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Colon Surface Registration Using Ricci Flow

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Abdomen and Thoracic Imaging

Abstract

Shape registration is very fundamental for shape analysis problems, especially for abnormality detection in medical applications. In virtual colonoscopy, CT scans are typically acquired with the patient in both supine and prone positions. The registration of these two scans is desirable so that the user can clarify situations or confirm polyp findings at a location in one scan with the same location in the other, thereby improving polyp detection rates and reducing false positives. However, this supine-prone registration is challenging because of the substantial distortions in the colon shape due to the patient’s change in position. In this work, we present an efficient algorithm and framework for performing this registration through the use of conformal geometry and Ricci flow to guarantee that the registration is a diffeomorphism (a one-to-one and onto mapping). The taeniae coli and colon flexures are automatically extracted for each supine and prone surface, employing the colon geometry. The two colon surfaces are then divided into several segments using flexures, and each segment is cut along a taenia coli and conformally flattened to the rectangular domain using Ricci flow. Corresponding feature points between supine and prone are found and used to adjust the conformal flattening to be quasi-conformal, such that the features become aligned. We present multiple methods of visualizing our results, including 2D flattened rendering, corresponding 3D endoluminal views, and rendering of distortion measurements. We demonstrate the efficiency and efficacy of our registration method by illustrating matched views on both the 2D flattened colon images and in the 3D volume rendered colon endoluminal view. We analytically evaluate the correctness of the results by measuring the distance between features on the registered colons.

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References

  1. Horner MJ, Ries LAG, Krapcho M, Neyman N, Aminou R, Howlader N, Altekruse SF, Feuer EJ, Huang L, Mariotto A, Miller BA, Lewis DR, Eisner MP, Stinchcomb DG, Edwards BK (eds.) SEER cancer statistics review, 1975–2006. National Cancer Institute,” 2009, http://seer.cancer.gov/csr/1975_2006/

  2. Center MM, Jemal A, Smith RA, Ward E (2009) Worldwide variations in colorectal cancer. CA: A Cancer J Clin 59(6):366–378

    Article  Google Scholar 

  3. Hong L, Muraki S, Kaufman A, Bartz D, He T (1997) Virtual voyage: Interactive navigation in the human colon. In: Proceedings of SIGGRAPH, ACM, pp 27–34

    Google Scholar 

  4. Johnson CD, Dachman AH (2000) CT colography: The next colon screening examination. Radiology 216(2):331–341

    Article  PubMed  CAS  Google Scholar 

  5. Hong W, Qiu F, Kaufman A (2006) A pipeline for computer aided polyp detection. IEEE Trans Visualiz Comput Graph 12(5):861–868

    Article  Google Scholar 

  6. Zhao L, Botha CP, Bescos JO, Truyen R, Vos FM, Post FH (2006) Lines of curvature for polyp detection in virtual colonoscopy. IEEE Trans Visualiz Comput Graph 12(5):885–892

    Article  Google Scholar 

  7. Zhu H, Liang Z, Pickhardt PJ, Barish MA, You J, Fan Y, Lu H, Posniak EJ, Richards RJ, Cohen HL (2010) Increasing computer-aided detection specificity by projection features for CT colonography. Medic Phys 37(4):1468–1481

    Article  Google Scholar 

  8. Williams D, Grimm S, Coto E, Roudsari A, Hatzakis H (2008) Volumetric curved planar reformation for virtual endoscopy. IEEE Trans Visualiz Comput Graph 14(1):109–119

    Article  Google Scholar 

  9. Raghupathi L, Grisoni L, Faure F, Marchal D, Cani M.-P, Chaillou C (2004) An intestinal surgery simulator: Real-time collision processing and visualization. IEEE Trans Visualiz Comput Graph 10(6):708–718

    Article  Google Scholar 

  10. Marino J, Qiu F, Kaufman A (2008) Virtually assisted optical colon-oscopy. Proc. of SPIE Med Imag 6916:69160J

    Article  Google Scholar 

  11. Acar B, Napel S, Paik DS, Li P, Yee J, Jeffrey Jr RB, Beaulieu C (2001) Medial axis registration of supine and prone CT colonography data. In: Proceedings of Engineering in Medicine and Biology Society (EMBS), IEEE CS Press, pp 2433–2436

    Google Scholar 

  12. de Vries AH, Truyen R, van der Peijl J, Florie J, van Gelder RE, Gerritsen F, Stoker J (2006) Feasibility of automated matching of supine and prone CT-colonography examinations. Br J Radiol 79:740–744

    Article  PubMed  Google Scholar 

  13. Näppi J, Okamura A, Frimmel H, Dachman A, Yoshida H (2005) Region-based supine-prone correspondence of false-positive CAD polyp candidates in CT colonography. Acad Radiol 12:695–707

    Article  PubMed  Google Scholar 

  14. Hong W, Gu X, Qiu F, Jin M, Kaufman A (2006) Conformal virtual colon flattening. In: Proceeings of ACM symposium on solid and physical modeling, ACM, pp 85–93

