Luca Serino

Distance-Driven Skeletonization in Voxel Images

A distance-driven method to compute the surface and curve skeletons of 3D objects in voxel images is described. The method is based on the use of the <;3,4,5>; weighted distance transform, on the detection of anchor points, and on the application of topology preserving removal operations. The obtained surface and curve skeletons are centered within the object, have the same topology as the object, and have unit thickness. The object can be almost completely recovered from the surface skeleton since this includes almost all of the centers of maximal balls of the object. Hence, the surface skeleton is a faithful representation. In turn, though only partial recovery is possible from the curve skeleton, this still provides an appealing representation of the object.

Object Decomposition Via Curvilinear Skeleton Partition

A method to decompose a complex 3D object into simpler parts is presented, based on a suitable partition of the curvilinear skeleton of the object. The curvilinear skeleton is divided into subsets, by taking into account the regions of influence that can be associated with its branch points. The obtained subsets are then used to recover the parts into which the object can be decomposed.

New removal operators for surface skeletonization

New 3×3×3 operators are introduced to compute the surface skeleton of a 3D object by either sequential or parallel voxel removal We show that the operators can be employed without creating disconnections, cavities, tunnels and vanishing of object components A final thinning process, aimed at obtaining a unit-thick surface skeleton, is also described.

From discs to parts of visual form

Object recognition can be favoured by the development of computational models leading to reliable descriptions of the shape of bidimensional patterns. We refer to the approach regarding a pattern as made up by a number of parts, and present a partition procedure where the parts are obtained by merging elementary regions grown from feature sets found on the Distance Transform. The feature sets include most of the centres of maximal discs, and are placed in correspondence with pattern subsets that can be qualitatively described as near-convex regions, protrusions and necks. The pattern partition found appears adequate to describe the pictorial data in a natural manner that does not lack psychological reality.

Using the skeleton for 3D object decomposition

An object decomposition method is presented, which is guided by a suitable partition of the skeleton. The method is easy to implement, has a limited computational cost and produces results in agreement with human intuition.

Skeletonization of labeled gray-tone images

A gray-tone image including perceptually meaningful elongated regions can be represented by a set of line patterns, the skeleton, consisting of pixels having different gray-values and mostly placed along the central positions of the regions themselves. In this paper, the image is considered as piecewise constant and a labeled image is created by computing the geodesic distance transformation for each image subset with constant gray-value. A sequential skeletonization process is performed on the labeled image, by employing topology preserving removal operations repeatedly applied to subsets with increasing label value. To obtain a one-pixel-thick skeleton, the topology preservation constraint is disregarded in correspondence with certain configurations in the gray-tone image which would otherwise constitute irreducible patterns.

On the computation of the {3, 4, 5} curve skeleton of 3D objects

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.

From 3D Discrete Surface Skeletons to Curve Skeletons

An algorithm to compute the curve skeleton of a 3D object starting from its surface skeleton is presented. The voxels of the surface skeleton are suitably classified to compute the geodesic distance transform of the surface skeleton and to identify anchor points. Voxels are examined in increasing distance order and are removed, provided that they are not anchor points and are not necessary to preserve topology. The resulting curve skeleton is topologically equivalent to the surface skeleton and reflects its geometry.

REGULARIZATION OF GRAPHLIKE SETS IN GRAY-TONE DIGITAL IMAGES

The repeated application of topology preserving reduction operations to a gray-tone digital image produces a homotopic image including a set S which has graphlike structure and may be regarded as a stylized version of the foreground, when it is perceived as an elongated subset of the image. To improve the capability of S to represent the foreground in a perceptually appealing way, it is convenient to modify some of the arcs of S by removing part or all of them. This regularization of S is discussed in the paper with respect to different significance measures for arc points, which allow an evaluation of the saliency of each arc. We deal with two types of regularization criteria, which are respectively applied while examining the arcs from end points and from normal points. Specific criteria depend on parameters which are allowed to vary within certain ranges and should be tuned with respect to the application at hand. Both types of criteria are concerned with the closeness of an arc to the part of the background surrounding it, but the former takes also into account the region elongation, while the latter is concerned with the indentations possibly present in the profile of the arc. Experimental work has been carried out on gray-tone images including neurons, and some results are shown.

Parallel reduction operators for gray-tone pictures

Reduction operators iteratively applied to gray-tone pictures cause dilation of the regions, the gray-value of which is locally minimal, so that a gray-tone picture with no distinction between foreground and background is transformed into a set of bottom regions separated by ridge lines. The set of ridge lines can be understood as the skeleton of what is perceived as foreground. We describe a two-subiteration parallel skeletonization algorithm employing new reduction operators which are based on the nonridge point condition and are topology preserving. The performance of the algorithm is discussed, in particular with respect to certain critical configurations, and experimental work is reported to evaluate the thinning capability of the proposed reduction operators.