Three dimensional integer rotation transform and improvement of its compatibility

In this paper, a new structure of three dimensional integer rotation transform is proposed. The number of rounding operations is reduced from nine to four by introducing multi input lifting branches. Furthermore, the best combination of order of input signals is determined to avoid singular points of multiplier coefficients in the lifting branches. As a result, variance of errors due to rounding of signals into integers is reduced by 42.9[%] at maximum and its compatibility to the conventional non integer rotation transform is improved.