Bernstein Polynomial and B´ezier-Bernstein Spline - Bezier and Splines in Image Processing and Machine Vision - page 26

a a

p c b −→ p c b

e d e

k

( a ) ( b )

Fig. 1.12. Deletion of pixels: (a) In absence of key pixel; (b) in presence of key
pixel.

Shifting of Pixels

Suppose a GE is generated, and a key pixel is reached. Now during the gen-
eration of a following GE, its first data point may put the preceding key pixel
on the interior contour. For example, consider the Figure 1.13(a). Here abk
is a part of the GE already generated. Now generating the next GE kcd ,

the first move from k to c makes the key pixel ( k ) lie on the interior of the
contour (assuming the enclosed region is on the right).
In such cases, the data point c is shifted as shown in Figure 1.13(b). This
preserves connectedness of the pixel c with both the GEs and also ensures
single-pixel width of the contour.

···

d d c

c k −→ k

b b

a a

( a ) ( b )

Fig. 1.13. Shifting of pixels: (a) Contour before shifting; (b) contour after shifting.

Undesirable Loop

Sometimes in the vicinity of key pixels an undesirable loop (contour with a
single pixel hole) may appear due to the generation procedure. For example,
consider Figure 1.14. Here GEs ak 1 k 2 k 3 are already generated. The next move
from k 3 to b creates an undesirable loop having a single-pixel hole.
To overcome this situation, the pixel b is shifted along with an insertion
of a new pixel e (as shown in Figure 1.14(b)). Since the shifting of b alone
loses the connectivity property between k 3 and the subsequent pixels, it ne-
cessitates insertion of a new pixel whose location is governed by the concept
of a minimum connected path.