Publications by Gabriella Sanniti di Baja et al. on Shape Symmetry elicitation :

• Characterising 3D Objects by Shape and Topology, 2003.
• Simplifying curve skeletons in volume images, 2003.
• Using distance transforms to decompose 3D discrete objects, 2002.
• Curve skeletonization of surface-like objects in 3D images guided by voxel classification, 2002.
• A new shape descriptor for surfaces in 3D images, 2002.
• Hierarchical Decomposition of Multiscale Skeletons, 2001.
• Shape and topology preserving grey-value pyramids for multiresolution skeletonization, 2001.
• Computing Skeletons in Three Dimensions, 1999.
• Finding Local Maxima in a Pseudo-Euclidean Distance Transform, 1988.

Gabriella Sanniti di Baja

• Istituto di Cibernetica "E. Caianiello", CNR
  Via Campi Flegrei 34 - 80078 Pozzuoli, Napoli, ITALY
  Email: < gsdb@imagm.cib.na.cnr.it > , < g.sannitidibaja@cib.na.cnr.it >

BibTeX references.

Information on the shape of an object can be combined with information on the shape of the complement of the object, in order to describe objects having complex shape. We present a method for decomposing and characterising the convex deficiencies of an object, i.e., the regions obtained by subtracting the object from its convex hull, into parts corresponding to cavities, tunnels, and concavities of the object. The method makes use of the detection of watersheds in a distance image.

Keywords: Distance transform, watershed segmentation, topological erosion, volume image.

The curve skeleton of a 3D solid object provides a useful tool for shape analysis tasks. In this paper, we use a recent skeletonization algorithm based on voxel classification that originates a nearly thin, i.e., at most two-voxel thick, curve skeleton. We introduce a novel way to compress the nearly thin curve skeleton to one-voxel thickness, as well as an efficient pruning algorithm able to remove unnecessary skeleton branches without causing excessive loss of information. To this purpose, the pruning condition is based on the distribution of significant elements along skeleton branches. The definition of significance depends on the adopted skeletonization algorithm. In our case, it is derived from the voxel classification used during skeletonization.

Object decomposition into simpler parts greatly diminishes the complexity of a recognition task. In this paper, we present a method to decompose a 3D discrete object into nearly convex or elongated parts. Object decomposition is guided by the distance transform (DT). Significant voxels in DT are identified and grouped into seeds. These are used to originate the parts of the object by applying the reverse and the constrained distance transformations. Criteria for merging less significant parts and obtaining a perceptually meaningful decomposition are also given. This approach is likely to be of interest in future applications due to the increasing number and the decreasing cost of devices for volume image acquisition.

Author Keywords: Decomposition; Shape representation; Volume image; Distance transform; Merging.

Skeletonization is a way to reduce dimensionality of digital objects. Here, we present an algorithm that computes the curve skeleton of a surface-like object in a 3D image, i.e., an object that in one of the three dimensions is at most two-voxel thick. A surface-like object consists of surfaces and curves crossing each other. Its curve skeleton is a 1D set centred within the surface-like object and with preserved topological properties. It can be useful to achieve a qualitative shape representation of the object with reduced dimensionality. The basic idea behind our algorithm is to detect the curves and the junctions between different surfaces and prevent their removal as they retain the most significant shape representation.

Keywords: Curve skeleton; Topology preservation; Shape representation; Volume image.

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 (CMGDs) 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.

Keywords: Surface; Distance transform; Volume image; Shape descriptor; Linear representation

This paper presents a new procedure to hierarchically decompose a multiscale discrete skeleton. The skeleton is a linear pattern representation that is generally recognized as a good shape descriptor. For discrete images, the discrete skeleton is often preferable. Multiresolution representations are convenient for many image analysis tasks. Our resulting skeleton decomposition shows two different types of hierarchy. The first type of hierarchy is one of different scales, as the original pattern is converted into an AND-pyramid and the skeleton is computed for each resolution level. The second type of hierarchy is established at each level of the pyramid by identifying and ranking skeleton subsets according to their permanence, where permanence is a property intrinsically related to local pattern thickness. To achieve the decomposition, both bottom-up and top-down analysis in the sense of moving from higher to lower resolution and vice versa are used. The bottom-up analysis is used to ensure that a part of the skeleton that is connected at a higher resolution level is also connected (if at all present) in the next, lower resolution level. The top-down analysis is used to build the permanence hierarchy ranking the skeleton components. Our procedure is based on the use of (3 × 3) local operations in digital images, so it is fast and easy to implement. This skeleton decomposition procedure is most effective on patterns having different thickness in different regions. A number of examples of decompositions of multiscale skeletons (with and without loops) will be shown. The skeletons are, in most cases, nicely decomposed into meaningful parts. The procedure is general and not limited to any specific application.

Index Terms- Skeleton, decomposition, multiresolution, binary pyramid.

Starting from a binary digital image, a multi-valued pyramid is built and suitably treated, so that shape and topology properties of the pattern are preserved satisfactorily at all resolution levels. The multi-valued pyramid can then be used as input data to any grey-level skeletonization algorithm. In this way, a multi-resolution skeleton is computed, which could be useful in many image analysis tasks.

Keywords: Shape; Grey-level skeleton; Multi-resolution; Binary pyramid.

Skeletonization will probably become as valuable a tool for shape analysis in 3D, as it is in 2D. We present a topology preserving 3D skeletonization method which computes both surface and curve skeletons whose voxels are labelled with the D6 distance to the original background. The surface skeleton preserves all shape information, so (close to) complete recovery of the object is possible. The curve skeleton preserves the general geometry of the object. No complex computations, large sets of masks, or extra memory are used, which make implementations efficient. Resulting skeletons for geometric objects in a number of 2 Mbyte images are shown as examples.

Author Keywords: Volume image; Shape representation; Surface skeleton; Curve skeleton; Thinning; Digital topology