Modelling and understanding shapes of objects is important for many applications, e.g. recognition, retrieval, segmentation, matching, etc. Shapes of anatomical objects (e.g. subcortical brain structures, muscles, bones, heart ventricles) have intricate shapes that vary across subjects, with age, disease, gender, etc. It is important to be able to model and understand this shape variability and utilize it towards clinical applications, e.g. diagnosis and therapy evaluation.  In the human body, multiple structures appear in certain configuration and hence it is important to capture this multi-region aspect of shapes. Medical images are the primary sources of information nowadays for studying shapes. However, medical image suffer from different artifacts (e.g. noise, partial volume effect) rendering the information we capture about shapes within uncertain.

The Isometric Log Ratio transform (ILR) is the approach we present here for  uncertainty-encoding, multi-region probabilistic shapes. It has interesting properties that make it an effective method (e.g. vector space, bijective,  isometric, full-rank). In these pages you can see some examples of how ILR improves on other methods, read the scientific theory behind ILR, see ILR in action in different applications, and download code so you can try ILR on your own data.... enjoy!