Barycentric Label Space
Ghassan Hamarneh, Neda Changizi · Medical Image Computing and Computer-Assisted Intervention · 2009
Multiple neighboring organs or structures in medical images are frequently represented by labeling the underlying image (e.g. a brain into WM, GM, CSF). Given the di! erent sources of uncertainties in shape boundaries (e.g. partial volum ee ! ect and fuzzy segmentation), it is favorable to adopt a labeling approach that not only encodes uncer- tainty but also facilitates algebraic label manipulation (e.g. performing PCA). In this work, we extend the label space representation of Mal- colm et al. (1) to barycentric label space, in which a proper invertible mapping between probability vectors and label space is proposed. The probability vectors act as barycentric coe! cients describing arbitrary la- bels in label space and a non-singular matrix inversion maps points in label space back to probabilities. The elimination of conversion errors compared to the original label space mapping is demonstrated quantita- tively and qualitatively on artificial objects and brain image data, and in the context of smoothing, linear statistics, and uncertainty calculation.