Segmentation of MRI brain images based on mixture density clustering segmentation using Radix4-Fast Fourier Transform

Abstract

Gaussian mixture models (GMMs) can be used as a powerful and flexible density clustering tool. The application of it to medical image segmentation faces some difficulties. First, GMM assumes that no spatial correlation exists and it is sensitive to noise. Moreover, the application of GMM to image segmentation is slow for large medical images. This paper proposes a new Magnetic Resonance (MR) image segmentation based on Radix4-Fast Fourier Transform (FFT) based Expectation and Maximization (EM)-GMM and Gaussian Mixture Regression algorithm (GMR). First we applied Radix 4- FFT to the input MR image. It decreases the number of required computations and enhances the smoothing in terms of improvement in signal to noise ratio. Secondly, we applied EM-GMM-Gaussian Mixture Regression (GMR).By applying Radix4-FFT to EM-GMM-GMR modeling, spatial correlation is enhanced since it takes into account of spatial information and thus classification accuracy is enhanced. After that the output is classified by a Bayesian classifier. This method effectively increases the speed of segmentation of large medical images because convolution is faster in frequency domain. It increases the classification accuracy and also the sensitivity to noise in homogeneous regions is reduced by taking into account of spatial information. Experimental results with the simulated brain MRI(Magnetic Resonance Imaging) and real brain MR images show that the proposed algorithm has better performance in terms of improvement of classification accuracy with an average DSM of 0.90, resistant to noise with an average PSNR as 60 dB and average speed of segmentation as 0.79 seconds, since the solution via FFT is significantly faster compared to the classical solution in spatial domain — it is just O(N log₂N) instead of O(N^2) .