    Google Scholar 

  15. Gurijala KC, Kaufman A, Zeng W, Gu X (2010) Extraction of landmarks and features from virtual colon models. In: The MICCAI’10 workshop on challenges and opportunities in virtual colonoscopy and abdominal imaging (MICCAI’10-VCAI), Beijing, China, 20 Sep 2010

    Google Scholar 

  16. Zeng W, Marino J, Gurijala K, Gu X, Kaufman A (2010) Supine and prone colon registration using quasi-conformal mapping. IEEE Trans Visualiz Comput Graph (IEEE TVCG) 16(6):1348–1357

    Article  Google Scholar 

  17. Nain D, Haker S, Grimson WEL, Cosman Jr E, Wells WW, Ji H, Kikinis R, Westin CF (2002) Intra-patient prone to supine colon registration for synchronized virtual colonoscop. In: Proceedings of MICCAI, Springer, pp 573–580

    Google Scholar 

  18. Huang A, Roy D, Franaszek M, Summers RM (2005) Teniae coli guided navigation and registration for virtual colonoscopy. In: Proceedings of IEEE Visualization, IEEE CS Press, pp 279–285

    Google Scholar 

  19. Huang A, Roy DA, Summers RM, Franaszek M, Petrick N, Choi JR, Pickhardt PJ (2007) Teniae coli-based circumferential localization system for CT colonography: Feasability study. Radiology 243(2):551–560

    Article  PubMed  Google Scholar 

  20. Umemoto Y, Oda M, Kitasaka T, Mori K, Hayashi Y, Suenaga Y, Takayama T, Natori H (2008) Extraction of teniae coli from CT volumes for assisting virtual colonoscopy. Proc. SPIE Med Imag 6916:69160D

    Article  Google Scholar 

  21. Suh JW, Wyatt CL (2009) Deformable registration of supine and prone colons for computed tomographic colonography. J Comput Assist Tomograp 33(6):902–911

    Article  Google Scholar 

  22. Plishker W, Shekhar R (2008) Virtual colonoscopy registration regularization with global chainmil. In: Proceedings of MICCAI workshop on virtual colonoscopy, IEEE CS Press, pp 116–121

    Google Scholar 

  23. Gu X, Wang Y, Chan TF, Thompson PM, Yau S-T (2004) Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans Med Imag 23(8):949–958

    Article  Google Scholar 

  24. Hamilton RS (1998) The Ricci flow on surfaces. Math General Relativ 71:237–262

    Article  Google Scholar 

  25. Chow B, Luo F (2003) Combinatorial Ricci flows on surfaces. J Different Geomet 63(1):97–129

    Google Scholar 

  26. Jin M, Kim J, Luo F, Gu X (2008) Discrete surface Ricci flow. IEEE Trans Visualiz Comput Graph 14(5):1030–1043

    Article  Google Scholar 

  27. Zeng W, Samaras D, Gu XD (2010) Ricci flow for 3D shape analysis. IEEE Trans Patt Anal Mach Intell 32(4):662–677

    Article  Google Scholar 

  28. Zhang M, Li Y, Zeng W, Yau S-T, Gu X (2012) Canonical conformal mapping for high genus surfaces with boundaries. Int J Comput Graph 36(5):417–426

    Article  CAS  Google Scholar 

  29. Zeng W, Jin M, Luo F, Gu X (2009) Computing canonical homotopy class representative using hyperbolic structure. In: IEEE international conference on shape modeling and applications (SMI’09), Beijing, China, 26–28 June 2009

    Google Scholar 

  30. Zeng W, Lui LM, Luo F, Chan T, Yau S-T, Gu X (2012) Computing quasiconformal maps using an auxiliary metric with discrete curvature flow. Numeriche Mathematica 121(4):671–703

    Article  Google Scholar 

  31. Zeng W, Yin XT, Zeng Y, Lai YK, Gu X, Samaras D (2008) 3D face matching and registration based on hyperbolic Ricci flow. In: The CVPR Workshop on 3D Face Processing (CVPR’08-3DFP), Anchorage, Alaska, 27 June 2008

    Google Scholar 

  32. Zeng W, Gu X (2011) Registration for 3D surfaces with large deformations using quasi-conformal curvature flow. In: IEEE conference on computer vision and pattern recognition (CVPR’11), Colorado Springs, Colorado, 20–25 June 2011

    Google Scholar 

  33. Jin M, Zeng W, Luo F, Gu X (2009) Computing Teichmüller shape space. IEEE Trans Visualiz Comput Graph 15(3):504–517

    Article  Google Scholar 

  34. Zeng W, Lui L, Shi L, Wang D, Chu WC, Cheng JC, Hua J, Yau S-T, Gu X (2010) Shape analysis of vestibular systems in adolescent idiopathic scoliosis using geodesic spectra. In: The 13th international conference on medical image computing and computer assisted intervention (MICCAI’10), Beijing, China, 20–24 Sept 2010

    Google Scholar 

  35. Wang Y, Shi J, Yin X, Gu X, Chan TF, Yau S-T, Toga AW, Thompson PM (2012) Brain surface conformal parameterization with the Ricci flow. IEEE Trans Med Imag 31(2):251–264

