A finite element contour approach to affine invariant shape representation

This paper¹ presents a novel shape representation approach, Finite Element Contour (FEC), based on studies of shape analysis from the perspective of Finite Element Method (FEM). We assume that an edge of a contour can be modeled as a bendable beam element. Linking finite number of beam elements end to end along the contour, we obtain a closed-loop Finite Element Contour model as an approximate physical model of the original shape. By this model, we can calculate its natural frequency, which is one of mechanical properties that directly related to the geometric shape, and employed it as the shape representation. FEC shape feature possesses translation and rotation invariant properties naturally. We also realized scale and unique affine normalization in few simple steps based on intrinsic physical properties of shape from FEM viewpoint. Experimental results validated that the proposed FEC feature is capable of identifying shape in object recognition task. It also can describe shape deformation. In the well-known MPEG 7 shape retrieval task, the enhanced FEC approach obtains Bullseye score 87.11%.