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An algorithm to compute the curve skeleton of 3D objects in voxel images is presented. The skeleton is stable under isometric transformations of the object, since the algorithm is based on the use of the weighted distance transform, which is a good approximation of the Euclidean distance transform. The weighted distance transform is used both to identify suitable anchor points, and to efficiently check object voxels according to their distance to the background. The curve skeleton is symmetrically placed within the object, is topologically equivalent to the object, is unit-wide and provides a satisfactory representation of the object. Though the size of the object reconstructed from the curve skeleton via the reverse distance transformation is not as thick as that of the input, shape information is mostly retained by the skeleton, since all regions perceived as significant in the input can still be found in the reconstructed object.

We present a method to assign to either the foreground or the background the regions into which a gray-level image is partitioned by watershed transformation. Our method is inspired by visual perception in the sense that the border separating any foreground component from the background is detected in correspondence with the locally maximal gray-level changes through the image. The method is implemented as consisting of three steps. The first two steps perform a basic assignment of the regions, while the remaining step examines again some regions tentatively assigned to the background during the second step and possibly changes their status. A feature of the method is that a hierarchical ranking of the regions assigned to the foreground is also accomplished.