MINIMAL DISTORTION MAPPINGS OF SURFACES FOR MEDICAL IMAGES

Eli Appleboim, Emil Saucan, Yehoshua Y. Zeevi

2006

Abstract

In this paper we present a simple method for minimal distortion development of triangulated surfaces for colon mapping and general analysis of medical images. The method is based on classical results of Gehring and Va¨isala¨ regarding the existence of quasi-comformal and quasi-isometric mappings between Riemannian manifolds. Random and curvature based variations of the algorithm are presented. In addition the algorithm enables the user to compute the maximal distortion errors. The algorithm was tested both on synthetic images of the human skull and on real CT images of the human colon.

References

  1. Caraman, P. (1974) n-Dimensional Quasiconformal (QCf) Mappings. Editura Academiei Romaˆne, Bucharest, Abacus Press, Tunbridge Wells Haessner Publishing, Inc., Newfoundland, New Jersey.
  2. Gehring, W. F. and Väisala, J. (1965). The coefficients of quasiconformality. In Acta Math. 114, pp. 1-70.
  3. Gu, X. and Yau, S. T. (2002). Computing Conformal Structure of Surfaces. In Communications In Information and Systems, Vol. 2, No. 2, pp. 121-146.
  4. Gu, X. and Yau, S. T. (2003). Global Conformal Surface Parameterization In Eurographics Symposium on Geometry Processing.
  5. Haker, S. Angenet, S. Tannenbaum, A. Kikinis, R. (2000) Non Distorting Flattening Maps and the 3-D visualization of Colon CT Images. IEEE Transauctions on Medical Imaging, Vol. 19, NO. 7.
  6. Haker, S. Angenet, S. Tannenbaum, A. Kikinis, R. Sapiro, G. Halle, M. (2000) Conformal Surface Parametrization for Texture Mapping. IEEE Transauctions on Visualization and Computer Graphics, Vol. 6, NO. 2.
  7. Hurdal, M. K., Bowers, P. L., Stephenson, K., Sumners, D. W. L., Rehm, K., Schaper. K., Rottenberg, D. A. (1999) Quasi Conformally Flat Mapping the Human Crebellum, In Medical Image Computing and Computer-Assisted Intervention -MICCAI'99, (C. Taylor and A. Colchester. eds), vol. 1679, pp. 279-289. Springer-Verlag, Berlin.
  8. Paik, D., Beaulieu, C., Jeffrey, R., Karadi C., and Napel, S. (1999) Visualizations modes for CT colonography using cylindrical and planar projections. Technical Report, Department of Radiology, Stanford University School of Medicine, Stanford, CA.
  9. Peyé, G. and Cohan, L. (2005) Geodesic Computations for Fast and Accurate Surface Flattening. preprint.
  10. Sheffer, A. de Stuler, E. (2001) Parametrization of Faceted Surfaces for Meshing Using Angle Based Flattening. In Enginneering with Computers, vol. 17, pp. 326- 337.
  11. Sorkine, O., Cohen-Or, Daniel, Goldenthal, R. and Lischinski, D. (2005) Bounded-distorsion Piecewise Mesh Parametrization. preprint.
  12. Väisalä, J. (1971). Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Mathematics 229, Springer-Verlag, Berlin - Heidelberg - New-York.
Download


Paper Citation


in Harvard Style

Appleboim E., Saucan E. and Y. Zeevi Y. (2006). MINIMAL DISTORTION MAPPINGS OF SURFACES FOR MEDICAL IMAGES . In Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, ISBN 972-8865-40-6, pages 422-427. DOI: 10.5220/0001376204220427


in Bibtex Style

@conference{visapp06,
author={Eli Appleboim and Emil Saucan and Yehoshua Y. Zeevi},
title={MINIMAL DISTORTION MAPPINGS OF SURFACES FOR MEDICAL IMAGES},
booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,},
year={2006},
pages={422-427},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001376204220427},
isbn={972-8865-40-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,
TI - MINIMAL DISTORTION MAPPINGS OF SURFACES FOR MEDICAL IMAGES
SN - 972-8865-40-6
AU - Appleboim E.
AU - Saucan E.
AU - Y. Zeevi Y.
PY - 2006
SP - 422
EP - 427
DO - 10.5220/0001376204220427