Abstract
Conformal mapping provides a unique way to flatten the three dimensional (3D) anatomically-complicated colon wall. Visualizing the flattened 2D colon wall supplies an alternative means for the task of detecting abnormality as compared to the conventional endoscopic views. In addition to the visualization, the flattened colon wall carries supplementary geometry and texture information for computer aided detection of abnormality. It is hypothesized that utilizing both the original 3D and the flattened 2D colon walls shall improve the detection capacity of currently available computed tomography colonography. One of the major challenges for the conformal colon flattening is how to make the input colon wall inner surface to be genus zero, as this is required by the flatten algorithm and will guarantee high flatten quality. This paper describes an efficient topological cleaning algorithm for the conformal colon flattening pipeline. Starting from a segmented colon wall, the Marching Cube algorithm was first applied to generate the surface, then we apply our topological clearance algorithm to remove the topological outliers to guarantee the output surface is exactly genus 0. The cleared or denoised colon surface was then flattened by an Ricci flow. The pipeline was tested by 14 patient datasets with comparison to our previous work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arbarello, E., Cornalba, M., Griffiths, P., Harris, J.: Topics in the Theory of Algebraic Curves (1938)
Balogh, E., Sorantin, E., Nyul, L.G., Palagyi, K., Kuba, A., Werkgartner, G., Spuller, E.: Colon unraveling based on electronic field: Recent progress and future work. In: Proceedings SPIE, pp. 713–721 (2002)
Bartrol, A.V., Wegenkittl, R., König, A., Gröller, E., Sorantin, E., Medgraph, T.: Virtual colon flattening (2001)
Erickson, J., Whittlesey, K.: Greedy optimal homotopy and homology generators. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 1038–1046 (2005)
Haker, S., Angenent, S., Kikinis, R.: Nondistorting flattening maps and the 3d visualization of colon ct images. IEEE Trans. on Medical Imaging 19, 665–670 (2000)
Hamilton, R.S.: The Ricci flow on surfaces. Mathematics and general relativity (Santa Cruz, CA, 1986). Contemp. Math. Amer. Math. Soc. Providence, RIÂ 71 (1988)
Hong, L., Kaufman, A., Wei, Y., Viswambharan, A., Wax, M., Liang, Z.: 3d virtual colonoscopy. In: IEEE Symposium on Frontier in Biomedical Visualization, pp. 26–32 (1995)
Hong, L., Liang, Z., Viswambharan, A., Kaufman, A., Wax, M.: Reconstruction and visualization of 3d models of the colonic surface. IEEE Transactions on Nuclear Science, 1297–1302 (1997)
Hong, W., Gu, X., Qiu, F., Jin, M., Kaufman, A.: Conformal virtual colon flattening. In: ACM Symposium on Solid and Physical Modeling, pp. 85–94 (2006)
Hong, W., Qiu, F., Kaufman, A.: A pipeline for computer aided polyp detection. IEEE Transactions on Visualization and Computer Graphics 12, 861–868 (2006)
Jin, M., Kim, J., Gu, X.D.: Discrete surface ricci flow: Theory and applications. In: IMA Conference on the Mathematics of Surfaces, pp. 209–232 (2007)
Massey, W.: Algebraic Topology: An Introduction. Springer (1967)
Paik, D., Beaulieu, C., Jeffrey, R., Karadi, C.A., Napel, S.: Visualization modes for ct colonography using cylindrical and planar map projections. Journal of Computer Assisted Tomography, 179–188 (2000)
Pickhardt, P.J., Choi, J.R., Hwang, I., Butler, J.A., Puckett, M.L., Hildebrandt, H.A., Wong, R.K., Nugent, P.A., Mysliwiec, P.A., Schindler, W.R.: Computed tomographic virtual colonoscopy to screen for colorectal neoplasia in asymptomatic adults. New England Journal of Medicine 349(23), 2191–2200 (2003)
Hong, W., Qiu, F., Kaufman, A.: A pipeline for computer aided polyp detection. IEEE Transactions on Visualization and Computer Graphics, 861–868 (2006)
Luboldt, W., Steiner, P., Bauerfeind, P., Pelkonen, P., Debatin, J.: Detection of mass lesions with mr colonoscopy: Preliminary report. Radiology 207, 59–65 (1998)
Wang, S., Li, L., Cohen, H., Mankes, S., Chen, J., Liang, Z.: An em approach to map solution of segmenting tissue mixture percentages with application to ct-based virtual colonoscopy. IEEE Transactions on Medical Imaging 28, 297–310 (2009)
Wang, Z., Li, B., Liang, Z.: Feature-based texture display for detection of colonic polyps on flattened colon volume. In: Intl. Conf. of IEEE Engineering in Medicine and Biology (2005)
Zeng, W., Samaras, D., Gu, X.D.: Ricci flow for 3D shape analysis. PAMI 32(4), 662–677 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shi, R., Zeng, W., Liang, J.Z., Gu, X.D. (2012). Efficient Topological Cleaning for Visual Colon Surface Flattening. In: Yoshida, H., Hawkes, D., Vannier, M.W. (eds) Abdominal Imaging. Computational and Clinical Applications. ABD-MICCAI 2012. Lecture Notes in Computer Science, vol 7601. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33612-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-33612-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33611-9
Online ISBN: 978-3-642-33612-6
eBook Packages: Computer ScienceComputer Science (R0)