Implicit planar and in-plane deformable mapping in medical images through high order graphs

In this paper we propose a novel method based on discrete optimization of high order graphs, to perform deformable slice-to-volume registration of 2D images and 3D volumes. To this end, a 2D grid superimposed to the image is considered with control points deforming in 3D and their deformations corresponding to the label space. Geometrical consistency (unique plane selection) and deformation smoothness (in-plane deformations) as well as image similarity (visual matching) are encoded in different third order cliques. The proposed formulation is optimized through its mapping to a factor graph using conventional graph optimization methods. A dataset composed of 2D slices and 3D MRI volumes of the heart was used to evaluate its accuracy leading to very promising results.