Image Processing Reference
In-Depth Information
(
a
)
(
b
)
(
c
)
Fig. 2.7.
Chain code representation for a 3D line figure: (
a
) Direction code for a 2D
line figure (8-connectivity); (
b
) direction code for a 3D line figure (6-connectivity);
(
c
) direction code for a 3D line figure (26-connectivity).
(1)
Axis symmetry
: Digital expression is symmetrical with respect to the co-
ordinate transformation or the exchange of coordinate axes. According to
the expression adopted in the text, the expression of a 3D line figure is
invariant with respect to exchange among
i
,
j
,and
k
and the inversion of
the order of numbering.
(2)
Direction symmetry
: By exchanging a starting point and an end point, the
order of the direction codes and each direction itself are both inverted.
(3)
Shift invariance
: A digital expression does not vary by a shift of an orig-
inal line figure by integer times of the sampling interval.
(4)
Finite memory
: Digital expression of a line figure does not depend on an
arbitrarily distant part of a curve. That is, local change in a line figure
causes only local change in its digital expression.
(5)
Line segment property
: A digital expression of a line segment in the con-
tinuous space is a digital arc.
(6)
Projection property
: A digital expression of a projection of a 3D curve to
x
y
plane is coincident to the projection of a 3D digital expression of
the same curve to the same
x
−
y
plane.
(7)
Minimal property
: Digitization of a curve in the 3D continuous space is
a result of the minimization of the distance (bias, discrepancy) in some
sense between an original continuous curve and its digital expression.
(8)
Compactness
: The number of codes (the number of chain codes, for exam-
ple) required for the digital expression of a given curve is minimal under
the condition that all of the above are satisfied.
−
These are only a guideline, as a method of digitization to satisfy all of them
does not seem to exist.
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