Local Junction Classification in .NET

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3.3 Local Junction Classification
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At the local level, we identify those voxels that are either an unambiguous junction or a junction candidate requiring further investigation. The local classification is based on the following definitions: Definition 4: A skeleton voxel p is a junction if it satisfies conditions: (1) fc26b p > 2 or (2) fc18w p = 1 (i.e. voxel p is internal). Definition 5: A skeleton voxel p is a junction candidate if it satisfies conditions: (1) fc26b p 2, (2) fc18w p = 1 (i.e. voxel p is a border voxel), and (3) p is not 26- adjacent to any junctions. Observation 1: Our curve thinning algorithm reduces a 3D image to single-stranded border voxels by progressively transforming 3D and surface internal voxels into border voxels [1]. However, the resulting skeleton F may contain an internal voxel p if p is surrounded by other skeleton voxels. Figure 20.2 illustrates a typical 3D nonreducible voxel configuration derived from the 2D example in [18]. A surface skeleton voxel p is naturally identified as a junction, since p is the merging location of its neighboring skeleton voxels in a local surface-like configuration. Adopting this classification approach, we can always segment a surface- like skeleton into 26-paths, which then can be stored with compact formats, e.g. a chain code [19], and further processed to determine the structural orientation. The 26-connected junction candidates are the source of ambiguity in the junction classification. Let S c be the voxel set containing all junction candidates identified in the local classification. The following definition of a thick junction is adopted: n , where n > 1 and T S c , is called a Definition 6: A 26-connected voxel set T = pi i = 1 thick junction if there exists a junction candidate pj T that satisfies the conditions: 1. T N 26 pj S c 26b 26b 2. fv pj = max fv pi i = 1 n .
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We call such a voxel pj the core of the thick junction T . This definition allows us to associate a single junction (the core) to each thick junction.
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Topological Segmentation of Discrete Curve Skeletons
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Figure 20.2 A voxel configuration which cannot be reduced to a unit-width skeleton with a 3D thinning algorithm based on 26-adjacency for black voxels. Shaded voxels are 3D internal skeleton voxels.
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3.4 Thick Junction Resolution
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In the second phase of junction classification, we eliminate thick junctions by identifying a core from each thick junction and restoring the status of the other junction candidates to branch nodes. Lee et al. [12] proposed a local procedure for resolving thick junctions in a 3D curve skeleton and a similar approach can be found in Abdullah et al. [20] for 2D junction classification. According to this approach, any junction candidate p first encountered in the sequential visit of S c may be selected as a junction, and all other junction candidates 26-adjacent to p are then transformed into nodes. Doing so, however, may produce redundant junctions if the selected voxel p is not the core of the thick junction. As shown in Figure 20.3, voxels p, q, r and s are all junction candidates according to Definition 5. 26b These junction candidates form a single thick junction with voxel r, fv r = 4, as the junction core 26b (according to Definition 6). However, if Lee s algorithm happens to select voxel p, fv p = 3, as the
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Figure 20.3 An example showing that the random selection of a junction from junction candidates may lead to the creation of redundant branches.
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Topological Segmentation
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junction, voxels q and r are transformed into nodes, and the remaining candidate s is then identified as another junction in a new sequential visit of the candidate junction set, likely yielding an undesirable skeleton model. To overcome this deficiency, we propose a global approach for the resolution of thick junctions:
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26b n in a descending order by the value of fv 1. Re-sort the candidate junction set S c = pi i = 1 26b 26b of each voxel in S c such that fv pi fv pi+1 for i = 1 n 1. 2. Sequentially visit each voxel p in S c and (a) set p as a junction; (b) transform all junction candidates in Ne26 p S c to nodes; and (c) update candidate voxel set S c S c = S c N 26 p S c .
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