Rotation-extended cepstrum technique optimized by systematic analysis of various sets of x-ray images

摘要

Abstract: Spatial registration is a major problem arising whenever several images of similar contents are to be compared. Considering translations only, two-dimensional cepstral techniques have been proven to be exact and robust against noise or intensity variations. Furthermore, the cepstral filtering is numerically more efficient than most common approaches to image registration based on cross-correlation or template matching. In a previous paper, we proposed a two- dimensional cepstrum based matching technique accessing rotations and translations. The logarithmic polar mapping of the power spectra of both images to be registered is used for the decoupling of rotations and translations (similar to the Fourier-Mellin transform). Rotations are detected first matching the mapped spectra by two-dimensional cepstrum analysis. After rotating back one image, the relative shift is determined using the same cepstrum technique. In clinical practice, the rotation detection step was discovered as the weakness of this registration technique. Based on 855 pairs of dental radiographs acquired in known positions, three different approaches of matching the mapped spectra are compared: the cepstrum technique, the cross-correlation, and the entropy of the one-dimensional histogram distribution function of the substraction image of the mapped spectra. The combination of the log-polar mapped power spectra of both x rays with the entropy-measure allows the best detection of rotations. The union with common cepstrum methods correcting translations results in a robust rotation- extended cepstrum technique. !30