Registration of the endoluminal surfaces of the colon derived from prone and supine CT colonography

Purpose: Computed tomographic (CT) colonography is a relatively new technique for detecting bowel cancer or potentially precancerous polyps. CT scanning is combined with three-dimensional (3D) image reconstruction to produce a virtual endoluminal representation similar to optical colonoscopy. Because retained fluid and stool can mimic pathology, CT data are acquired with the bowel cleansed and insufflated with gas and patient in both prone and supine positions. Radiologists then match visually endoluminal locations between the two acquisitions in order to determine whether apparent pathology is real or not. This process is hindered by the fact that the colon, essentially a long tube, can undergo considerable deformation between acquisitions. The authors present a novel approach to automatically establish spatial correspondence between prone and supine endoluminal colonic surfaces after surface parameterization, even in the case of local colon collapse.Methods: The complexity of the registration task was reduced from a 3D to a 2D problem by mapping the surfaces extracted from prone and supine CT colonography onto a cylindrical parameterization. A nonrigid cylindrical registration was then performed to align the full colonic surfaces. The curvature information from the original 3D surfaces was used to determine correspondence. The method can also be applied to cases with regions of local colonic collapse by ignoring the collapsed regions during the registration.Results: Using a development set, suitable parameters were found to constrain the cylindrical registration method. Then, the same registration parameters were applied to a different set of 13 validation cases, consisting of 8 fully distended cases and 5 cases exhibiting multiple colonic collapses. All polyps present were well aligned, with a mean (+/- std. dev.) registration error of 5.7 (+/- 3.4) mm. An additional set of 1175 reference points on haustral folds spread over the full endoluminal colon surfaces resulted in an error of 7.7 (+/- 7.4) mm. Here, 82% of folds were aligned correctly after registration with a further 15% misregistered by just onefold.Conclusions: The proposed method reduces the 3D registration task to a cylindrical registration representing the endoluminal surface of the colon. Our algorithm uses surface curvature information as a similarity measure to drive registration to compensate for the large colorectal deformations that occur between prone and supine data acquisitions. The method has the potential to both enhance polyp detection and decrease the radiologist's interpretation time. (C) 2011 American Association of Physicists in Medicine. [DOI: 10.1118/1.3577603

Free-boundary conformal parameterization of point clouds

With the advancement in 3D scanning technology, there has been a surge of interest in the use of point clouds in science and engineering. To facilitate the computations and analyses of point clouds, prior works have considered parameterizing them onto some simple planar domains with a fixed boundary shape such as a unit circle or a rectangle. However, the geometry of the fixed shape may lead to some undesirable distortion in the parameterization. It is therefore more natural to consider free-boundary conformal parameterizations of point clouds, which minimize the local geometric distortion of the mapping without constraining the overall shape. In this work, we develop a free-boundary conformal parameterization method for disk-type point clouds, which involves a novel approximation scheme of the point cloud Laplacian with accumulated cotangent weights together with a special treatment at the boundary points. With the aid of the free-boundary conformal parameterization, high-quality point cloud meshing can be easily achieved. Furthermore, we show that using the idea of conformal welding in complex analysis, the point cloud conformal parameterization can be computed in a divide-and-conquer manner. Experimental results are presented to demonstrate the effectiveness of the proposed method