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Image Computing Based on Bayesian Models (BM)

  • Zhong Xue
  • Stephen Wong
Chapter
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 14)

Abstract

Many medical image computing tasks apply the prior knowledge about the variability of shapes or deformations to improve the performance of shape analysis, segmentation, registration, as well as group comparison or computer-aided diagnosis. Statistical model-based algorithms play important roles in capturing such prior information and applying them for robust image segmentation and registration. Given the prior distribution of a high-dimensional data, which can be a shape description, a deformation field, or other feature vectors from the training images, the objectiveis to come up with the best estimation of the shape, the deformation, or feature vectors from an observed data/image. The traditional maximum a posteriori (MAP) framework is the most commonly used methodology to incorporate the prior information in the estimation. One example of MAP estimation is the active shape model (ASM), which encodes the prior information of object shapes using principal component analysis (PCA) and then extracts the shape of an object from the PCA model that matches the image the best. Such statistical model-based method is constrained by the prior distribution from sample data for improved robustness. However, ASM takes directly the reconstructed object shape as the matching result, and it may not be able to match a new image accurately if the variations of the shape are not presented in the sample data, or if the number of model modes has been truncated too severely. This chapter introducesa new Bayesian model (BM) for accurate and robust medical image computing. BM overcomes the limitation of MAP by incorporating an intermediate variable and jointly estimating the result and the intermediate variable simultaneously. In this way the BM framework allows for convenient incorporation of additional constraints, reduces the constraints of the prior distributions, and increases the flexibility of shape matching. In this chapter, after a brief literature review of the statistical model-based image analysis methods, we first introduce the BM framework in both segmentation and registration and then present our two works that apply the BM methodology. From the techniques presented we can see that image segmentation and registration can be uniformly formulated in the same BM framework, and such formulation can also easily facilitate other image computing tasks.

Keywords

Maximum a posteriori Bayesian model Segmentation Registration 

Abbreviations

ASM

Active shape model

BM

Bayesian model

BSM

Bayesian shape model

GM

Gray matter

MAP

Maximum a posteriori

MR

Magnetic resonance

PDE

Partial differential equation

PVA

Principal component analysis

ROI

Region of interest

SMD

Statistical models of deformations

SPM

Statistical parametric mapping

SVM

Support vector machine

TS

Temporal smoothness

WM

White matter

WPT

Wavelet packet transform

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Houston Methodist Research InstituteHouston Methodist HospitalHoustonUSA
  2. 2.Weill Cornell Medical CollegeNew YorkUSA

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