  The same type of objects in different images may vary in their shapes because
of rigid and non-rigid shape deformations, occluding foreground as well as
cluttered background. The problem concerned in this work is the shape
extraction in such challenging situations. We approach the shape extraction
through shape alignment and recovery. This paper presents a novel and general
method for shape alignment and recovery by using one example shapes based on
deterministic energy minimization. Our idea is to use general model of shape
deformation in minimizing active contour energies. Given \emph{a priori} form
of the shape deformation, we show how the curve evolution equation
corresponding to the shape deformation can be derived. The curve evolution is
called the prior variation shape evolution (PVSE). We also derive the
energy-minimizing PVSE for minimizing active contour energies. For shape
recovery, we propose to use the PVSE that deforms the shape while preserving
its shape characteristics. For choosing such shape-preserving PVSE, a theory of
shape preservability of the PVSE is established. Experimental results validate
the theory and the formulations, and they demonstrate the effectiveness of our
method.
