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Cerebral arteriovenous malformations and their assessment
Interactions of blood happens at different scales, where large-scale flow is connected to cellular and sub-cellular biology. On the largest scale, blood flows from the heart through arteries to all other parts of the body. Then, arteries branch and become smaller as they reach other tissues until their size decreases to capillaries, which are at cellular scale. The capillary bed is where the exchange process of oxygen and nutrients on the one hand, and waste on the other, actually happens. Then blood is collected through the veins, vessels that bring blood back to the heart. Injured blood vessels in the heart, can lead to chest pain and heart attacks; of the arteries of the neck and brain, to strokes. An arteriovenous malformation (AVM) is a complex tangle of abnormal arteries and veins that are connected directly without a capillary bed. This « knot » is called nidus (its
schematic illustration can be seen in Figure 2).
There is typically high blood flow through the nidus of the AVM, but it is unknown if this flow is a cause or an effect of the abnormal vessels, or both. One hypothesis is that high-pressure blood uses the path of least resistance. Another is that the AVM itself uses blood vessels. In any case, the blood goes through the AVM and not through available capillary beds. This redirection is called a shunt. With time, due to the shunting, the AVM dilates. This dilation weakens veins making them susceptible to haemorrhage and feeder arteries becoming susceptible to aneurysms. A haemorrhage in the brain is a type of stroke where a blood vessel ruptures and bleeds into the brain. Each time blood leaks into tissues, these are damaged. This results in loss of temporary or permanent normal function. The amount of damage depends on how much blood was leaked. AVM can also occur in other parts of the body: spleen, lung, kidney, spinal cord, liver, intercostal space, iris, and spermatic cord.
spatially-variant mathematical morphology operators
Spatially-variant (SV) basic mathematical morphology operators, in this chapter, are the four standard basic morphology operators: erosion, dilation, opening and closing, using structuring elements (SE) that are not invariant by translation, i.e. that differ according to the location of their origin. Such operators are useful because they can reflect local content in actual images, which is seldom stationary except in some statistical models. For instance, structuring elements may vary according to orientation or perspective. Many well-known operators, such as some algebraic openings and closings (e.g. area operators) are spatially-variant in nature, but do not derive from spatially-variant erosions and dilations, rather from compositions of spatially invariant openings and closings.
Spatially-variant mathematical morphology (SVMM) has been known for a long time (it is mentioned in Serra’s 1982 book), and even recently has been the topic of a few publications [CCS94, BCCS08, BS08], and was significantly mentioned in a special session at ICIP 2009 on adaptive morphology [MV09].
Many researchers and practitioners wish to be able to use adaptive structuring elements that vary according to the location in the image. Applications include adaptive filtering [LDM07], segmentation taking advantage of perspective information [DD08] or local orientation [TTDP09b, VMA08].
While using spatially-variant erosions and dilation may be relatively easy, the same cannot be said of openings and closings using compositions of spatially variant erosions and dilations. Indeed, the computation of adjunct operators for spatially-variant erosions and dilations is not trivial.
Morphological operators and adjunctions
While the basic morphological erosions and dilation are interesting by themselves, they are even more useful when combined to create openings and closings. However not every dilation and erosion can combine to form an opening or a closing, only those forming adjunctions do.
The notion of adjunction is central to morphology, as it encompasses the dual nature of the theory. Morphological filters come in pairs: those that work on the foreground and those that work on the background.
Table of contents :
1 introduction
1.1 Thin objects analysis
1.2 Medical image applications
1.2.1 Cerebral arteriovenous malformations and their assessment
1.2.2 Coronary heart disease
1.3 Outline
2 thin objects filtering and segmentation methods
2.1 Thin objects filtering
2.1.1 Review of thin objects filtering techniques
2.2 Detection and segmentation methods
2.2.1 Surveys of vessel segmentation methods
2.2.2 Region growing methods
2.2.3 Derivatives-based methods
2.2.4 Model-based filtering
2.2.5 Deformable models
2.2.6 Statistical approaches
2.2.7 Minimal path techniques
2.2.8 Tracking
2.2.9 Morphological methods
2.3 Combinations of methods
2.4 Conclusion and discussion
3 vascular network analysis and representation methods
3.1 Introduction
3.2 Short presentation of digital topology
3.2.1 Points classification in 3D
3.3 Skeletonization
3.3.1 Simple points in 2D and 3D
3.3.2 Thinning process
3.4 Vascular tree construction
3.4.1 Vascular tree analysis
3.5 Visualization
3.6 Discussion
4 morpho-hessian filter
4.1 Feature detection with Gaussian derivatives
4.1.1 Frangi’s vesselness function
4.1.2 Sato’s vesselness
4.1.3 Hysteresis thresholding
4.1.4 Scale-space
4.2 Spatially-variant mathematical morphology operators
4.2.1 An illustrative example
4.2.2 Morphological operators and adjunctions
4.3 Direction field regularization
4.4 Algorithm
4.5 Conclusion and discussion
5 cerebral vessels segmentation and analysis
5.1 Motivation
5.2 Vessel filtering
5.3 Vessel segmentation
5.3.1 Seeded region growing
5.4 Vascular network analysis
5.5 Algorithm
5.6 Methods evaluation
5.6.1 Evaluation on synthetic data
5.6.2 Angiography image data
5.7 Conclusion and discussion
5.8 Acknowledgments
6 guidewire detection
6.1 Guidewire detection methods
6.1.1 Steerable filters
6.1.2 Parametric opening
6.1.3 Path openings
6.1.4 Structure tensor
6.2 Guidewire detection results
6.2.1 Evaluation framework
6.2.2 Results
6.3 Conclusion and discussion
6.4 Acknowledgements
7 conclusion and perspectives
7.1 Contributions
7.2 Perspectives
bibliography
