Two-Pass Image and Volume Rotation

Abstract

We present a novel two-pass approach for both 2D image and 3D volume rotation. Each pass is a pseudo shear. However, it has the similar regularity to a pure shear in that a beam remains rigid. Furthermore, the 3D pseudo shear guarantees that beams within one major axis slice remain in the same directional plane after the shearing. These properties make it feasible to implement the pseudo shears on a multi-pipelined hardware or a massively parallel machine. Compared with the existing decompositions, ours offer a minimum number of shears to realize an arbitrary 3D rotation. Our decomposition also preserves the image/volume quality by guaranteeing no minification for the first pass shear.

Rotation of 3D volumes by Fourier-interpolated shears

“…The k-space rotation method effectively assigns more bits for the phase information, reducing this source of error, so for these tests k-space methods produce better results. For Table 2 equivalent values have been computed using various orders of polynomial interpolation for comparison 5 . Because all finite impulse response filters have a limited passband, one expects that higher order interpolating filters or non-polynomial interpolating filters such as those derived using the Parks-McClellan algorithm [20,6] would produce results intermediate between those of the given polynomial interpolators and the Fourier methods.…”

“…In the literature of direct volume rendering, Chen and Kaufman [4,5] have examined 3D rotation using four shears of a variety of types; the results reported here are a generalization and formalization of their beam-shear method. Their implementation uses polynomial resampling for speed in the implementation of volume rotation; this paper uses Fourier methods to produce results which are statistically unbiased and information-preserving.…”

“…Their implementation uses polynomial resampling for speed in the implementation of volume rotation; this paper uses Fourier methods to produce results which are statistically unbiased and information-preserving. A generalized shearing transformation called a beam-slice shear with five free parameters is introduced by [5]. This transformation allows a 3D rotation to be decomposed into only two such shears, but because of the extra free parameters the shears cannot be implemented by Fourier methods.…”

Fully reversible image rotation by 1-D filtering

“…The quality of this method is very poor, however. It should also be stressed that other decompositions of rotations have been proposed in the literature [3,4,5], but they use scaling operations in addition to shears, that necessarily imply some loss of information; hence, they can not be made reversible.…”