In this paper we shall present the derivation of two new forms of the Kalman filter equations; the first is for a pure lognormally distributed random variable, while the second set of Kalman filter equations will be for a combination of Gaussian and lognormally distributed random variables. We shall show that the appearance is similar to that of the Gaussian based equations, but that the analysis state is a multivariate median and not the mean. We also show results of the mixed distribution Kalman filter with the Lorenz 1963 model with lognormal errors for the background and observations of the ɀ component, and compare them to analysis results from a traditional Gaussian based extended Kalman filter and show that under certain circumstances the new approach produces more accurate results.

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In this study we discuss different types of texture features such as Fractal Dimension (FD) and Multifractional Brownian Motion (mBm) for estimating random structures and varying appearance of brain tissues and tumors in magnetic resonance images (MRI). We use different selection techniques including KullBack - Leibler Divergence (KLD) for ranking different texture and intensity features. We then exploit graph cut, self organizing maps (SOM) and expectation maximization (EM) techniques to fuse selected features for brain tumors segmentation in multimodality T1, T2, and FLAIR MRI. We use different similarity metrics to evaluate quality and robustness of these selected features for tumor segmentation in MRI for real pediatric patients. We also demonstrate a non-patient-specific automated tumor prediction scheme by using improved AdaBoost classification based on these image features.

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