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

5th Intensive Course on Soil Micromorphology - Naples 2001 Image 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 2001 Image 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 2001 Image 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 2001 Image 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 2001 Image 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. Where represents the convolution operation In Fourier Space the equivalent relationship is:- Thus we can recover the Fourier Transform of the unblurred image from:

5th Intensive Course on Soil Micromorphology - Naples 2001 Image 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 2001 Image Analysis - Lecture 10: Advanced Image Restoration In reality, there will always be noise present. i.e. An estimate of the point Spread function in Fourier Space is given by:- 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 2001 Image 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 2001 Image Analysis - Lecture 10: Batch Processing Some Results of consolidated Kaolin and Silt/Clay Mixtures

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration Image 1Note that though the contrast is less, the detail and resolution is much better in restored image.

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration Image 2

Image 3 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration

Image 4 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration

Image 5 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration

Image 6 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration

Image 7 - Consolidated Silt (Quartz) / Kaolin 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration

Image 8 - Consolidated Silt (Quartz) / Kaolin 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration

Image 9 - Consolidated Silt (Quartz) / Kaolin 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Advanced Image Restoration

5th Intensive Course on Soil Micromorphology - Naples 2001 Image 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 2001 Image 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 2001 Image 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 2001 Image Analysis - Lecture 10: Objective Thresholding

5th Intensive Course on Soil Micromorphology - Naples 2001 Image 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 2001 Image Analysis - Lecture 10: Objective Thresholding Image 1

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Objective Thresholding Image 3 Surprisingly horizontal domains are more porous than vertical ones

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 10: Objective Thresholding The advantages of Image Restoration are seen in binary images Binary Image of OriginalBinary Image of Restored Image

5th Intensive Course on Soil Micromorphology - Naples 2001 Image 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