C. Arcelli

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. >

Characterising 3D Objects by Shape and Topology

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.

Parallel pattern compression by octagonal propagation

A 4-subiteration parallel thinning algorithm, based on 3×3 operations, is proposed. It is shown that by taking into account bidirectional compression in each subiteration, pixels belonging to a pair of successive contours, a 4-contour and an 8-contour, are removed from the pattern in every iteration. Therefore, contour pixel removal proceeds towards the inner part of the pattern according to the octagonal metric. This provides a resulting medial line which is centered in the pattern in a quasi-Euclidean sense and is less sensitive to pattern rotation. The performance of the algorithm is discussed and compared with that of some well-known parallel algorithms.

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.

DECOMPOSING 3D OBJECTS IN SIMPLE PARTS CHARACTERIZED BY RECTILINEAR SPINES

The distance labeled curve skeleton of a 3D object is used to guide the decomposition of the object into disjoint parts. To this aim, the skeleton is polygonally approximated by taking into account spatial coordinates and distance values of its voxels. The obtained skeleton segments are characterized by the absence of significant changes of curvature. Moreover, along each skeleton segment distance values are constant or show a linearly changing trend. Each segment can be interpreted as the spine of a simple part, which is characterized by the absence of significant curvature changes along its boundary, and by local thickness that is constant or evolves linearly along the part. By using exclusively the spatial coordinates and distance values of the vertices of the spines, quantitative information on shape, size, position and orientation of the corresponding simple parts can be obtained. Alternative decompositions of the object can be computed by selecting different values for the threshold used during polygonal approximation of the skeleton. Some criteria are also discussed for the selection of optimal threshold values originating approximated skeletons having a small number of segments, but still producing decompositions rather well adapting the input object boundary.

Finding cavities and tunnels in 3D complex objects

Topological properties are global features that can be useful for recognition of digital objects. For example, this is the case for objects having a complex shape without being decomposable into meaningful simple parts. In the case of 3D binary images, topological features are the object components, cavities, and tunnels. While object components and cavities are easy to define and identify, to our knowledge, no computationally convenient way to find tunnels is available. The aim of the paper is to fill this gap by presenting a convenient procedure to detect and represent tunnels in 3D objects.

From the zones of influence of skeleton branch points to meaningful object parts

A 3D object decomposition method is presented, which is based on the decomposition of the linear skeleton guided by the zones of influence. These are the connected components of voxels obtained by applying the reverse distance transformation to the branch points of the skeleton. Their role is to group sufficiently close branch points and to detect perceptually meaningful skeleton branches that are in a one-to-one relation with the object parts.

A New Set of Topology Preserving Removal Operations in the 3D Space

A new set of 3times3times3 topology preserving removal operations is introduced to compute the surface skeleton of a 3D object. We show that this set of operations can be appropriately employed in a parallel process, without creating disconnections, cavities, tunnels and vanishing of object components

Medial lines by parallelwise erosion of successive contour pairs

An iterated parallel thinning algorithm, using 3*3 local operations, is presented. Every iteration is split into four subiterations, each allowing pixel removal from two directions simultaneously. At each iteration, a layer of the pattern, characterized by nearly constant thickness in the Euclidean sense, is possibly removed. Consequently, the pattern is thinned down isotropically. Information regarding the local width of the pattern is also labeled on the pixels of the medial line.<<ETX>>

Linear representation of discrete surfaces in 3D

A method to compute a linear medial representation of a complex surface in the 3D discrete space is presented. The method involves voxel classification, surface labeling, anchor point detection, and voxel removal.