Skip to main content
SpringerLink
Log in

Neighborhood Filters and the Recovery of 3D Information

  • Living reference work entry
  • First Online:
Book cover Handbook of Mathematical Methods in Imaging

  • 472 Accesses

Abstract

Following their success in image processing (see Chapter Local Smoothing Neighborhood Filters), neighborhood filters have been extended to 3D surface processing. This adaptation is not straightforward. It has led to several variants for surfaces depending on whether the surface is defined as a mesh, or as a raw data point set. The image gray level in the bilateral similarity measure is replaced by a geometric information such as the normal or the curvature. The first section of this chapter reviews the variants of 3D mesh bilateral filters and compares them to the simplest possible isotropic filter, the mean curvature motion.In a second part, this chapter reviews applications of the bilateral filter to a data composed of a sparse depth map (or of depth cues) and of the image on which they have been computed. Such sparse depth cues can be obtained by stereovision or by psychophysical techniques. The underlying assumption to these applications is that pixels with similar intensity around a region are likely to have similar depths. Therefore, when diffusing depth information with a bilateral filter based on locality and color similarity, the discontinuities in depth are assured to be consistent with the color discontinuities, which is generally a desirable property. In the reviewed applications, this ends up with the reconstruction of a dense perceptual depth map from the joint data of an image and of depth cues.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Adams, A., Gelfand, N., Dolson, J., Levoy, M.: Gaussian kd-trees for fast high-dimensional filtering. ACM Trans. Graph. 28(3), 1–12 (2009)

    Article  Google Scholar 

  2. Ansar, A., Castano, A., Matthies, L.: Enhanced real-time stereo using bilateral filtering. In: Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium (3DPVT ’04), Washington, DC, pp. 455–462. IEEE Computer Society (2004)

    Google Scholar 

  3. Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4(2), 490–530 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Buades, T., Coll, B., Morel, J.-M.: Neighborhood filters and pde’s. Numerische Mathematik 105(1), 11–34 (2006)

    Article  MathSciNet  Google Scholar 

  5. Calderero, F., Caselles, V.: Recovering relative depth from low-level features without explicit t-junction detection and interpretation. Int. J. Comput. Vis. 104(1), 38–68 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Choudhury, P., Tumblin, J.: The trilateral filter for high contrast images and meshes. In: ACM SIGGRAPH 2005 Courses (SIGGRAPH ’05), Los Angeles, p. 5. ACM, New York (2005)

    Google Scholar 

  7. Delage, E., Lee, H., Ng, Y.: A dynamic bayesian network model for autonomous 3d reconstruction from a single indoor image. In: International Conference on Computer Vision and Pattern Recognition (CVPR), New York, pp. 1–8 (2006)

    Google Scholar 

  8. Delon, J., Rougé, B.: Small baseline stereovision. J. Math. Imaging Vis. 28(3), 209–223 (2007)

    Article  Google Scholar 

  9. Digne, J., Morel, J.-M., Mehdi-Souzani, C., Lartigue, C.: Scale space meshing of raw data point sets. Comput. Graph. Forum, 30(6), 1630–1642 (2011)

    Article  Google Scholar 

  10. Dimiccoli, M.: Monocular depth estimation for image segmentation and filtering. PhD thesis, Technical University of Catalonia (UPC) (2009)

    Google Scholar 

  11. Dimiccoli, M., Morel, J.M., Salembier, P.: Monocular depth by nonlinear diffusion. In: Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP), Bhubaneswar, Dec 2008

    Google Scholar 

  12. Dunn, J.C.: A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters. J. Cybern. 3(3), 32–57 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  13. Facciolo, G., Caselles, V.: Geodesic neighborhoods for piecewise affine interpolation of sparse data. In: International Conference on Image Processing, Cairo (2009)

    Google Scholar 

  14. Facciolo, G., Lecumberry, F., Almansa, A., Pardo, A., Caselles, V., Rougé, B.: Constrained anisotropic diffusion and some applications. In: British Machine Vision Conference, Edinburgh (2006)

    Google Scholar 

  15. Fleishman, S., Drori, I., Cohen-Or, D.: Bilateral mesh denoising. ACM Trans. Graph. 22(3), 950–953 (2003)

    Article  Google Scholar 

  16. Gamble, E., Poggio, T.: Visual integration and detection of discontinuities: the key role of intensitiy edges. Technical report 970, MIT AI Lab Memo (1987)

