publication . Thesis . 2011

Energy functionals for medical image segmentation: choices and consequences

McIntosh, Christopher;
Open Access
  • Published: 01 Nov 2011
  • Country: Canada
Abstract
Medical imaging continues to permeate the practice of medicine, but automated yet accurate segmentation and labeling of anatomical structures continues to be a major obstacle to computerized medical image analysis. Though there exists numerous approaches for medical image segmentation, one in particular has gained increasing popularity: energy minimization-based techniques, and the large set of methods encompassed therein. With these techniques an energy function must be chosen, segmentations must be initialized, weights for competing terms of the energy functional must be tuned, and the resulting functional minimized. There are a lot of choices involved, and th...
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2 Background and Motivations 4 2.1 Definitions and Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Energy Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Segmentation Representation . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Image Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.4 Training Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.5 Minimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.6 Related Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 MIS via Energy Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 GA-HRPCA 48 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1.1 Shape Model Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.2 Optimizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.1.3 Contributions and Related Work . . . . . . . . . . . . . . . . . . . . . 54 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2.1 Statistically-Constrained Localized and Intuitive Deformations . . . . 57 4.2.2 Building a Fitness Function . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.3 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2.4 Genetic Algorithms for HRPCA . . . . . . . . . . . . . . . . . . . . . 69 4.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.1 Experiment Set A: Validating GA-HRPCA . . . . . . . . . . . . . . . 74 4.3.2 Experiment Set B: Fidelity versus Convexity . . . . . . . . . . . . . . 79 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.1 Error results for our proposed GA-HRPCA . . . . . . . . . . . . . . . . . . . 78

4.2 Error results for our proposed GA-HRPCA continued . . . . . . . . . . . . . 79

4.3 Fidelity vs Optimizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.4 Error comparison between tested methods for CC images . . . . . . . . . . . 82

3.1 An energy minimization segmentation process under different weights . . . . 22

3.2 Segmenting ellipses in noisy images . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Ideal energy functionals on an image manifold . . . . . . . . . . . . . . . . . . 26

3.4 Varying the shape of energy functionals . . . . . . . . . . . . . . . . . . . . . 31

3.5 Overview of our proposed weight optimization method . . . . . . . . . . . . . 34

3.6 Histograms of learned weights for the CC-images . . . . . . . . . . . . . . . . 39

3.7 Ventricle segmentation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.8 Visualization of the learned weighting function . . . . . . . . . . . . . . . . . 43

3.9 CC segmentation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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