- •Biological and Medical Physics, Biomedical Engineering
- •Medical Image Processing
- •Preface
- •Contents
- •Contributors
- •1.1 Medical Image Processing
- •1.2 Techniques
- •1.3 Applications
- •1.4 The Contribution of This Book
- •References
- •2.1 Introduction
- •2.2 MATLAB and DIPimage
- •2.2.1 The Basics
- •2.2.2 Interactive Examination of an Image
- •2.2.3 Filtering and Measuring
- •2.2.4 Scripting
- •2.3 Cervical Cancer and the Pap Smear
- •2.4 An Interactive, Partial History of Automated Cervical Cytology
- •2.5 The Future of Automated Cytology
- •2.6 Conclusions
- •References
- •3.1 The Need for Seed-Driven Segmentation
- •3.1.1 Image Analysis and Computer Vision
- •3.1.2 Objects Are Semantically Consistent
- •3.1.3 A Separation of Powers
- •3.1.4 Desirable Properties of Seeded Segmentation Methods
- •3.2 A Review of Segmentation Techniques
- •3.2.1 Pixel Selection
- •3.2.2 Contour Tracking
- •3.2.3 Statistical Methods
- •3.2.4 Continuous Optimization Methods
- •3.2.4.1 Active Contours
- •3.2.4.2 Level Sets
- •3.2.4.3 Geodesic Active Contours
- •3.2.5 Graph-Based Methods
- •3.2.5.1 Graph Cuts
- •3.2.5.2 Random Walkers
- •3.2.5.3 Watershed
- •3.2.6 Generic Models for Segmentation
- •3.2.6.1 Continuous Models
- •3.2.6.2 Hierarchical Models
- •3.2.6.3 Combinations
- •3.3 A Unifying Framework for Discrete Seeded Segmentation
- •3.3.1 Discrete Optimization
- •3.3.2 A Unifying Framework
- •3.3.3 Power Watershed
- •3.4 Globally Optimum Continuous Segmentation Methods
- •3.4.1 Dealing with Noise and Artifacts
- •3.4.2 Globally Optimal Geodesic Active Contour
- •3.4.3 Maximal Continuous Flows and Total Variation
- •3.5 Comparison and Discussion
- •3.6 Conclusion and Future Work
- •References
- •4.1 Introduction
- •4.2 Deformable Models
- •4.2.1 Point-Based Snake
- •4.2.1.1 User Constraint Energy
- •4.2.1.2 Snake Optimization Method
- •4.2.2 Parametric Deformable Models
- •4.2.3 Geometric Deformable Models (Active Contours)
- •4.2.3.1 Curve Evolution
- •4.2.3.2 Level Set Concept
- •4.2.3.3 Geodesic Active Contour
- •4.2.3.4 Chan–Vese Deformable Model
- •4.3 Comparison of Deformable Models
- •4.4 Applications
- •4.4.1 Bone Surface Extraction from Ultrasound
- •4.4.2 Spinal Cord Segmentation
- •4.4.2.1 Spinal Cord Measurements
- •4.4.2.2 Segmentation Using Geodesic Active Contour
- •4.5 Conclusion
- •References
- •5.1 Introduction
- •5.2 Imaging Body Fat
- •5.3 Image Artifacts and Their Impact on Segmentation
- •5.3.1 Partial Volume Effect
- •5.3.2 Intensity Inhomogeneities
- •5.4 Overview of Segmentation Techniques Used to Isolate Fat
- •5.4.1 Thresholding
- •5.4.2 Selecting the Optimum Threshold
- •5.4.3 Gaussian Mixture Model
- •5.4.4 Region Growing
- •5.4.5 Adaptive Thresholding
- •5.4.6 Segmentation Using Overlapping Mosaics
- •5.6 Conclusions
- •References
- •6.1 Introduction
- •6.2 Clinical Context
- •6.3 Vessel Segmentation
- •6.3.1 Survey of Vessel Segmentation Methods
- •6.3.1.1 General Overview
- •6.3.1.2 Region-Growing Methods
- •6.3.1.3 Differential Analysis
- •6.3.1.4 Model-Based Filtering
- •6.3.1.5 Deformable Models
- •6.3.1.6 Statistical Approaches
- •6.3.1.7 Path Finding
- •6.3.1.8 Tracking Methods
- •6.3.1.9 Mathematical Morphology Methods
