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Segmentation of the cord canal and intervertebral discs in MRI data
Koban, Martin ; Odstrčilík, Jan (referee) ; Jakubíček, Roman (advisor)
The concern of this thesis is development of the method for the spinal canal and intervertebral discs segmentation in volume MRI data. The primary aim is to achieve the highest possible level of automation and accuracy allowing for reliable quantitative evaluation of the results. The algorithm is based on the random walk model in combination with a specific active contour method formulated through level set concept. The proposed approach is tested using a database of three-dimensional T2-weighted MR images, which also contains referential manual segmentation of intervertebral discs.
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Random walk
Baňasová, Barbora ; Omelka, Marek (advisor) ; Dostál, Petr (referee)
Random walk is a well-known mathematical model used in various scientific fields. The aim of this thesis is to explain and to show the relation between the basic characteristics of simple random walk. The paper summarizes theoretical knowledge concerning this mathematical model in terms of its symmetrical or asymmetrical version. It deals with the derivation of absorbing probabilities, probability of the first and repeated return to origin and clasification of simple random walk states. The final part presents random walk in a wider perspective as a martingale. The conditions under which a random walk equals a martingale are established as well. It is also shown how it is possible to apply this more general mathematical structure on the model of random walk.
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Segmentation of the cord canal and intervertebral discs in MRI data
Koban, Martin ; Odstrčilík, Jan (referee) ; Jakubíček, Roman (advisor)
The concern of this thesis is development of the method for the spinal canal and intervertebral discs segmentation in volume MRI data. The primary aim is to achieve the highest possible level of automation and accuracy allowing for reliable quantitative evaluation of the results. The algorithm is based on the random walk model in combination with a specific active contour method formulated through level set concept. The proposed approach is tested using a database of three-dimensional T2-weighted MR images, which also contains referential manual segmentation of intervertebral discs.
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|
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Random walk
Baňasová, Barbora ; Omelka, Marek (advisor) ; Dostál, Petr (referee)
Random walk is a well-known mathematical model used in various scientific fields. The aim of this thesis is to explain and to show the relation between the basic characteristics of simple random walk. The paper summarizes theoretical knowledge concerning this mathematical model in terms of its symmetrical or asymmetrical version. It deals with the derivation of absorbing probabilities, probability of the first and repeated return to origin and clasification of simple random walk states. The final part presents random walk in a wider perspective as a martingale. The conditions under which a random walk equals a martingale are established as well. It is also shown how it is possible to apply this more general mathematical structure on the model of random walk.
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