Bayesian and non-Bayesian probabilistic models for medical image analysis

Abstract Bayesian approaches to data analysis are popular in machine vision, and yet the main advantage of Bayes theory, the ability to incorporate prior knowledge in the form of the prior probabilities, may lead to problems in some quantitative tasks. In this paper we demonstrate examples of Bayesian and non-Bayesian techniques from the area of magnetic resonance image (MRI) analysis. Issues raised by these examples are used to illustrate difficulties in Bayesian methods and to motivate an approach based on frequentist methods. We believe this approach to be more suited to quantitative data analysis, and provide a general theory for the use of these methods in learning (Bayes risk) systems and for data fusion. Proofs are given for the more novel aspects of the theory. We conclude with a discussion of the strengths and weaknesses, and the fundamental suitability, of Bayesian and non-Bayesian approaches for MRI analysis in particular, and for machine vision systems in general.

[1]  J. Neyman.  Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability , 1937 .

[2]  Neil A. Thacker,et al.  Non-Parametric Image Subtraction for MRI , 2001 .

[3]  Robert M. Haralick,et al.  Performance Characterization in Computer Vision , 1993, BMVC.

[4]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .

[5]  W. J. Lorenz,et al.  Quantification of regional cerebral blood flow and volume with dynamic susceptibility contrast-enhanced MR imaging. , 1994, Radiology.

[6]  N. L. Johnson,et al.  Encyclopedia of Statistical Sciences 2. , 1984 .

[7]  Karl J. Friston,et al.  Analysis of functional MRI time‐series , 1994, Human Brain Mapping.

[8]  Neil A. Thacker,et al.  Non-Parametric Image Subtraction using Grey Level Scattergrams , 2000, BMVC.

[9]  Neil A. Thacker,et al.  Identification of Enhancing MS Lesions in MR Images using Non-Parametric Image Subtraction , 2002 .

[10]  S. Cook,et al.  Triple‐Dose Versus Single‐Dose Gadoteridol in Multiple Sclerosis Patients , 1994, Journal of neuroimaging : official journal of the American Society of Neuroimaging.

[11]  Neil A. Thacker,et al.  The Importance of Partial Voluming in Multi-dimensional Medical Image Segmentation , 2001, MICCAI.

[12]  Enrico Gobbetti,et al.  Developing a virtual reality environment for petrous bone surgery : a “ state-ofthe-art ” review , 2001 .

[13]  M. Way,et al.  Precise measurement of Γ(Λ0 → p + e− + ν)/Γ(Λ0 → p + π−) , 1980 .

[14]  Jacques Blanc-Talon,et al.  Imaging and vision systems: theory, assessment and applications , 2001 .

[15]  Neil A. Thacker,et al.  Non-parametric image subtraction using grey level scattergrams , 2002, Image Vis. Comput..

[16]  Karl J. Friston,et al.  Detecting Activations in PET and fMRI: Levels of Inference and Power , 1996, NeuroImage.

[17]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[18]  Neil A. Thacker,et al.  The Bhattacharyya metric as an absolute similarity measure for frequency coded data , 1998, Kybernetika.

[19]  N. A. Thacker,et al.  Multi-dimensional Medical Image Segmentation with Partial Voluming , 2001 .

[20]  Giovanni Calderini,et al.  A precise measurement of ΓZ→bb/ΓZ→hadrons , 1993 .

[21]  R. Cousins,et al.  A Unified Approach to the Classical Statistical Analysis of Small Signals , 1997, physics/9711021.

[22]  Neil A. Thacker.  Using quantitative statistics for the construction of machine vision systems , 2003, SPIE OPTO-Ireland.

[23]  David H. Laidlaw,et al.  Partial-volume Bayesian classification of material mixtures in MR volume data using voxel histograms , 1997, IEEE Transactions on Medical Imaging.

[24]  Stavros Stivaros,et al.  Dementing disorders: volumetric measurement of cerebrospinal fluid to distinguish normal from pathologic findings -- feasibility study. , 2002, Radiology.

[25]  Michael I. Jordan,et al.  On Convergence Properties of the EM Algorithm for Gaussian Mixtures , 1996, Neural Computation.

[26]  M. Bahn,et al.  A Single‐Step Method for Estimation of Local Cerebral Blood Volume from Susceptibility Contrast MRI Images , 1995, Magnetic resonance in medicine.

[27]  N. A. Thacker,et al.  Performance Characterisation in Computer Vision: The Role of Statistics in Testing and Design , 2003 .

[28]  Ian Poole.  Optimal probabilistic relaxation labeling , 1990, BMVC.

[29]  Alan Jackson,et al.  Using Bayesian tissue classification to improve the accuracy of vestibular schwannoma volume and growth measurement. , 2002, AJNR. American journal of neuroradiology.

[30]  Michael Brady,et al.  Estimating the bias field of MR images , 1997, IEEE Transactions on Medical Imaging.

[31]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..