A 3D C1 Stereotactic Deformation Model to Merge Multimodality Images and Atlas Data

A C1 deformation model (ensuring the continuity of the first derivative) based on the same anatomical references is proposed, made upon a tri-variate cubic polynomial system which is the parametric representation of the deformation between two proportional squaring’s along the three main axes according to particular constraints.

Abstract

A major issue of future medical workstations is their ability to merge heterogeneous data such as multimodality in-vivo images and atlases. A classical way to merge multimodal information and especially images is to use external markers which can be seen on the different data to find out the correct geometrical transformations between them. A more difficult problem is to fuse this information with data from another patient or moreover with an atlas in order to have a better understanding of the anatomical or functional environment. A solution is to use the proportional squaring (PS) referential concept based on the localization of the AC-PC line (Anterior Commissura — Posterior Commissura), the two associated verticals (VAC, VPC) and the brain dimensions. The authors have already shown in previous papers that any 3D point of a brain can be accurately assigned to a 3D location in an other brain by using linear transformation (Proportional Squaring Model). A limit of this system concerns the continuity of the transformation (C0 for the global volume: zero order continuity). In this paper, we propose a C1 deformation model (ensuring the continuity of the first derivative) based on the same anatomical references. This model is made upon a tri-variate cubic polynomial system which is the parametric representation of the deformation between two proportional squaring's along the three main axes according to particular constraints. The principle, implementation and evaluation issues including the comparison with the linear model are further explained and illustrated.