Abstract
This chapter discusses the non-rigid motion of a small surface patch in terms of the deformation and motion of a small volume element embedding the surface patch. This is an adequate representation because given the deformation parameters of the volume element the deformation of the embedded surface is computable. Only those deformation parameters can be recovered from the image flow field that affect the embedded surface patch. An alternative representation of surface deformation can be obtained by using a curvilinear coordinate system fixed in the surface. In this system, geometric points on the surface are labeled by two independent parameters and the partial derivatives of the velocities of material particles on the surface with respect to these parameters represent the surface deformation parameters.
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