A Forward Model to Build Unbiased Atlases from Curves and Surfaces

Building an atlas from a set of anatomical data relies on (1) the construction of a mean anatomy (called template or prototype) and (2) the estimation of the variations of this template within the population. To avoid biases introduced by separate processing, we jointly estimate the template and its deformation, based on a consistent statistical model. We use here a forward model that considers data as noisy deformations of an unknown template. This di ers from backward schemes which estimate a template by pulling back data into a common reference frame. Once the atlas is built, the likelihood of a new observation depends on the Jacobian of the deformations in the backward setting, whereas it is directly taken into account while building the atlas in the forward scheme. As a result, a speci c numerical scheme is required to build atlases. The feasibility of the approach is shown by building atlases from 34 sets of 70 sulcal lines and 32 sets of 10 deep brain structures.