    Google Scholar 

  17. Gehrig, S.K., Franke, U.: Improving stereo sub-pixel accuracy for long range stereo. In: Proceedings of the 11th International Journal of Computer Vision, pp. 1–7 (2007)

    Google Scholar 

  18. Hoiem, D., Stein, A.N., Efros, A.A., Hebert, M.: Recovering occlusion boundaries from a single image. In: Proceedings of the International Conference on Computer Vision (ICCV), Rio de Janeiro, Brazil, pp. 1–8 (2007)

    Google Scholar 

  19. Hou, Q., Bai, L., Wang, Y.: Mesh smoothing via adaptive bilateral filtering. In: Springer (ed.) Computational Science – ICCS 2005, Atlanta, pp. 273–280. Springer (2005)

    Google Scholar 

  20. Jones, T.R., Durand, F., Desbrun, M.: Non-iterative, feature-preserving mesh smoothing. In: ACM SIGGRAPH 2003 Papers (SIGGRAPH ’03), San Diego, pp. 943–949. ACM, New York (2003)

    Google Scholar 

  21. Jones, T.R., Durand, F., Zwicker, M.: Normal improvement for point rendering. IEEE Comput. Graph. Appl. 24(4), 53–56 (2004)

    Article  Google Scholar 

  22. Kellman, P.J., Shipley, T.F.: Visual interpolation in object perception. Curr. Dir. Psychol. Sci. 1(6), 193–199 (1991)

    Article  Google Scholar 

  23. Koller, D., Trimble, J., Najbjerg, T., Gelfand, N., Levoy, M.: Fragments of the city: Stanford’s digital forma urbis romae project. In: Proceedings of the Third Williams Symposium on Classical Architecture, Rome. Journal of Roman Archaeology Supplementary, vol. 61, pp. 237–252 (2006)

    Google Scholar 

  24. Kopf, J., Cohen, M., Lischinski, D., Uyttendaele, M.: Joint bilateral upsampling. ACM Trans. Graph. 25(3), 38–68 (2007)

    Google Scholar 

  25. Lafarge, F., Descombes, X., Zerubia, J., Pierrot-Deseilligny, M.: Automatic building extraction from dems using an object approach and application to the 3d-city modeling. J. Photogramm. Remote Sens. 63(3), 365–381 (2008)

    Article  Google Scholar 

  26. Lee, J.-S.: Digital image smoothing and the sigma filter. Comput. Vis. Graph. Image Process. 24(2), 255–269 (1983)

    Article  Google Scholar 

  27. Liu, Y.-S., Yu, P.-Q., Yong, J.-H., Zhang, H., Sun, J.-G.: Bilateral filter for meshes using new predictor. In: Springer (ed.) Computational and Information Science. Lecture Notes in Computer Science, vol. 3314/2005, pp. 1093–1099. Springer, Heidelberg (2005)

    Google Scholar 

  28. Mattoccia, S., Giardino, S., Gambin, A.: Accurate and efficient cost aggregation strategy for stereo correspondence based on approximated joint bilateral filtering. In: Asian Conference on Computer Vision (ACCV09), Xi’an (2009)

    Google Scholar 

  29. Metzger, W.: Gesetze des Sehens. Waldemar, Kramer (1975)

    Google Scholar 

  30. Miropolsky, A., Fischer, A.: Reconstruction with 3d geometric bilateral filter. In: Proceedings of the Ninth ACM Symposium on Solid Modeling and Applications (SM ’04), Genoa, pp. 225–229. Eurographics Association, Aire-la-Ville (2004)

    Google Scholar 

  31. Ohtake, Y., Belyaev, A.G., Seidel, H.-P.: Mesh smoothing by adaptive and anisotropic Gaussian filter applied to mesh normals. In: VMV, Erlangen, pp. 203–210 (2002)

    Google Scholar 

  32. Paris, S., Durand, F.: A fast approximation of the bilateral filter using a signal processing approach. Int. J. Comput. Vis. 81(1), 24–52 (2009)

    Article  Google Scholar 

  33. Paris, S., Kornprobst, P., Tumblin, J., Durand, F.: Bilateral Filtering: Theory and Applications. Found. Trends Comput. Graph. Vis. 4(1), 1–73 (2008). Hanover (2009)

    Google Scholar 

  34. Rother, D., Sapiro, G.: Seeing 3d objects in a single 2D image. In: 2009 IEEE 12th International Conference on Computer Vision (ICCV), Kyoto, pp. 1819–1826 (2009)

