Efficient voxel lookup in non-uniformly spaced images using virtual uniform axes

Medical image data is usually represented by a uniformly spaced grid of voxels. However, CT scanners for example are capable of producing non-uniformly spaced slice images. This is desirable when for a particular patient some regions (lesions) need to be imaged with a high resolution, while a lower resolution would be sufficient in other areas. Such an adaptive slice spacing can significantly reduce X-ray dose, thus directly benefiting the patient. Unfortunately, computational handling of the resulting volume data is far less efficient than that of uniformly spaced images. To deal with this problem, the present paper introduces a novel data structure for non-uniformly spaced image coordinates, the so-called virtual uniform axes. By a generalization of Euclid’s greatest common divider (GCD) algorithm, a table of virtual voxels on a uniform grid is produced. Each of the uniform voxels in the virtual grid holds a pointer to the corresponding voxel in the original, non-uniform grid. Finding a voxel in the virtual uniform image can be done in constant time as compared to logarithmic time for finding a voxel in a non-uniform image. This is achieved with significantly less additional storage than by resampling the image data itself to a uniform grid. Interpolation artifacts are also completely avoided.