1-d B-B Spline Polynomial and Hilbert Scan for Graylevel Image Coding - Bezier and Splines in Image Processing and Machine Vision - page 57

Fig. 3.1. Hilbert curve with different resolutions.
Fig. 3.2. Four stages of the Hilbert curve.
rule, in step n we obtain H n from four copies of H n− 1 , which are connected
by three line segments of length 1/2 n and this curve contains 4 n copies of
H 0 (scaled by 1/2 n ). A different approach (normally known as the L-system
approach) for construction of the Hilbert curve can be found in [134]. Since in
image compression problem we are concerned with mapping gray tone images
of different sizes into corresponding Hilbert scanned images, we construct
Hilbert curve with different resolutions using Freeman's four connected chain
code. The chain code is shown in Figure 3.3. Using this chain code, the curves
H 0 , H 1 ,and H 2 are respectively given below:
H 0 : 123.
H 1 : 214,1,123,2,123,3,432.