1-d B-B Spline Polynomial and Hilbert Scan for Graylevel Image Coding - Bezier and Splines in Image Processing and Machine Vision - page 75

(a) (b)

(c) (d)

Fig. 3.6. Results for Algorithm 1 due to Hilbert scan: (a) bpp = 0.69, PSNR
=26.937; (b) bpp = 0.60, PSNR = 27.346; (c) bpp = 1.28, PSNR = 29.757; (d) bpp
= 0.97, PSNR = 27.923.

The approximation technique described is different from the conventional
least square method of approximation. Instead of minimizing the global
squared sum of errors, it controls an absolute maximum error for each data
point. It should be noticed in this context that if the pixels of a segment have
low intensity variation, then the techniques based on conventional quadratic
least square and the quadratic B-B polynomial approximation will produce
the same result. Since the proposed method of approximation controls an
absolute local error instead of global sum of errors, it is expected that even
for moderate variation of intensity within data points, the proposed method
will produce better results. Also, given an error term, the conventional least