Riemannian geometry and the theory of quotient spaces facilitate the analysis of medical imaging algorithms dealing with organ shapes. These algorithms often start with the computation of a template organ shape that serves as a reference for normalizing the measurements of each individual data into a common space. The template represents the organ's “prototype” for further analysis. The template is modeled as a parameter of a generative model that is estimated from the observed data, that is, from noisy images of organs. A usual procedure for template estimation is the computation of the Fréchet mean of the observed data projected in a quotient space. In this chapter we introduce the geometry of quotient spaces and use it to show that the usual template estimation procedure is biased. Riemannian geometry allows us to explain the origin of the bias and to design bias correction methods to improve statistical analysis on organ shapes.