G. Sanniti di Baja

A one-pass two-operation process to detect the skeletal pixels on the 4-distance transform

A skeletonizing procedure is illustrated that is based on the notion of multiple pixels as well as on the use of the 4-distance transform. The set of the skeletal pixels is identified within one sequential raster scan of the picture where the 4-distance transform is stored. Two local conditions, introduced to characterize the multiple pixels are employed. Since the set of the skeletal pixels is at most two pixels wide, the skeleton can be obtained on completion of an additional inspection of the picture, during which time standard removal operations are applied. Besides being correct and computationally convenient, the procedure produces a labeled skeleton, i.e. a skeleton whose adequacy for shape description purposes is generally acknowledged. >

Curve skeletonization of surface-like objects in 3D images guided by voxel classification

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 ...

Hierarchical decomposition of multiscale skeletons

The paper presents a novel 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/spl times/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) are shown. The skeletons are, in most cases, nicely decomposed into meaningful parts. The procedure is general and not limited to any specific application.

Methods for hierarchical analysis of concavities

Presents an iterative parallel procedure for computing concavity trees of a digital shape in a multi-resolution structure. The pattern is, at all resolution levels, covered by an almost convex polygon, closely fitting the pattern itself. When the polygons have been created, a hierarchical structure is built, which points out the relations among the concavities at different resolution levels. Also some properties characterizing the added regions are computed. On the highest resolution level, a meta-concavity tree is built up. This tree can be used to analyse and hierarchically rank the shape concavities.<<ETX>>

Skeletonizing the distance transform on the hexagonal grid

An efficient skeletonizing algorithm is presented for the hexagonal grid. The skeleton has unit width, except at crossings and in regions of the shape having even width. Otherwise the skeleton has all the properties generally required for correct skeletons. It includes all local maxima, so complete recovery of the original shape is obtained by using the reverse distance transformation. The algorithm uses only local operations. Thus it can be performed both on sequential and parallel computers. In the sequential case described only three passes through the image are necessary, two to compute the distance transform and one for the identification of skeletal pixels.<<ETX>>

Simplification of 3D skeletons using distance information

We present a method to simplify the structure of the surface skeleton of a 3D object, such that loss of information can be kept under control. Our approach is to prune surface border jaggedness by removing peripheral curves. The surface border is detected and all curves belonging to it are identified. Then, distance information is used to distinguish the short curves, whose voxels are possibly deleted, provided that the topology is not changed. Our method is simple, fast, and can be applied also to two-voxel thick surface skeletons. It prunes only curves which correspond to minor features of the object, without shortening the remaining more significant curves. The structure of the surface skeleton becomes significantly simplified. The simplified set can be used directly for shape representation, or as input to curve skeleton computation. If we extract the curve skeleton from the simplified set, its structure is more manageable than if the curve skeleton is obtained from the non-simplified set.

Geometric properties of the union of maximal neighborhoods

The problem of computing area and perimeter of a digital figure presented by its discrete medial axis transform (MAT) is addressed. The figure is seen as the union of the square-shaped maximal neighborhoods centered on the local maxima of the MAT. The contribution given by each maximal neighborhood to figure area and perimeter is computed while tracing the MAT. Multiple overlaps among the maximal neighborhoods are possible. However, due to the properties of the local maxima and their associated maximal neighborhoods a single tracing of the MAT is provided to be sufficient to obtain the desired result. Thus, the procedure requires O(N) time, where N is the number of MAT pixels. >

Using grey-level and distance information for medial surface representation of volume images

A medial surface representation of a grey-level volume image is computed. The foreground is reduced to a subset topologically equivalent to the initial foreground and mainly consisting of surfaces centred within regions having locally higher intensities, here, regarded as more informative. This result is obtained by combining distance information with grey-level information. A surface skeleton is first computed, where excessive shortening is prevented by a regularity condition defined on the distance transform. The structure of the surface skeleton is then simplified by removing some peripheral surfaces, so obtaining the desired medial surface representation.

Representing volumetric vascular structures using curve skeletons

This paper describes a technique to represent relevant information of tree-like structures in a compact way. The technique is general. In the application described here, the images are obtained with contrast-enhanced magnetic resonance angiography (MRA). After segmentation, the vessels are reduced to fully reversible surface skeletons. Thereafter a novel approach to curve skeletonization based on the detection of junctions and curves in the surface skeleton is used. This procedure results in a good description of the tree structure of the vessels, where they are represented with a much smaller number of voxels. This representation is suitable for further quantitative analysis, e.g., measurements of vessel width and length.

Editing 3D binary images using distance transforms

A method for editing 3D binary images using distance information is presented. The distance transform of the whole image, i.e., of both the object and the background, is used to simultaneously remove object protrusions, cavities and components of negligible size. Our method can be useful when smoothing of an object is needed, e.g., for removal of noise before computing the skeleton of an object. It can also be used to guide decomposition of a complex objects consisting of components with different thickness. Preliminary results of the decomposition algorithm are shown.