    Google Scholar 

  35. Sabater, N.: Reliability and accuracy in stereovision. Application to aerial and satellite high resolution image. PhD thesis, ENS Cachan (2009)

    Google Scholar 

  36. Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. Int. J. Comput. Vis. 47(1–3), 7–42 (2002)

    Article  MATH  Google Scholar 

  37. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proceedings of the Sixth International Conference on Computer Vision (ICCV ’98), Bombay, p. 839. IEEE Computer Society, Washington, DC (1998)

    Google Scholar 

  38. Wang, C.: Bilateral recovering of sharp edges on feature-insensitive sampled meshes. IEEE Trans. Vis. Comput. Graph. 12(4), 629–639 (2006)

    Article  Google Scholar 

  39. Wang, L., Liao, M., Gong, M., Yang, R., Nistér, D.: High-quality real-time stereo using adaptive cost aggregation and dynamic programming. In: Third International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), Chapel Hill (2006)

    Google Scholar 

  40. Wang, L., Yuan, B., Chen, J.: Robust fuzzy c-means and bilateral point clouds denoising. In: 2006 8th International Conference on Signal Processing, Beijing, vol. 2, pp. 16–20 (2006)

    Google Scholar 

  41. Wang, R.-F., Zhang, S.-Y., Zhang, Y., Ye, X.-Z.: Similarity-based denoising of point-sampled surfaces. J. Zhejiang Univ. 9(6), 807–815 (2008)

    Article  MATH  Google Scholar 

  42. Yang, Q., Wang, L., Yang, R., Stewénius, H., Nistér, D.: Stereo matching with color-weighted correlation, hierarchical belief propagation and occlusion handling. IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 1–13 (2006)

    Google Scholar 

  43. Yang, Q., Yang, R., Davis, J., Nistér, D.: Spatial-depth super resolution for range images. In: International Conference on Computer Vision and Pattern Recognition (CVPR), Minneapolis (2007)

    Google Scholar 

  44. Yaroslavsky, L.P.: Digital Picture Processing. An Introduction. Springer Series in Information Sciences, vol. 9 . Springer, Berlin/Heidelberg (1985)

    Google Scholar 

  45. Yin, J., Cooperstock, J.R.: Improving depth maps by nonlinear diffusion. In: Proceedings of 12th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), Plzen-Bory, pp. 1–8 (2004)

    Google Scholar 

  46. Yoon, K.-J., Kweon, S.: Adaptive support-weight approach for correspondence search. IEEE Trans. Pattern Anal. Mach. Intell. 28(4), 650–656 (2006)

    Article  Google Scholar 

  47. Yoshizawa, S., Belyaev, A., Seidel, H.-P.: Smoothing by example: mesh denoising by averaging with similarity-based weights. In: Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006 (SMI’06), Matsushima, p. 9. IEEE Computer Society, Washington, DC (2006)

    Google Scholar 

Download references

Acknowledgements

The David raw point set is courtesy of the Digital Michelangelo Project, Stanford University. Fragment “31u” is courtesy of the Stanford Forma Urbis Romae Project, Stanford University and the Sovraintendenza of Rome. The Screw Nut point set is provided by the AIM@SHAPE repository and is courtesy of Laurent Saboret, INRIA. Research is partially financed by Institut Farman, ENS Cachan, the Centre National d’Etudes Spatiales (MISS Project), the European Research Council (advanced grant Twelve Labours), and the Office of Naval research (grant N00014-97-1-0839).

Author information

Authors and Affiliations

  1. LIRIS, Centre National de la Recherche Scientifique (CNRS), Lyon, France

    Julie Digne

  2. École normale supérieure de Cachan, Cachan, France

    Julie Digne

  3. Image Processing Group, Pompeu Fabra University (UPF), Barcelona, Spain

    Mariella Dimiccoli

  4. CMLA, École normale supérieure de Cachan, Cachan, France

    Neus Sabater

  5. Department of Signal and Communication, Universitat Politechnica de Catalunya, Barcelona, Spain

    Philippe Salembier

Authors
  1. Julie Digne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mariella Dimiccoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Neus Sabater
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Philippe Salembier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julie Digne .

Editor information

Editors and Affiliations

  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Digne, J., Dimiccoli, M., Sabater, N., Salembier, P. (2014). Neighborhood Filters and the Recovery of 3D Information. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27795-5_27-5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27795-5_27-5

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-3-642-27795-5

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation