Introduction

In both the fields of medical and seismic imaging, automated interpretation of volumetric data is becoming very important. A classical medical imaging problem is how to deform a template image to match an observed image Kjems et al. (1996). This deformation process is also known as warping Wolberg (1990), and is the subject of a large literature within the medical imaging community that is reviewed by Toga and Thompson (1998).

Applications of warping, however, are not limited to medical imaging: automated coregistration algorithms may be useful whenever multiple datasets need to be compared directly with one another. In the field of seismic exploration, Grubb and Tura (1997) used a warping algorithm when estimating AVO uncertainties: they migrated a field with multiple equiprobable velocity fields, and colocated the images with cross-correlation derived warp functions. In another seismic application, Rickett and Lumley (1998) included warping as part of a time-lapse reservoir monitoring cross-equalization flow, specifically to address the effects of migrations with different velocity fields. They also found a link between statistically derived warp functions and deterministic residual migration Rothman et al. (1985) or velocity continuation Fomel (1997a) operators.