This paper presents an implicit shape representation for describing anatomical shapes with high inter-patient variability based on the expected boundary hitting time of a random walk, which happens to be the solution to the Poisson equation. The main contribution of this paper is to test the validity of the Poisson-based mapping for learning anatomical shape variability, comparing its compactness and completeness with the commonly used Signed Distance Transform and using the liver and the caudate nucleus as examples. Based on these findings, we discuss its use as a shape prior for image segmentation.