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Variable Model Type

Finally it is possible to vary spatially the models or equations causing deformation. This type of inhomogeneity can achieve completely affine transformations within selected regions while deforming intervening or surrounding areas. Boundary conditions are set between model type regions such that a continuity of mapping is ensured across the image. Examples of such algorithms are the Combination MultiQuadric (C-MTQ), Sect. 3.2, the three component Finite Element (3C-FEM), Sect. 3.1, and a version of the modified fluid 2 (MF2), Sect. 4.2. In the case of 3C-FEM and MF2, the updating of nodal displacements or of pixel velocities is prohibited within selected areas. This is an easy and effective method of ensuring that these regions remain rigid; additionally they remain motionless.

We define here the concept of a rigid body within the deforming source, together with two paradigms of a rigid region.


\begin{definition}A region $\Theta \subset \Omega$\space is said to be {\em rigi... ...\space if the transformation $\vec{u}(\Theta)$\space is linear. \end{definition}


\begin{definition}A region $\Theta \subset \Omega$\space is said to be {\em moti... ...Theta, \forall\, t $\space and if $ \vec{u}(\Theta, 0) = 0 $ . \end{definition}

It may be desirable to have rigid but independently-moving regions:
\begin{definition}A region $\Theta \subset \Omega$\space is said to be {\em inde... ...\space satisfies the regularisation of a likelihood and prior. \end{definition}

The main application of such algorithms will be in the modelling of movement of hard and soft tissue during surgery.

next up previous contents
Next: Review of Inhomogeneous Registration Up: Spatial Inhomogoneneities in Registration Previous: Variable Deformability
Hava LESTER
1999-03-24