The N-finder algorithm (N-FINDR) suffers from several issues in its practical implementation. One is its search region which is usually the entire data space. Another related issue is its excessive computation. A third issue is its use of random initial conditions which causes inconsistency in final results that can not be reproducible if a search for endmembers is not exhaustive. This paper resolves the first two issues by developing two approaches to speed-up of the N-FINDR computation while implementing a recently developed random pixel purity index (RPPI) to alleviate the third issue. First of all, it narrows down the search region for the N-FINDR to a feasible range, called region of interest (ROI), where two ways are proposed, data sphering/thresholding and RPPI, to be used as a pre-processing to find a desired ROI. Second, three methods are developed to reduce computing load of simplex volume computation by simplifying matrix determinant. Third, to further reduce computational complexity three sequential N-FINDR algorithms are implemented by finding one endmember after another in sequence instead of finding all endmembers together at once. The conducted experiments demonstrate that while the proposed fast algorithms can greatly reduce computational complexity, their performance remains as good as the N-FINDR is and is not compromised by reduction of the search region to an ROI
A new TRIO algorithm method integrating three different algorithms is proposed to perform brain MRI segmentation in the native coordinate space, with no need of transformation to a standard coordinate space or the probability maps for segmentation. The method is a simple voxel-based algorithm, derived from multispectral remote sensing techniques, and only requires minimal operator input to depict GM, WM, and CSF tissue clusters to complete classification of a 3D high-resolution multislice-multispectral MRI data. Results showed very high accuracy and reproducibility in classification of GM, WM, and CSF in multislice-multispectral synthetic MRI data. The similarity indexes, expressing overlap between classification results and the ground truth, were 0.951, 0.962, and 0.956 for GM, WM, and CSF classifications in the image data with 3% noise level and 0% non-uniformity intensity. The method particularly allows for classification of CSF with 0.994, 0.961 and 0.996 of accuracy, sensitivity and specificity in images data with 3% noise level and 0% non-uniformity intensity, which had seldom performed well in previous studies. As for clinical MRI data, the quantitative data of brain tissue volumes aligned closely with the brain morphometrics in three different study groups of young adults, elderly volunteers, and dementia patients. The results also showed very low rates of the intra- and extra-operator variability in measurements of the absolute volumes and volume fractions of cerebral GM, WM, and CSF in three different study groups. The mean coefficients of variation of GM, WM, and CSF volume measurements were in the range of 0.03% to 0.30% of intra-operator measurements and 0.06% to 0.45% of inter-operator measurements. In conclusion, the TRIO algorithm exhibits a remarkable ability in robust classification of multislice-multispectral brain MR images, which would be potentially applicable for clinical brain volumetric analysis and explicitly promising in cross-sectional and longitudinal studies of different subject groups.
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