    Article  CAS  Google Scholar 

  36. Zeng W, Shi R, Wang Y, Yau S-T, Gu X (2013) Teichmüller shape descriptor and its application to Alzheimer’s disease study. Int J Comput Vision (IJCV), 105(2):155–170

    Google Scholar 

  37. Zeng W, Li H, Chen L, Morvan J-M, Gu X (2013) An automatic 3d expression recognition framework based on sparse representation of conformal images. In: The 10th IEEE international conference on face and gesture recognition (FG’13), Shanghai, China, 22–26 April 2013

    Google Scholar 

  38. Qiu F, Fan Z, Yin X, Kauffman A, Gu X (2009) Colon flattening with discrete Ricci flow. In: Proceedings of MICCAI

    Google Scholar 

  39. Sarkar R, Yin X, Gao J, Gu X (2009) Greedy routing with guaranteed delivery using ricci flows. In: International conference on information processing in sensor networks (IPSN’09), IEEE CS Press, pp 121–132

    Google Scholar 

  40. Zeng W, Sarkar R, Luo F, Gu X, Gao J (2010) Resilient routing for sensor networks using hyperbolic embedding of universal covering space. In: The 29th IEEE conference on computer communications (INFOCOM’10), San Diego, California, 15–19 March 2010

    Google Scholar 

  41. Sarkar R, Zeng W, Gao J, Gu X (2010) Covering space for in-network sensor data storag. In: International conference on information processing in sensor networks (IPSN’10), Stockholm, Sweden, 12–16 April 2010

    Google Scholar 

  42. Jiang R, Ban X, Goswami M, Zeng W, Gao J, Gu X (2011) Exploration of path space using sensor network geometry. In: International conference on information processing in sensor networks (IPSN’11), Chicago, Illinois, 12–14 April 2011

    Google Scholar 

  43. Farkas HM, Kra I (1991) Riemann surfaces (graduate texts in mathematics). Springer, Berlin

    Google Scholar 

  44. Papadopoulos A (2007) Handbook of Teichmüller theory. European Mathematical Society

    Google Scholar 

  45. Ahlfors L (1966) Lectures in quasiconformal mappings. Van Nostrand Reinhold, New York

    Google Scholar 

  46. Schoen R, Yau S-T (1994) Lectures on differential geometry. International Press of Boston, Boston

    Google Scholar 

  47. Chow B (1991) The Ricci flow on the 2-sphere. J Different Geom 33(2):325–334

    Google Scholar 

  48. Bitter I, Kaufman AE, Sato M (2001) Penalized-distance volumetric skeleton algorithm. IEEE Trans Visualiz Comput Graph 7(3):195–206

    Article  Google Scholar 

  49. Chowdhury AS, Yao J, Vanuitert R, Linguraru M, Summers R (2008) Detection of anatomical landmarks in human colon from computed tomographic colonography images. In: Proceedings of the 19th international conference on pattern recognition (ICPR), IEEE CS Press, pp 1–4

    Google Scholar 

  50. Lamy J, Summers RM (2007) Teniae coli detection from colon surface: Extraction of anatomical markers for virtual colonoscopy. In: Proceedings of the third annual symposium on visual computing, Springer, pp 199–207

    Google Scholar 

  51. Wang Z, Liang Z, Li L, Li B, Eremina D, Lu H (2006) An improved electronic colon cleansing method for detection of colonic polyps by virtual colonoscopy. IEEE Trans Biomed Eng 53(8):1635–1646

    Article  PubMed  Google Scholar 

  52. Gibson SFF (1998) Constrained elastic surface nets: Generating smooth surfaces from binary segmented data. In: Proceedings of MICCAI, Springer, pp 888–898

    Google Scholar 

  53. Li P, Napel S, Acar B, Paik DS, Jeffrey Jr RB Beaulieu CF (2004) Registration of central paths and colonic polyps between supine and prone scans in computed tomography colonography: Pilot study. Med Phys 31(10):2912–2923

    Article  PubMed  Google Scholar 

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Author information

Authors and Affiliations

  1. Florida International University, 11200 SW 8th St, Miami, FL, 33199, USA

    Wei Zeng

  2. Stony Brook University, 100 Nicolls Rd, Stony Brook, NY, 11790, USA

    Rui Shi, Zhengyu Su & David Xianfeng Gu

Authors
  1. Wei Zeng
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  2. Rui Shi
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  3. Zhengyu Su
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  4. David Xianfeng Gu
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Correspondence to Wei Zeng .

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Editors and Affiliations

  1. Department of Bioengineering, University of Louisville, Louisville, Kentucky, USA

    Ayman S. El-Baz

  2. University of Cagliari, Cagliari, Italy

    Luca Saba

  3. Biomedical Technologies, Inc Idaho State University (Affiliated), Roseville, California, USA

    Jasjit Suri

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Zeng, W., Shi, R., Su, Z., Gu, D.X. (2014). Colon Surface Registration Using Ricci Flow. In: El-Baz, A., Saba, L., Suri, J. (eds) Abdomen and Thoracic Imaging. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-8498-1_15

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  • DOI: https://doi.org/10.1007/978-1-4614-8498-1_15

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  • Online ISBN: 978-1-4614-8498-1

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