Identification of deformation using invariant surface information

To compensate for soft-tissue deformation during image-guided surgical procedures, non-rigid methods are often used as compensation. However, most of these algorithms first implement a rigid registration to provide an initial alignment. In liver tumor resections, the organ is deformed on a large scale, causing visual shape change on the organ. Unlike neurosurgery, there is no rigid reference available, so the initial rigid alignment is based on the organ surface. Any deformation present might lead to misalignment of non-deformed areas. This study attempts to develop a technique for the identification of organ deformation and its separation from the problem of rigid alignment. The basic premise is to identify areas of the surface that are minimally deformed and use only these regions for a rigid registration. To that end, two methods were developed. First, the observation is made that deformations of this scale cause noticeable changes in measurements based on differential geometry, such as surface normals and curvature. Since these values are sensitive to noise, smooth surfaces were tesselated from point cloud representations. The second approach was to develop a cost function which rewarded large regions with low closest point distances. Experiments were performed using analytic and phantom data, acquiring surface data both before and after deformation. Multiple registration trials were performed by randomly perturbing the post-deformed surface from a ground truth position. After registration, subsurface target positions were compared with those of the ground truth. While the curvature-based algorithm was successful with analytic data, it could not identify enough significant changes in the surface to be useful for phantom data. The minimal distance algorithm proved much more effective in separating the registration, providing significantly improved error measurements for subsurface targets throughout the whole surface.