A 2-Simplex representing a single “pixel” of a probabilistic 3-region shape. Note how the probability vector must lie in the triangle so the positive probabilities add up to 1

The mapping between the 2-simplex and Euclidean space

Entropy (uncertainty) on the simplex. Brighter means more uncertain

Probabilistic brain segmentation via ILR

Segmenting the thigh muscle group (11 muscles) based on an ILR shape representation

Sample images...