- •6.3.1.10 Hybrid Methods
- •6.4 Vessel Modeling
- •6.4.1 Motivation
- •6.4.1.1 Context
- •6.4.1.2 Usefulness
- •6.4.2 Deterministic Atlases
- •6.4.2.1 Pioneering Works
- •6.4.2.2 Graph-Based and Geometric Atlases
- •6.4.3 Statistical Atlases
- •6.4.3.1 Anatomical Variability Handling
- •6.4.3.2 Recent Works
- •References
- •7.1 Introduction
- •7.2 Linear Structure Detection Methods
- •7.3.1 CCM for Imaging Diabetic Peripheral Neuropathy
- •7.3.2 CCM Image Characteristics and Noise Artifacts
- •7.4.1 Foreground and Background Adaptive Models
- •7.4.2 Local Orientation and Parameter Estimation
- •7.4.3 Separation of Nerve Fiber and Background Responses
- •7.4.4 Postprocessing the Enhanced-Contrast Image
- •7.5 Quantitative Analysis and Evaluation of Linear Structure Detection Methods
- •7.5.1 Methodology of Evaluation
- •7.5.2 Database and Experiment Setup
- •7.5.3 Nerve Fiber Detection Comparison Results
- •7.5.4 Evaluation of Clinical Utility
- •7.6 Conclusion
- •References
- •8.1 Introduction
- •8.2 Methods
- •8.2.1 Linear Feature Detection by MDNMS
- •8.2.2 Check Intensities Within 1D Window
- •8.2.3 Finding Features Next to Each Other
- •8.2.4 Gap Linking for Linear Features
- •8.2.5 Quantifying Branching Structures
- •8.3 Linear Feature Detection on GPUs
- •8.3.1 Overview of GPUs and Execution Models
- •8.3.2 Linear Feature Detection Performance Analysis
- •8.3.3 Parallel MDNMS on GPUs
- •8.3.5 Results for GPU Linear Feature Detection
- •8.4.1 Architecture and Implementation
- •8.4.2 HCA-Vision Features
- •8.4.3 Linear Feature Detection and Analysis Results
- •8.5 Selected Applications
- •8.5.1 Neurite Tracing for Drug Discovery and Functional Genomics
- •8.5.2 Using Linear Features to Quantify Astrocyte Morphology
- •8.5.3 Separating Adjacent Bacteria Under Phase Contrast Microscopy
- •8.6 Perspectives and Conclusions
- •References
- •9.1 Introduction
- •9.2 Bone Imaging Modalities
- •9.2.1 X-Ray Projection Imaging
- •9.2.2 Computed Tomography
- •9.2.3 Magnetic Resonance Imaging
- •9.2.4 Ultrasound Imaging
- •9.3 Quantifying the Microarchitecture of Trabecular Bone
- •9.3.1 Bone Morphometric Quantities
- •9.3.2 Texture Analysis
- •9.3.3 Frequency-Domain Methods
- •9.3.4 Use of Fractal Dimension Estimators for Texture Analysis
- •9.3.4.1 Frequency-Domain Estimation of the Fractal Dimension
- •9.3.4.2 Lacunarity
- •9.3.4.3 Lacunarity Parameters
- •9.3.5 Computer Modeling of Biomechanical Properties
- •9.4 Trends in Imaging of Bone
- •References
- •10.1 Introduction
- •10.1.1 Adolescent Idiopathic Scoliosis
- •10.2 Imaging Modalities Used for Spinal Deformity Assessment
- •10.2.1 Current Clinical Practice: The Cobb Angle
- •10.2.2 An Alternative: The Ferguson Angle
- •10.3 Image Processing Methods
- •10.3.1 Previous Studies
- •10.3.2 Discrete and Continuum Functions for Spinal Curvature
- •10.3.3 Tortuosity
- •10.4 Assessment of Image Processing Methods
- •10.4.1 Patient Dataset and Image Processing
- •10.4.2 Results and Discussion
- •10.5 Summary
- •References
- •11.1 Introduction
- •11.2 Retinal Imaging
- •11.2.1 Features of a Retinal Image
- •11.2.2 The Reason for Automated Retinal Analysis
- •11.2.3 Acquisition of Retinal Images
