Image Processing Reference
In-Depth Information
skeleton extraction includes two 3D arrays of the same size as an input image,
two 1D arrays, and one table (1D array).
This algorithm consists of performing the squared DT and confirming that
the restoration of an input figure is possible. It extracts voxels as the skeleton,
which are effective for restoration of an input figure. Therefore, if skeleton
extraction and restoration of an input figure are performed only once, skeleton
extraction is not so significant. On the contrary, once we have extracted a
skeleton, then an input figure can be restored from the skeleton and DT
values on it at any time.
5.5.12 Distance transformation of a line figure
Distance transformation of a line figure is the process that gives the distance
to each voxel of a line figure in turn starting at the edge point. It is defined
both for a binary image and a grey-tone line image. Various algorithms to
perform this have been studied in detail [Toriwaki79, Toriwaki82a, Toriwaki88,
Suzuki85], and all of them can be extended to a 3D line pattern without
significant modification. Practical applications including structure analysis of
a figure is not studied in depth, although some properties specific to 3D images
are expected to exist.
5.6 Border surface following
5.6.1 Outline
Border surface (boundary surface) following is a process to extract all border
voxels in a 3D image by the methods satisfying a given set of requirements.
The requirements include the following:
(i) All border voxels should be extracted. In other words, coordinates (the
numbers of rows, columns, and planes) of each border voxels are recorded
in a list.
(ii) Extracted voxels in a list are separated according to connected compo-
nents that they belong to. According to the notation in Def. 4.15, border
voxels are classified according to a component to which border voxels be-
long. That is, borders are classified according to each pair of figures P
and Q in Def. 4.15.
(iii) Border voxels are recorded in the list according to the order specific to
an individual algorithm utilized in border voxel extraction.
(iv) A border voxel belonging to each border surface is extracted only once
except for exceptional cases such as voxels existing on a plane of one voxel
width almost everywhere.
(v) The adjacency relation among border voxels are kept unchanged on the
resulting list excluding a few exceptional cases.
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