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Elasticity-based matching by minimising the symmetric difference of shapes

Elasticity-based matching by minimising the symmetric difference of shapes

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The authors consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearised elasticity theory and the finite-element method, they seek an elastic deformation that is caused by simple external boundary forces and accounts for the difference between the two shapes. The main contribution is in proposing a cost function and an optimisation procedure to minimise the symmetric difference between the deformed and the target shapes as an alternative to point matches that guide the matching in other techniques. The authors show how to approximate the non-linear optimisation problem by a sequence of convex problems. They demonstrate the utility of the proposed method in experiments and compare it to an iterative closest point like matching algorithm.

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