An algorithm for affine transformation of three-dimensional objects registered with run format.

The authors have previously proposed an efficient affine transformation algorithm for the two-dimensional binary image, where the image is represented by the run format called PXY table and the transformation is executed combining the skew and the transpose manipulations. This paper proposes a new affine transformation algorithm for the three-dimensional object (three-dimensional binary image) represented by the three-dimensional run format, called SPXY table. The SPXY table is composed by stacking the two-dimensional PXY tables. The affine transformation on the SPXY table is realized as a combination of the three-dimensional skew and the transpose manipulations, as an extension of the case of the two-dimensional PXY table. As the result of experiment, it is shown that the proposed method is faster, by a factor of 36 to 389, than the primitive method which applies the transformation to each voxel. It is also shown that the CPU time for the affine transformation by the proposed method is proportional to the number of runs in the representation of the three-dimensional object. The result of the affine transformation by the proposed method contains an error, which may be greater than the rounding error when the result is converted to an integer by rounding the subdecimal. The error analysis is applied to the three-dimensional rotation, which is used most frequently among the affine transformations. As a result, it is seen that the absolute error of each coordinate in the proposed method is 1.4 at the maximum. © 1998 Scripta Technica. Syst Comp Jpn, 29(3): 18–27, 1998 [ABSTRACT FROM AUTHOR]