Confidence Regions for Statistical Model Based Shape Prediction From Sparse Observations

Shape prediction from sparse observation is of increasing interest in minimally invasive surgery, in particular when the target is not directly visible on images. This can be caused by a limited field-of-view of the imaging device, missing contrast or an insufficient signal-to-noise ratio. In such situations, a statistical shape model can be employed to estimate the location of unseen parts of the organ of interest from the observation and identification of the visible parts. However, the quantification of the reliability of such a prediction can be crucial for patient safety. We present here a framework for the estimation of complete shapes and of the associated uncertainties. This paper formalizes and extends previous work in the area by taking into account and incorporating the major sources of uncertainties, in particular the estimation of pose together with shape parameters, as well as the identification of correspondences between the sparse observation and the model. We evaluate our methodology on a large database of 171 human femurs and synthetic experiments based on a liver model. The experiments show that informative and reliable confidence regions can be estimated by the proposed approach.