Classification of 3D volume data using finite mixture models

Abstract

The 3D imaging provides better view of objects from three directions as compared to 2D imaging where front face of object can be viewed only. It involves a complex relationship as compared to 2D imaging and hence computationally expensive also. But it also includes more information which helps in visualizing the object, its shape, boundary similar to real world phenomenon. The segmentation method should take care of 3D relationship that exists between voxels. The multi channel 3D imaging provides exibility in changing voxel size by changing echo pulse signals which helps in analysis of soft tissues. The application of 3D imaging in MRI brain images help in understanding more clearly the brain anatomy and function. Mixture model based image segmentation methods provide platform to many real life segmentation problems. Finite Mixture Model (FMM) segmentation techniques have been applied in 2D imaging successfully. But these methods do not involve spatial relationship among neighboring pixels. To overcome this drawback, Spatially Variant Finite Mixture Model (SVFMM) was given for classification purpose. In the medical imaging, the probability of noise is high due to environment, technician expertise level, etc. So, a robust method is required which can reduce the noise effect of the images. The Gaussian Distribution is more preferred in the literature but it is not robust against the noisy data. The Student's t Distribution uses Mahalanobis squared distance to reduce the effect of outlier data. A comparative study has been presented between these two distribution functions. In Medical Imaging, segmentation procedures provide facility to separate out different type of tissues instead of manual processing which requires time and efforts. The segmentation methods automate this classification procedure. To reduce the computation time in 3D medical imaging, a sampling based approach called Column Sampling is used. The variance of a column is taken as a measure in sample selection. A comparison is presented for time taken in sample selection from whole volume with Random Sampling. The selected samples are provided to the estimation technique. The parameters of mixture model are estimated using Maximum Likelihood Estimation and Bayesian Learning Estimation in the presented work. The method for estimating parameters of SVFMM using Bayesian Learning is proposed. The Misclassification Rate (MCR) is used for quantitative measure among these methods. This work analyzes FMM and SVFMM models with different probability distribution over two different estimation techniques. The MCR and computational time are considered as quantitative measures for performance evaluation. The different sampling percentage is tried out to estimate the parameters and their MCR and computational time are presented. In conclusion, Bayesian learning estimation SVFMM using Student's t distribution gives comparatively better results.