5th Intensive Course on Soil Micromorphology Naples 2001 12th - 14th September Image Analysis Lecture 10 Advanced Image Restoration Other Methods - Batch.

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.


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.


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.


•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:


Image Restoration.

Image 1: Rosette Diagram: Diffraction Pattern (Fourier Transform)

Note: high frequency peaks at large Fourier Spacings


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


Image 1 Note that though the contrast is less, the detail and resolution is much better in restored image.


Image 2

Image 3


Image 4


Image 5


Image 6


Image 7 - Consolidated Silt (Quartz) / Kaolin






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:


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:


Binary Segmentation with and without image reconstruction.

Porosity is approximately the same in both cases.

But Void Size / Particle Size distribution is very different



•Original Image

•Restored Image

•Objective Threshold

•Combination with Domain-Segmentation

Stages in Analysis


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


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


The advantages of Image Restoration are seen in binary images

Binary Image of Original Binary Image of Restored Image


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

5th Intensive Course on Soil Micromorphology Naples 2001 12th - 14th September Image Analysis Lecture 10 Advanced Image Restoration Other Methods - Batch.

Documents

image analysis lecture

image analysis lecture

actual image

unblurred image

restored image

sem image restoration

image restoration example

soil micromorphology