- •11.3 Preprocessing of Retinal Images
- •11.4 Lesion Based Detection
- •11.4.1 Matched Filtering for Blood Vessel Segmentation
- •11.4.2 Morphological Operators in Retinal Imaging
- •11.5 Global Analysis of Retinal Vessel Patterns
- •11.6 Conclusion
- •References
- •12.1 Introduction
- •12.1.1 The Progression of Diabetic Retinopathy
- •12.2 Automated Detection of Diabetic Retinopathy
- •12.2.1 Automated Detection of Microaneurysms
- •12.3 Image Databases
- •12.4 Tortuosity
- •12.4.1 Tortuosity Metrics
- •12.5 Tracing Retinal Vessels
- •12.5.1 NeuronJ
- •12.5.2 Other Software Packages
- •12.6 Experimental Results and Discussion
- •12.7 Summary and Future Work
- •References
- •13.1 Introduction
- •13.2 Volumetric Image Visualization Methods
- •13.2.1 Multiplanar Reformation (2D slicing)
- •13.2.2 Surface-Based Rendering
- •13.2.3 Volumetric Rendering
- •13.3 Volume Rendering Principles
- •13.3.1 Optical Models
- •13.3.2 Color and Opacity Mapping
- •13.3.2.2 Transfer Function
- •13.3.3 Composition
- •13.3.4 Volume Illumination and Illustration
- •13.4 Software-Based Raycasting
- •13.4.1 Applications and Improvements
- •13.5 Splatting Algorithms
- •13.5.1 Performance Analysis
- •13.5.2 Applications and Improvements
- •13.6 Shell Rendering
- •13.6.1 Application and Improvements
- •13.7 Texture Mapping
- •13.7.1 Performance Analysis
- •13.7.2 Applications
- •13.7.3 Improvements
- •13.7.3.1 Shading Inclusion
- •13.7.3.2 Empty Space Skipping
- •13.8 Discussion and Outlook
- •References
- •14.1 Introduction
- •14.1.1 Magnetic Resonance Imaging
- •14.1.2 Compressed Sensing
- •14.1.3 The Role of Prior Knowledge
- •14.2 Sparsity in MRI Images
- •14.2.1 Characteristics of MR Images (Prior Knowledge)
- •14.2.2 Choice of Transform
- •14.2.3 Use of Data Ordering
- •14.3 Theory of Compressed Sensing
- •14.3.1 Data Acquisition
- •14.3.2 Signal Recovery
- •14.4 Progress in Sparse Sampling for MRI
- •14.4.1 Review of Results from the Literature
- •14.4.2 Results from Our Work
- •14.4.2.1 PECS
- •14.4.2.2 SENSECS
- •14.4.2.3 PECS Applied to CE-MRA
- •14.5 Prospects for Future Developments
- •References
- •15.1 Introduction
- •15.2 Acquisition of DT Images
- •15.2.1 Fundamentals of DTI
- •15.2.2 The Pulsed Field Gradient Spin Echo (PFGSE) Method
- •15.2.3 Diffusion Imaging Sequences
- •15.2.4 Example: Anisotropic Diffusion of Water in the Eye Lens
- •15.2.5 Data Acquisition
- •15.3 Digital Processing of DT Images
- •15.3.2 Diagonalization of the DT
- •15.3.3 Gradient Calibration Factors
- •15.3.4 Sorting Bias
- •15.3.5 Fractional Anisotropy
- •15.3.6 Other Anisotropy Metrics
- •15.4 Applications of DTI to Articular Cartilage
- •15.4.1 Bovine AC
- •15.4.2 Human AC
- •References
- •Index
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plots the tortuosity of the first quintile of its length (closest to the optic disk) with the tortuosity of the entire vessel, for the 46 vessels of the marked database shown in Fig. 12.7. The correlation coefficient is 0.5777, corresponding to p < 0.0001. This indicates that there is little significant change in tortuosity along the length of a vessel, and therefore the tortuosity of the entire vessel can be confidently used to characterize each vessel.
