We propose an efficient computational engine for solving linear combination problems that arise in tissue classification on dual-echo MRI data. In 2D feature space, each pure tissue class is represented by a central point, together with a circle representing a noise tolerance. A given unclassified voxel can be approximated by a linear combination of these pure tissue classes. With more than three tissue classes, multiple combinations can represent the same point, thus heuristics are employed to resolve this ambiguity. An optimised implementation is capable of classifying 1 million voxels per second into four tissue types on a 1.5GHz Pentium 4 machine. Used within a region-growing application, it is found to be at least as robust and over 10 times faster than numerical optimization and linear programming methods.
Spatial inhomogeneity due to the radio-frequency coil in MR imaging can confound segmentation results. In 1994, Sled introduced the N3 technique, using histogram deconvolution, for reducing inhomogeneity. We found some scans whose steep inhomogeneity gradient was not fully eliminated by N3. We created a multi-scale application of N3 that further reduces this gradient, and validated it on MNI BrainWeb and actual MRI data. The algorithm was applied to proton density simulated BrainWeb scans (with known inhomogeneity) and 100 standard MRI scans. Intra-slice and inter-slice inhomogeneity measures were created to compare the technique with standard N3. The slope of the estimated bias versus the known bias of BrainWeb data was 1.0 (r=0.9844) for N3 and 1.04 (r=0.9828) for multi-scale N3. The bias field estimated by multi-scale N3 was within 1% root-mean-square of that of standard N3. Over 100 MS patient scans, the average intra-slice measure (0 meaning bias-free) was 0.0694 (uncorrected), 0.0530 (N3) and 0.0402 (multi-scale). The average inter-slice measure (1 meaning bias-free) was 0.9121 (uncorrected), 0.9367 (N3) and 0.9508 (multi-scale). The multi-scale N3 algorithm showed a greater inhomogeneity reduction than N3 in the small percentage of scans bearing a strong gradient, and results similar to N3 in the remaining scans.