[Title Page]

 

 

Contents

 


1 Introduction

2 Literature Survey

3 Algorithm Development

4 Manual Delineation Experiments

5 Parameter Setting Experiments

6 Active Contour Model Experiments

7 Discussion

8 Conclusion

Appendices


1 Introduction

 

1.1 Leg Ulcers: Causes and Concerns

 

1.2 Background to the Thesis

 

1.3 Practical Wound Measurement

 

1.4 Proposed Solution

 

1.5 Contribution of this Work

 

1.6 Definition of Measurement Terms


2 Literature Survey

 

2.1 Image Segmentation Methods

 

2.1.1 Histogram Analysis

 

2.1.2 Region Growing and Split-and-Merge Schemes

 

2.1.3 Colour-Space Analysis and Segmentation

 

2.1.4 Pixel Classification for Segmentation

 

2.1.5 Gradient Operators, Edge and Zero-Crossing Detectors

 

2.1.6 Watershed Segmentation

 

2.1.7 Radial Search Algorithms

 

2.1.8 Boundary Following Algorithms

 

2.1.9 Summary

 

2.2 Active Contour Models

 

2.2.1 Modelling of the Contour

 

2.2.2 Formulation of the Energy Functional

 

2.2.3 Minimisation of the Energy Functional

 

2.2.3.1 Elastic Energy and Forces

 

2.2.3.2 Bending Energy and Forces

 

2.2.4 Weaknesses of the Kass Model

 

2.2.5 Solution of Euler-Lagrange Equations

 

2.2.6 Spatial Discretisation

 

2.2.6.1 Finite Element Shape Functions

 

2.2.6.2 Stiffness Matrix Equations

 

2.2.7 Time Discretisation

 

2.2.8 Stability of the Iterative Solution Method

 

2.2.9 Direct Energy Minimisation Approaches

 

2.2.10 Element Collapse Problem

 

2.2.10 Modified Internal Energy and Forces

 

2.2.10 Region Pressure Energy

 

2.2.10 Directional External Energy and Forces

 

2.2.14 Setting the Contour Regularisation Parameters

 

2.2.15 Initialisation of Active Contour Models

 

2.2.16 Global Energy Minimum Seeking

 

2.3 Summary


3 Algorithm Development

 

3.1 Producing the External Potential Field

 

3.1.1 Depletion of the External Energy and Attractive Forces

 

3.1.2 Translation of Edges

 

3.1.3 Scale Descent Algorithm

 

3.2 The Ground-Attract (GA) Algorithm

 

3.2.1 Stability of the Solution

 

3.2.2 Properties of the Model

 

3.2.3 Minimisation Algorithm

 

3.2.4 Possible Improvement of the Model

 

3.3 The Tangent-Normal (TN) Algorithm

 

3.3.1 External Force Made Normal to the Contour

 

3.3.2 Elastic Force Made Tangential to the Contour

 

3.3.3 Implementation of Tangential-Only Elastic Force

 

3.3.4 Stability of the Solution

 

3.3.5 Minimisation Algorithm

 

3.4 Normalisation of Parameters

 

3.5 The Minimax Algorithms (MX and MG)

 

3.5.1 Continuity Term

 

3.5.2 Curvature Term

 

3.5.3 Gradient External Energy Term

 

3.5.4 Gray Level External Energy Term

 

3.5.5 Continuous Domain Minimisation

 

3.5.6 Iteration and Convergence of Direct Minimisation Algorithms

 

3.6 Summary


4 Manual Delineation Experiments

 

4.1 General Assessment of Manual Delineation Performance

 

4.1.1 Objectives

 

4.1.2 Experimental Set-up and Procedure

 

4.1.3 Hypothesis Test for Bias: ANOVA Fixed Effect Model

 

4.1.3.1 The ANOVA Bias Test Model

 

4.1.3.2 Pre-ANOVA Checks for Violation of Assumptions

 

4.1.3.3 Inspection of Images for Regions of Ambiguity:

Median Boundary Method

 

4.1.4 Model for Delineator Precision

 

4.1.5 Results

 

4.1.5.1 Summary of Pre-ANOVA Check Results

 

4.1.5.2 Variance Analysis

 

4.1.5.3 Bias Analysis

 

4.1.5.4 Test for Overall Delineator Bias

 

4.1.5.5 Precision Estimates

 

4.1.6 Discussion

 

4.1.7 Conclusions

 

4.2 The Effect of Image Display Size on Delineation Accuracy

 

4.2.1 Objectives

 

4.2.2 Development of Regression Model for Bias

 

4.2.3 Development of Regression Model for Variance

 

4.2.4 Experimental Set-up and Procedure

 

4.2.4.1 Creation of Phantom Wound Image

 

4.2.5 Bias Model Results

 

4.2.6 Variance Model Results

 

4.2.7 Discussion

 

4.2.8 Conclusions


 

Plates 1 & 2 Original Colour Plates of Wound Images

 


5 Parameter Setting Experiments

 

5.1 Introduction and Preliminary Notes

 

5.1.1 A Note on Varying the Initial Contour Position

 

5.1.2 Calculation of Contour Area

 

5.1.3 Calculation of Area Precision

 

5.2 Contour Regularisation Parameters

 

5.2.1 Range and Resolution of Parameter Levels

 

5.2.2 GA Algorithm: Parameter Varying Results

 

5.2.3 TN Algorithm: Parameter Varying Results

 

5.2.4 Setting Contour Regularisation Parameters

 

5.2.5 Summary

 

5.3 Scale Descent Parameters

 

5.3.1 Performance Measures

 

5.3.2 Scale Descent Results

 

5.3.3 Optimal Scale-Parameter Determination

 

5.4 Summary


6 Active Contour Model Experiments

 

6.1 Objectives

 

6.2 Experimental Procedure

 

6.2.1 Additional Image Set

 

6.2.2 Seeding the Algorithms: Manual Delineation

 

6.3 Development of Analytical Procedures

 

6.3.1 A Note on the Application of Statistical Methods

 

6.3.2 Improvement of Manual Results

 

6.3.3 Development of Graphical Procedure

 

6.3.4 Comparison of Algorithms: Overall Test for Precision

 

6.3.5 Quantification of Bias and Precision

 

6.4 Experimental Results

 

6.4.1 Detection and Analysis of Outliers

 

6.4.2 Relative Improvement of Algorithms

 

6.4.3 Overall Precision Test Results

 

6.4.4 Bias and Precision Results

 

6.5 Summary


7 Discussion

 

7.1 General Performance of Algorithms

 

7.1.1 Precision Measurement

 

7.1.2 Bias Measurement

 

7.2 Analysis of Failure Cases

 

7.2.1 Cases of Both Failure Modes

 

7.2.2 Insignificant Cases of Variance Ratio

 

7.2.3 Cases Where Bias is Significant

 

7.2.4 Identifiable Causes of Bias Errors

 

7.3 Consequences of Errors


8 Conclusions

 

8.1 Manual Performance

 

8.2 Algorithm Performance

 

8.3 General Statement

 

8.4 Limitations of this Work

 

8.5 Recommendations for Further Work


Appendices

A Formulation of B-Spline and Hermite Finite Element Models

B Manual Delineation Experimental Data

C Active Contour Model Experimental Data

References