.74
Overall 45.22
Image 1
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
Domain area porosity(%) (%)
vertical (|) 34.39 47.79inclined (/) 16.81 45.86horizontal (-) 10.72 47.98inclined (\) 32.98 48.19random (O) 4.88 52.42
Overall 47.99
Image 3
Surprisingly horizontal domains are more porous than vertical ones
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
The advantages of Image Restoration are seen in binary images
Binary Image of Original Binary Image of Restored Image
5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 10: Objective Thresholding
Summary
Image Restoration provides a best estimate of what image would be without degradation from optics/recording system
resolution is significantly improved
important for void / particle size distribution
Objective thresholding is possible using Relative Contrast Histogram Method
consistent results - avoid subjectivity
Can be combined with domain segmentation to examine porosity in different domain
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