The curvature function evolved in scale-space as a representation of biological shapes

A new and simple approach for calculating the curvature functions of arbitrary non-analytical (biological) contours of planar shapes is described. This approach does not require either parametrization or the evaluation of derivatives, which eliminates sources of error and noise amplification. It is shown that this method provides better results than the traditional procedure and the procedure employing polar coordinates. The paper describes how to evolve contours in scale-space, and it is discussed how, due to its invariant properties, curvature functions, evolved in scale-space, are suitable as representations of shapes. The techniques described are applied to the digitized contours of isolated corneal endothelial cells.