A new shape descriptor for surfacesin 3D images

We introduce a linear shape descriptor for (open) surfaces in 3D images. To extract the shape descriptor, the border of the surface is first identified. Then, the distance transform of the surface is computed, where each voxel in the surface is labelled with the minimum distance to its closest border voxel. On the distance transform, the centres of the maximal geodesic discs are detected. These voxels are suitably linked to each other by growing paths in the direction of the steepest gradient, to finally obtain the linear shape descriptor of the surface. The shape descriptor can be extracted from any open surface-like object, i.e.,~an object with thickness at most two- voxel.