2D and 3D digital shape modelling strategies

Rueda Lopez, Silvia (2010) 2D and 3D digital shape modelling strategies. PhD thesis, University of Nottingham.

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Abstract

Image segmentation of organs in medical images using model-based approaches requires a priori information which is often given by manually tagging landmarks on a training set of shapes. This is a tedious, time-consuming, and error prone task. To overcome some of these drawbacks, several automatic methods were devised. Identification of the same homologous set of points in a training set of object shapes is the most crucial step in Active Shape Modelling, which has encountered several challenges. The most crucial among these are: (C1) defining and characterizing landmarks; (C2) obtaining landmarks at the desired level of detail; (C3) ensuring homology; (C4) generalizing to n>2 dimensions; (C5) achieving practical computations. This thesis proposes several novel modelling techniques attempting to meet C1-C5. In this process, this thesis makes the following key contributions: the concept of local scale for shapes; the idea of allowing level of detail for selecting landmarks; the concept of equalization of shape variance for selecting landmarks; the idea of recursively subdividing shapes and letting the sub-shapes guide landmark selection, which is a very general n-dimensional strategy; the idea of virtual landmarks, which may be situated anywhere relative to, not necessarily on, the shape boundary; a new compactness measure that considers both the number of landmarks and the number of modes selected as independent variables.

The first of three methods uses the c-scale shape descriptor, based on the new concept of curvature-scale, to automatically locate mathematical landmarks on the mean of the training shapes. The landmarks are propagated to the training shapes to establish correspondence among shapes. Since all shapes of the same family do not necessarily present exactly the same shape features, another novel method was devised that takes into account the real shape variability existing in the training set and that is guided by the strategy of equalization of the variance observed in the training set for selecting landmarks. By incorporating the above basic concepts into modelling, a third family of methods with numerous possibilities was developed, taking into account shape features, and the variability among shapes, while being easily generalized to the 3D space. Its output is multi-resolutional allowing landmark selection at any lower resolution trivially as a subset of those found at a higher resolution. The best strategy to use within the family will have to be determined according to the clinical application at hand.

All methods were evaluated in terms of compactness on two data sets - 40 CT images of the liver and 40 MR images of the talus bone of the foot. Further, numerous artificial shapes with known salient points were also used for testing the accuracy of the proposed methods. The results show that, for the same number of landmarks, the proposed methods are more compact than manual and equally spaced annotations. Besides, the accuracy (in terms of false positives and negatives and the location of landmarks) of the proposed shape descriptor on artificial shapes is considerably superior to a state-of-the-art scale space approach to finding salient points on shapes.

Item Type:Thesis (PhD)
Supervisors:Pridmore, T.P.
Udupa, J.K.
Faculties/Schools:UK Campuses > Faculty of Science > School of Computer Science
ID Code:1366
Deposited By:Dr Silvia Rueda Lopez
Deposited On:19 Feb 2011 15:47
Last Modified:19 Feb 2011 15:47

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