Graphics Reference
In-Depth Information
A reconstructed image normally deviates from its original version if the
reconstruction is not perfect. Therefore, to observe the deviation of the im-
age quality, one can compute different objective measures. One such is to
provide the error in area and shape compactness between the original and
reconstructed images. Kulpa [96] provided a good way to compute the area
and perimeter. Since the key pixels are always on the contour and the recon-
structed arcs between them are restricted by the respective Bezier character-
istic triangles, the maximum error for an arc is the area of its pair of Bezier
characteristic triangles. Also, for this constraint, shape compactness is a good
measure for distortion in reconstructed images.
Table 1.2.
Error in regeneration.
Figure
% error
Compactness
Compactness
in area
of original
generated figure by
Mtd 1 Mtd 2
Figure
Mtd 1
Mtd 2
Butterfly
8.63
10.07
0.024635
0.025393 0.025551
Chromosome
6.8
6.28
0.016061
0.016672 0.016359
Table 1.2 shows both the percentage error and the compactness of images
associated with the two different methods. The reconstructed image in each
case is a faithful reproduction of its input version. The butterfly contour,
having the larger number of GEs, incurs the higher percent of error in their
regeneration. Furthermore, since the regeneration/reconstruction procedure
uses the quadratic Bezier approximation, the reconstruction is very fast.
1.8 Concluding Remarks
Bernstein polynomial together with its properties and approximation capa-
bilities provides a major step in the formulation of Bezier spline model. Some
of the properties of this polynomial are very powerful, and they serve the
basic background for the development of a new branch in mathematics as
well as in computer graphics. The widespread use and importance of B-spline
mathematics is basically a generalization of Bezier-Bernstein spline. Similarly,
the formulation of computer graphics algorithms for curve and surface design,
based on this spline model, plays a major role in various engineering design
and painting of computer drawn pictures.
The illustrative example provided in the text, to find the order of the
Bernstein polynomial, is helpful to readers to approximate a function in the
continuous domain by the Bernstein polynomial. The techniques and strate-
gies discussed in this chapter for approximating a set of data points in the
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