Skip to main content
Log in

3D reconstruction from 2D images with hierarchical continuous simplices

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

This paper presents an effective framework for the reconstruction of volumetric data from a sequence of 2D images. The 2D images are first aligned to generate an initial 3D volume, followed by the creation of a tetrahedral domain using the Carver algorithm. The resulting tetrahedralization preserves both the geometry and topology of the original dataset. Then a solid model is reconstructed using simplex splines with fitting and faring procedures. The reconstructed heterogenous volumetric model can be quantitatively analyzed and easily visualized. Our experiments demonstrated that our approach can achieve high accuracy in the data reconstruction. The novel techniques and algorithms proposed in this paper can be applied to reconstruct a heterogeneous solid model with complex geometry and topology from other visual data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bardinet, E., Ourselin, S., Malandain, G., Tande, D., Parain, K., Ayache, N., Yelnik, J.: Three dimensional functional cartography of the human basal ganglia by registration of optical and histological serial sections. In: Proceedings of IEEE International Symposium on Biomedical Imaging, pp. 329–332 (2002)

  2. Chan, H., Chung, A.: Efficient 3D–3D vascular registration based on multiple orthogonal 2D projections. In: Second International Workshop on Biomedical Image Registration(WBIR 2003), vol. 2717, pp. 301–310. Springer (2003)

  3. Choi, S., Lee, J., Kim, J., Kim, M.: Volumetric object reconstruction using the 3D-MRF model-based segmentation. IEEE Trans. Med. Imaging 16(6), 887–892 (1997)

    Article  Google Scholar 

  4. Cignoni, P., Constanza, D., Montani, C., Rocchini, C., Scopigno, R.: Simplification of tetrahedral meshes with accurate error evaluation. In: Proceedings of the Conference on Visualization ’00, pp. 85–92. IEEE Computer Society (2000)

  5. Cignoni, P., De Floriani, L., Montani, C., Puppo, E., Scopigno, R.: Multiresolution modeling and visualization of volume data based on simplicial complexes. In: Proceedings of the 1994 Symposium on Volume Visualization, pp. 19–26. IEEE Computer Society (1994)

  6. Dahmen, W., Micchelli, C.A., Seidel, H.: Blossoming begets B-spline bases built better by b-patches. Math. Comput. 59(199), 97–115 (1992)

    Article  MATH  Google Scholar 

  7. Edelsbrunner, H.: Geometry and Topology for Mesh Generation. P.G. Ciarlet, A. Iserles, R.V. Kohn, M.H. Wright, eds. Cambridge University Press (2001)

  8. Greiner, G., Seidel, H.: Modeling with triangular B-splines. IEEE Comput. Graph. Appl. 14(2), 56–60 (1994)

    Article  Google Scholar 

  9. Hua, J., He, Y., Qin, H.: Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines. In: Proceedings of the Ninth ACM Symposium on Solid Modeling and Applications, pp. 47–58 (2004)

  10. Hua, J., He, Y., Qin, H.: Trivariate simplex splines for inhomogeneous solid modeling in engineering design. ASME Trans. J. Comput. Information Sci. Eng. 5(2), 149–157 (2005)

    Article  Google Scholar 

  11. Hua, J., Qin, H.: Haptics-based volumetric modeling using dynamic spline-based implicit functions. In: Proceedings of IEEE Symposium on Volume Visualization and Graphics, pp. 55–64 (2002)

  12. Hua, J., Qin, H.: Haptics-based dynamic implicit solid modeling. IEEE Trans. Vis. Comput. Graph. 10(5), 574–586 (2004)

    Article  Google Scholar 

  13. Lee, S., Bajcsy, P.: Feature based registration of fluorescent LSCM imagery using region centroids. In: Proceedings of SPIE International Symposium in Medical Imaging, vol. 5747, pp. 170–181 (2005)

  14. Lee, S., Bajcsy, P.: Three-dimensional volume reconstruction based on trajectory fusion from confocal laser scanning microscope images. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition(CVPR 06), vol. 2, pp. 2221–2228 (2006)

  15. Looney, R., Boyd, A., Totterman, S., Seo, G., Tamez-Pena, J., Campbell, D., Novotny, L., Clcott, C., Martell, J., Hayes, F., O’Keefe, R., Schwarz, E.: Volumetric computerized tomography as a measurement of periprosthetic acetabular osteolysis and its correlation with wear. Arthritis Res. 4(1), 59–63 (2002)

    Article  Google Scholar 

  16. Martin, W., Cohen, E.: Representation and extraction of volumetric attributes using trivariate splines: A mathematical framework. In: Proceedings of the 7th ACM Symposium on Solid Modeling and Applications, pp. 234–240 (2001)

  17. Pauly, M., Gross, M., Kobbelt, L.: Efficient simplification of point-sampled surfaces. In: IEEE Visualization 02 Proceedings pp. 163–170 (2002)

  18. Pauly, M., Keiser, R., Kobbelt, L., Gross, M.: Shape modeling with point-sampled geometry. In: SIGGRAPH 03 Proceedings pp. 641–650 (2003)

  19. Pfeifle, R., Seidel, H.: Fitting triangular B-splines to functional scattered data. In: Proceedings of Graphics Interface ’95, pp. 80–88 (1995)

  20. Raviv, A., Elber, G.: Three dimensional freeform sculpting via zero sets of scalar trivariate functions. In: Proceedings of 5th ACM Symposium on Solid Modeling and Applications, pp. 246–257 (1999)

  21. Rosa, R., Chirco, P., Massari, R.: Reconstruction corrections in advanced neutron tomography algorithms. IEEE Trans. Nucl. Sci. 52(1), 400–403 (2005)

    Article  Google Scholar 

  22. Roxborough, T., Nielson, G.M.: Tetrahedron based, least squares, progressive volume models with application to freehand ultrasound data. In: Proceedings of the conference on Visualization’00, pp. 93–100 (2000)

  23. Schmitt, B., Pasko, A., Schlick, C.: Constructive modeling of FRep solids using spline volumes. In: Proceedings of the 6th ACM Symposium on Solid Modeling and Applications, pp. 321–322 (2001)

  24. Tan, Y., Hua, J., Dong, M.: Feature curve-guided volume reconstruction from 2D images. In: Proceedings of IEEE International Symposium on Biomedical Imaging (2007)

  25. Trotts, I., Hamann, B., Joy, K.: Simplification of tetrahedral meshes with error bounds. IEEE Trans. Vis. Comput. Graph. 5(3), 224–237 (1999)

    Article  Google Scholar 

  26. Yao, J., Taylor, R.: Tetrahedral mesh modeling of density data for anatomical atlases and intensity-based registration. In: Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 531–540 (2000) LSCM imagery

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jing Hua.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tan, Y., Hua, J. & Dong, M. 3D reconstruction from 2D images with hierarchical continuous simplices. Visual Comput 23, 905–914 (2007). https://doi.org/10.1007/s00371-007-0157-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-007-0157-0

Keywords

Navigation