State-space approach to roundoff error analysis of fractal image coding

• Published in: 1997 IEEE International Symposium on Circuits and Systems Vol. 2; pp. 1341 - 1344 vol.2
• Main Authors: Choong Ho Lee, Kawamata, M., Higuchi, T.
• Format: Conference Proceeding
• Language: English; Japanese
• Published: IEEE 22.11.2002
• Subjects: Analysis of variance; Degradation; Error analysis; Fractals; Hardware; Image analysis; Image coding; Iterative decoding; Noise measurement; Roundoff errors
• ISBN: 9780780335837; 078033583X
• DOI: 10.1109/ISCAS.1997.622108

Roundoff error due to iterative computation with finite wordlength degrades the quality of decoded images in fractal image coding that employs a deterministic iterated function system. This paper presents a state-space approach to roundoff error analysis of fractal image coding for grey-scale images. The output noise variance matrix and the noise matrix are derived for the measures of error and the output noise variance is newly defined as the pixel mean of diagonal elements of the output noise matrix. A quantitative comparison of experimental roundoff error with analytical result is made for the output noise variance. The result shows that our analysis method is valid for the fractal image coding. Our analysis method is useful to design a real-time and low-cost decoding hardware with finite wordlength for fractal image coding.