ABSTRACT
We present an efficient colon flattening algorithm using a conformal structure, which is angle-preserving and minimizes the global distortion. Moreover, our algorithm is general as it can handle high genus surfaces. First, the colon wall is segmented and extracted from the CT data set of the abdomen. The topology noise (i.e., minute handle) is located and removed automatically. The holomorphic 1-form, a pair of orthogonal vector fields, is then computed on the 3D colon surface mesh using the conjugate gradient method. The colon surface is cut along a vertical trajectory traced using the holomorphic 1-form. Consequently, the 3D colon surface is conformally mapped to a 2D rectangle. The flattened 2D mesh is then rendered using a direct volume rendering method accelerated with the GPU. Our algorithm is tested with a number of CT data sets of real pathological cases, and gives consistent results. We demonstrate that the shape of the polyps is well preserved on the flattened colon images, which provides an efficient way to enhance the navigation of a virtual colonoscopy system.
- Balogh, E., Sorantin, E., Nyul, L. G., Palagyi, K., Kuba, A., Werkgartner, G., and Spuller, E. 2002. Colon unraveling based on electronic field: Recent progress and future work. Proceedings SPIE 4681, 713--721.Google Scholar
- Bartrolì, A. V., Wegenkittl, R., König, A., and Gröller, E. 2001. Nonlinear virtual colon unfolding. IEEE Visualization, 411--418. Google ScholarDigital Library
- Bartrolì, A. V., Wegenkittl, R., König, A., Gröller, E., and Sorantin, E. 2001. Virtual colon flattening. VisSym Joint Eurographics - IEEE TCVG Symposium on Visualization, 127--136. Google ScholarDigital Library
- Bolz, J., Farmer, I., Grinspun, E., and Schröder, P. 2003. Sparse matrix solvers on the gpu: Conjugate gradients and multi-grid. ACM Transactions on Graphics 22, 3, 917--924. Google ScholarDigital Library
- Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. 2001. Introduction to Algorithms, Second Edition. The MIT Press. Google ScholarDigital Library
- Desbrun, M., Meyer, M., and Alliez, P. 2002. Intrinsic parameterization of triangle meshes. Eurographics (Computer Graphics Forum), 209--218.Google Scholar
- Dey, T. K., and Schipper, H. 1995. A new technique to compute polygonal schema for 2-manifolds with application to null-homotopy detection. Discrete and Computational Geometry 14, 93--110.Google ScholarDigital Library
- Ei-Sana, J., and Varshney, A. 1997. Controlled simplification of genus for polygonal models. IEEE Visualization, 403--412. Google ScholarDigital Library
- Éric Colin De Verdière, and Lazarus, F. 2005. Optimal system of loops on an orientable surface. Discrete and Computational Geometry 33, 3, 507--534.Google ScholarDigital Library
- Erickson, J., and Har-Peled, S. 2003. Optimally cutting a surface into a disk. ACM Symposium on Computational Geometry, 215--228. Google ScholarDigital Library
- Erickson, J., and Whittlesey, K. 2005. Greedy optimal homotopy and homology generators. ACM-SIAM Symposium on Discrete Algorithms, 1038--1046. Google ScholarDigital Library
- Floater, M. S., and Hormann, K. 2005. Surface parameterization: a tutorial and survey. Advances in Multiresolution for Geometric Modelling, 157--186.Google Scholar
- Gu, X., and Yao, S.-T. 2003. Global conformal surface parameterization. ACM Symposium on Geometry Processing, 127--137. Google ScholarDigital Library
- Gu, X., Gortler, S. J., and Hoppe, H. 2002. Geometry images. ACM Transactions on Graphics 21, 3, 355--361. Google ScholarDigital Library
- Guskov, I., and Wood, Z. 2001. Topological noise removal. Graphics Interface, 19--26. Google ScholarDigital Library
- Haker, S., Angenent, S., Tannenbaum, A., and Kikinis, R. 2000. Nondistorting flattening maps and the 3d visualization of colon ct images. IEEE Transactions on Medical Imaging 19, 7, 665--670.Google ScholarCross Ref
- Hong, L., Muraki, S., Kaufman, A., Bartz, D., and He, T. 1997. Virtual voyage: Interactive navigation in the human colon. Proceedings of ACM SIGGRAPH, 27--34. Google ScholarDigital Library
- Jost, J. 2002. Compact Riemann Surfaces. Springer.Google Scholar
- Lakare, S., Wan, M., Sato, M., and Kaufman, A. 2000. 3d digital cleansing using segmentation rays. IEEE Visualization, 37--44. Google ScholarDigital Library
- Lazarus, F., Pocchiola, M., Vegter, G., and Verroust, A. 2001. Computing a canonical polygonal schema of an orientable triangulated surface. ACM Symposium on Computational Geometry, 80--89. Google ScholarDigital Library
- Lévy, B., Petitjean, S., Ray, N., and Maillot, J. 2002. Least squares conformal maps for automatic texture atlas generation. ACM Transactions on Graphics 21, 3, 362--371. Google ScholarDigital Library
- Massey, W. S. 1990. Algebraic Topology: An Introduction. Springer.Google Scholar
- Paik, D. S., Beaulieu, C. F., Jeffrey, R. B. J., Karadi, C. A., and Napel, S. 2000. Visualization modes for ct colonography using cylindrical and planar map projections. Journal of Computer Assisted Tomography 24, 179--188.Google ScholarCross Ref
- Pinkall, U., and Polthier, K. 1993. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2, 1, 15--36.Google ScholarCross Ref
- Reddy, J. N. 2004. An Introduction to Nonlinear Finite Element Analysis. Oxford University Press.Google Scholar
- Schoen, R., and Yau, S.-T. 1997. Lectures on Harmonic Maps. International Press.Google Scholar
- Wan, M., Liang, Z., Ke, Q., Hong, L., Bitter, I., and Kaufman, A. 2002. Automatic centerline extraction for virtual colonoscopy. IEEE Transactions on Medical Imaging 21, 1450--1460.Google ScholarCross Ref
- Wang, G., and Vannier, M. W. 1995. Gi tract unraveling by spiral ct. Proceedings SPIE 2434, 307--315.Google Scholar
- Wang, G., McFarland, E. G., Brown, B. P., and Vannier, M. W. 1998. Gi tract unraveling with curved cross section. IEEE Transactions on Medical Imaging 17, 318--322.Google ScholarCross Ref
- Wang, G., Dave, S. B., Brown, B. P., Zhang, Z., McFarland, E. G., Haller, J. W., and Vannier, M. W. 1999. Colon unraveling based on electronic field: Recent progress and future work. Proceedings SPIE 3660, 125--132.Google Scholar
- Zhang, N., Hong, W., and Kaufman, A. 2004. Dual contouring with topolgy-preserving simplification using enhanced cell representation. IEEE Visualization, 505--512. Google ScholarDigital Library
Index Terms
- Conformal virtual colon flattening
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