Finding shape axes using magnetic fields

This paper presents a novel method, based on magnetic field principles, for obtaining the axes of shapes. The method is based on directional information of the shape's boundary. By simulating a parallel algorithm, we are able to generate the inner as well as the outer axes (axes of concavities) of the shape. The preprocessing phase for this algorithm involves obtaining the shape's gradient. Each point of the gradient is substituted by a minute magnetic dipole. The cumulative magnetic field due to these dipoles is accumulated at all points in the image in a one-pass algorithm. The magnitude of the final magnetic vector field has valleys that are created from mutual and directionally balanced cancellations of opposing boundary segments. These valleys signify the axes of the shape. The axes are obtained by performing a valley search. The magnetic field modeling (MFM) method has an advantage over previous approaches since it utilizes not only the location information of the boundary, but also its directional information. As demonstrated, experimental results of the MFM method are much improved, compared to other skeletonization algorithms which tend to generate spurious and noisy axes.