Combination Multiquadric Spline (C-MTQ)

 Little et. al. [6] have constructed a variant of the landmark spline, incorporating regions which undergo independent linear transformations only. The method is applied to pre-segmented images, with regions classified as hard or soft tissue. The hard tissue regions form a set $\mathcal{O}$ of n rigid bodies $\{O_i\}$ such that $\mathcal{O} = \bigcup_{i=1}^{n} O_i$, where one body O_i, can consist of separate parts (all undergoing the same linear transformation) but no two bodies may overlap. The method uses a distance transform to weight differently the linear and non-linear components of the overall image mapping, such that the non-linear terms are smoothly reduced to zero as the rigid bodies are approached, and each rigid body is constrained to its own linear mapping while contributing to the underlying linear drift of the non-rigid areas.