FEM EIGENMODES AS SHAPE FEATURES
Mike Syn and Richard Prager
The Finite Element Method (FEM) solution of the wave equation which governs the behaviour of elastic structures leads to a generalised eigenproblem. The eigenvectors of this eigenproblem are known as eigenmodes or mode shapes, which we present as an ideal set of shape features for use in model-based 3D ultrasound imaging.
We derive from first principles a framework for the modelling of volumetric linear elastic structures, using the Principal of Virtual Work. This allows us to construct mass and stiffness matrices which describe the shape and physical properties of a shape model.
We go on to examine the properties of the FEM eigenmodes of an elastic shape model, and the suitability of such a model in describing shape changes in biological structures. We show that there is an intimate connection between this model, and a growth model based on diffusion processes.
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