Distributions of 3D DCT coefficients for video

The three-dimensional discrete cosine transform (3D DCT) has been proposed as an alternative to motion-compensated transform coding for video content. However, so far no definitive study has been done on the distribution of 3D DCT coefficients of video sequences. This study performs two goodness-of-fit tests, the Kolmogorov-Smirnov (KS) test and the x²-test, to determine the distribution that best fits the 3D DCT coefficients of the luminance components of video sequences with low motion or structured motion. The results indicate that the DC coefficient can be well approximated by a Gaussian distribution and a majority of the high-energy AC coefficients can be approximated by a Gamma distribution. Knowledge of the coefficient distributions can be used to design quantizers optimized for 3D DCT coefficients and hence achieve better coding efficiency.