Volumetric colon wall unfolding using harmonic differentials

Volumetric colon wall unfolding is a novel method for virtual colon analysis and visualization with valuable applications in virtual colonoscopy (VC) and computer-aided detection (CAD) systems. A volumetrically unfolded colon enables doctors to visualize the entire colon structure without occlusions due to haustral folds, and is critical for performing efficient and accurate texture analysis on the volumetric colon wall. Though conventional colon surface flattening has been employed for these uses, volumetric colon unfolding offers the advantages of providing the needed quantities of information with needed accuracy. This work presents an efficient and effective volumetric colon unfolding method based on harmonic differentials. The colon volumes are reconstructed from CT images and are represented as tetrahedral meshes. Three harmonic 1-forms, which are linearly independent everywhere, are computed on the tetrahedral mesh. Through integration of the harmonic 1-forms, the colon volume is mapped periodically to a canonical cuboid. The method presented is automatic, simple, and practical. Experimental results are reported to show the performance of the algorithm on real medical datasets. Though applied here specifically to the colon, the method is general and can be generalized for other volumes.

[1]  J. Ferlay,et al.  Global Cancer Statistics, 2002 , 2005, CA: a cancer journal for clinicians.

[2]  Peter Shirley,et al.  A polygonal approximation to direct scalar volume rendering , 1990, SIGGRAPH 1990.

[3]  F. M. Vos,et al.  Three-dimensional display modes for CT colonography: conventional 3D virtual colonoscopy versus unfolded cube projection. , 2003, Radiology.

[4]  Wei Zeng,et al.  Supine and Prone Colon Registration Using Quasi-Conformal Mapping , 2010, IEEE Transactions on Visualization and Computer Graphics.

[5]  I. Bitter,et al.  Detection of Colon Wall Outer Boundary and Segmentation of the Colon Wall Based on Level Set Methods , 2006, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[6]  Eduard Gröller,et al.  Virtual Colon Flattening , 2001, VisSym.

[7]  Craig Gotsman,et al.  Discrete one-forms on meshes and applications to 3D mesh parameterization , 2006, Comput. Aided Geom. Des..

[8]  Hugues Hoppe,et al.  Design of tangent vector fields , 2007, SIGGRAPH 2007.

[9]  S. Yau,et al.  Global conformal surface parameterization , 2003 .

[10]  Feng Qiu,et al.  Conformal virtual colon flattening , 2006, SPM '06.

[11]  A. Jemal,et al.  Global Cancer Statistics , 2011 .

[12]  Santiago V. Lombeyda,et al.  Discrete multiscale vector field decomposition , 2003, ACM Trans. Graph..

[13]  Pierre Alliez,et al.  Designing quadrangulations with discrete harmonic forms , 2006, SGP '06.

[14]  D. White,et al.  6th International Meshing Roundtable '97 , 1997 .

[15]  Ge Wang,et al.  GI tract unraveling with curved cross sections , 1998, IEEE Transactions on Medical Imaging.

[16]  Feng Qiu,et al.  A Pipeline for Computer Aided Polyp Detection , 2006, IEEE Transactions on Visualization and Computer Graphics.

[17]  David H. Kim,et al.  CT colonography versus colonoscopy for the detection of advanced neoplasia. , 2007, The New England journal of medicine.

[18]  E. Zhang,et al.  Rotational symmetry field design on surfaces , 2007, SIGGRAPH 2007.

[19]  Carlo Tomasi,et al.  A graph method for the conservative detection of the polyps in the colon , 2000 .

[20]  Xiaotian Yin,et al.  Colon Flattening with Discrete Ricci Flow , 2008 .

[21]  Martin Kraus,et al.  Hardware-accelerated volume and isosurface rendering based on cell-projection , 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

[22]  E. Grinspun.  Discrete differential geometry : An applied introduction , 2008, SIGGRAPH 2008.

[23]  Hiroyuki Yoshida,et al.  Three-dimensional computer-aided diagnosis scheme for detection of colonic polyps , 2001, IEEE Transactions on Medical Imaging.

[24]  Dirk Bartz,et al.  Virtual voyage: interactive navigation in the human colon , 1997, SIGGRAPH.

[25]  Joyoni Dey,et al.  > Replace This Line with Your Paper Identification Number (double-click Here to Edit) < , 2022 .

[26]  Hiroyuki Yoshida,et al.  Computerized detection of colorectal masses in CT colonography based on fuzzy merging and wall-thickening analysis. , 2004, Medical physics.

[27]  Eduard Gröller,et al.  Nonlinear virtual colon unfolding , 2001, Proceedings Visualization, 2001. VIS '01..

[28]  Ge Wang,et al.  Colon unraveling based on electrical field: recent progress and further work , 1999, Medical Imaging.

[29]  Ge Wang,et al.  GI tract unraveling by spiral CT , 1995, Medical Imaging.

[30]  Klaus Gärtner,et al.  Meshing Piecewise Linear Complexes by Constrained Delaunay Tetrahedralizations , 2005, IMR.

[31]  D S Paik,et al.  Visualization modes for CT colonography using cylindrical and planar map projections. , 2000, Journal of computer assisted tomography.

[32]  Ron Kikinis,et al.  Nondistorting flattening maps and the 3-D visualization of colon CT images , 2000, IEEE Transactions on Medical Imaging.

[33]  Zhengrong Liang,et al.  Reduction of false positives by internal features for polyp detection in CT-based virtual colonoscopy. , 2005, Medical physics.

[34]  Guy Marchal,et al.  Computer-aided diagnosis in virtual colonography via combination of surface normal and sphere fitting methods , 2002, European Radiology.