12.7 Summary and Future Work
It has been recognized that the local flow hemodynamics of a curved vessel may dispose it to the formation of an aneurysm. The geometry of intracranial arteries, for example, has been implicated in the formation of aneurysms [10]. The branching patterns of the vessel network may also be useful in diagnosing and evaluating the severity of a disease such as diabetic retinopathy [34, 42].
We have shown that tortuosity is related to microaneurysm count, and we suggest that tortuosity increases with severity of diabetic retinopathy. It is too early to say with this limited data whether tortuosity could be used as an alternate predictor of the severity of such retinopathy. Longitudinal data would help to resolve the matter. Local flow hemodynamics will be affected by the tortuosity of the vessels, and it will affect the number of microaneurysms formed. Precisely which is cause and which is effect is difficult to ascertain, but as diabetic retinopathy becomes more severe it is likely that both tortuosity and microaneurysm count will increase, and our results confirm this trend. Blood pressure and the diameter of the vessels are also likely implicated in the changes. It may be that tortuosity is related to an integral effect of blood pressure, while microaneurysm responds more to local maxima.
Tortuosity can be measured easily from the digitized tracings of vessels in retinal images, and these tracings can be obtained using a semiautomated program such as NeuronJ. Fully automated tracing is an enticing prospect, although current algorithms would seem to require customized preprocessing of the image, which would then render the process semiautomatic again.
Fractal dimension (or the fractal signature [63]) may be an alternative method of measuring the bending within a blood vessel. Initial studies demonstrated that the blood vessels of the optic fundus are fractal, and that the fractal dimension can be used to identify PDR [64, 65]. Preliminary analysis of the skeletonized vascular patterns in the normal and NPDR macula suggested that vascular morphology had already changed by this relatively early stage of retinal disease [66].
A disadvantage of fractal dimension is that it is constrained within very tight limits (1–2 for a vessel tracing), and this limits its sensitivity. Another limitation is that different algorithms can result in different values [67]. Perhaps, its greatest potential is that it can deliver a quantitative summary value for the geometric complexity of a network, rather than a single vessel, and could therefore summarize the complete retinal vascular branching pattern in an image. Recent computerized studies [68, 69] suggest that increased fractal dimension of the retinal vasculature,
12 Tortuosity as an Indicator of the Severity of Diabetic Retinopathy |
287 |
reflecting increased geometric complexity of the retinal vascular branching pattern, is associated with early diabetic retinopathy microvascular damage. Although the differences in fractal dimension were small [69], the average fractal dimension was higher in participants with retinopathy than in those without retinopathy (median 1.46798 [interquartile range 1.45861–1.47626] compared with 1.46068 [1.44835–1.47062], respectively; p < 0.001). After adjustments for age and sex, greater fractal dimension was significantly associated with increased odds of retinopathy (odds ratio [OR] 4.04 [95%CI 2.21–7.49] comparing highest to lowest quartile of fractal dimension; OR 1.33 for each 0.01 increase in fractal dimension). This association remained with additional adjustments for diabetes duration, blood sugar, blood pressure, body mass index (BMI), and total cholesterol levels. Further adjustment for retinal arteriolar or venular caliber had minimal impact on the association (OR 3.92 [95% CI 1.98–7.75]).
Acknowledgments We acknowledge with thanks the help and assistance of Dr. Eric Meijering, Dr. Michal Sofka, and Dr. Michael Cree on issues regarding their respective software. A database of retinal images, with the microaneurysms manually identified by experts, was kindly supplied by Dr. Jean-Claude Klein of the Center of Mathematical Morphology of MINES, Paris Tech. One of us (G.D.) acknowledges the award of a Fulbright Senior Scholarship, which provided the opportunity to expand work in this area and others.
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