1-d B-B Spline Polynomial and Hilbert Scan for Graylevel Image Coding - Bezier and Splines in Image Processing and Machine Vision - page 76

(a) (b)

(c) (d)

Fig. 3.7. Results for Algorithm 2 due to Hilbert scan: (a) bpp = 0.72, PSNR =
28.446; (b) bpp = 0.67, PSNR = 28.811; (c) bpp = 1.34, PSNR = 30.821; (d) bpp
= 1.33, PSNR = 27.543.

square technique does not ensure that all the data points will satisfy the error
criterion, whereas in the proposed method this is not the case. Furthermore,
it is not needed to compute any functional distance to justify the goodness of
approximation because the error term itself quantifies this.
Note further that our intention here is to demonstrate, through an appli-
cation, the effectiveness of one-dimensional B-B spline function in image data
compression for both the raster and Hilbert scanned images. The algorithms
are ecient for the Hilbert scanned images because of strong correlation be-
tween pixels over long segments. Both the schemes are fast and simple in
hardware implementation. However, it is needless to mention that the two-