Calculation of the correlation coefficient in the DCT domain

• Published in: Electronics & communications in Japan. Part 3, Fundamental electronic science Fundamental electronic science, 2004-12, Vol.87 (12), p.49-59
• Main Authors: Inazumi, Yasuhiro, Warashina, Takuji, Yoshida, Toshiyuki
• Format: Article
• Language: English
• Subjects: amount of computation; coefficient of correlation between pixels; DCT coefficient; direct calculation
• ISSN: 1042-0967; 1520-6440
• DOI: 10.1002/ecjc.10153

A method is studied for deriving the coefficient of correlation ρ between pixels from the DCT coefficient. The simplest way is to derive the pixel values by applying the fast inverse DCT to the DCT coefficients of interest and then to calculate ρ according to the definition in the image domain. When only the value of ρ is needed, the decoding operation by application of the inverse DCT is redundant. In this paper, a method of direct calculation of ρ in the DCT domain is proposed. First, the definition of ρ in the image domain is expressed in terms of the DCT coefficients. By using the orthogonality of DCT, the total amount of calculation is reduced so that ρ can be calculated with only 50% as much calculation as in the case with the fast inverse DCT. Next, for data such as picture images with high correlation, the energy of the DCT coefficients is concentrated in the lower frequencies. This property is used in reducing the amount of calculation to about 30% by neglecting the DCT coefficients at higher frequencies. The proposed method is applied to a number of picture images to verify its validity. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(12): 49–59, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10153