Bayesian Minimum Error Classifier for Classes of Gaussian Distributions

This application illustrates the use of MRI Bias field correction utilities.

What is a Gaussian Minimum Error Classifier?
In this application, each class (a group of pixels) is represented by a Gaussian (normal) density function of gray level intensity values. The Gaussian density functions have two shape parameters, the mean and the covariance per each density function. Minimum error means Bayesian minimum error. In other words, this classifier assigns  the class whose a posteriori probability is the largest for the pixel. A posteriori probability is the product of a priori probability and class-conditional probability. [1] [2] [3]

For more information, please refer to the Statistical Pattern Classification chapter of the Users Guide. You can get the document by checking out InsightDocuments repository from itk.org using cvs. You can find download instruction for the InsightDocuments at http://www.itk.org/HTML/Download.htm .


What is the Purpose of this Application
This application shows how to use the components (classes and functions) in the itk::Statistics (Code/Numerics/Statistics directory) namespace for implementing a statistical pattern classifier. This application is not intended to be a practical application. The focus of this application is show the possible use of ITK's statistical components. As illustrated in the following diagram, there is no one big classifier class. The diagram assumes there are only two classes.

Gaussian minimum error classifier


How Can This Be Used for Image Analysis?
This application is not for any practical image analysis. However, it is not so difficult to creates complex statistical pattern classifier using the components for image segmentation or registration.


References
[1] Richard O. Duda, Peter E. Hart, and David G Stork, Pattern classification, New York : Wiley, 2nd edition, 2000.  
[2] Keinosuke Fukunaga, Introduction to statistical pattern recognition, Boston : Academic Press, 2nd edition, 1990.
[3] Thomas W. Rauber, Pattern Recognition, course material, < http://www.inf.ufes.br/~thomas/pubs/jai97-bk.ps.gz >


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