Vertex Chain Code

The **Vertex
Chain Code (VCC) **is a chain code for representing any two-dimensional (2D) shape
composed of regular cells (for instance pixels). This boundary chain code is
based on the numbers of cell vertices which are in touch with the bounding
contour of the shape. The VCC is invariant under translation and rotation.
Also, it may be starting point normalized and invariant under mirroring
transformation. Using this concept of chain code it is possible to relate the
chain length to the *contact perimeter*,
which corresponds to the sum of the boundaries of neighboring cells of the
shape; also, to relate the chain nodes to the contact vertices, which
correspond to the vertices of neighboring cells. So, in this way these
relations among the chain and the characteristics of interior of the shape
allow us to obtain interesting properties. This work is motivated by the idea
of obtaining various shape features computed directly from the VCC without
going to Cartesian-coordinate representation.

Some important characteristics of the VCC are:

1.
The VCC is
invariant under translation and rotation, and optionally may be invariant under
starting point and mirroring transformation.

2.
Using the VCC it
is possible to represent shapes composed of triangular, rectangular, and
hexagonal cells.

3.
The chain
elements represent real values not symbols such as other chain codes, are part
of the shape, indicate the number of cell vertices of the contour nodes, may be
operated for extracting interesting shape properties.

4.
Using the VCC it
is possible to obtain relations between the bounding contour and interior of
the shape.

The VCC was proposed by E. Bribiesca in 1999.

References:

-Bribiesca E., A New Chain Code, **Pattern
Recognition**. Vol. 32, No. 2, pp. 235-251 (1999).