André Aichert

Epipolar Consistency in Transmission Imaging

Two X-ray projection images of a rigid object may have different points of view, yet redundant information can be identified in such images. Not unlike a checksum, these occur naturally in the data and are known as consistency conditions. Real acquisitions, however, result from a measurement process which is affected by inaccurate geometric calibration of the scanner, physical effects such as scatter and beam-hardening or in some applications patient motion. These effects can be observed as differences between theoretically redundant information in the data and, to some extent, can be corrected.

Consistency conditions have been known for decades, yet only few practical applications have been demonstrated. State-of-the-art often assumes 2D parallel or fan-beam geometries in a perfect circle around the object. Extension of these findings to flat-panel detector geometry are not straight-forward. Meanwhile, however, practical applicability in flat-detector computed tomography has been demonstrated for a set of pairwise conditions known as epipolar consistency (EC). Their advantage is that they can be applied, in principle, to any two 2D projection images.

This thesis first gives a brief introduction to data consistency conditions in two and three dimensions, providing a context for the main part of this work. The reader is then introduced to projective geometry of real two- and three-space and the geometry of X-ray imaging. This provides the mathematical tools for a derivation of the novel epipolar consistency conditions and demonstrates the connection to wellunderstood computer vision tasks. Three flavors of a metric to measure epipolar inconsistency in two images are suggested and a framework for motion compensation is introduced. Finally, the metric is used for motion correction in three applications of FDCT imaging. First, an unknown object under fluoroscopy is tracked relative to a small set of reference views. Second, respiratory and cardiac motion in rotational angiography is estimated. And third, the alignment of two computed tomography acquisitions is estimated from their raw data.