Abstract
This paper presents a method to decompose a field of surface normals (needle-map). A diffusion process is used to model the flow of height information induced by a field of surface normals. The diffusion kernel can be decomposed into eigenmodes, each corresponding to approximately independent modes of variation of the flow. The surface normals can then be diffused using a modified kernel with the same eigenmodes but different coefficients. When used as part of a surface integration process, this procedure allows choosing the trade-off between local and global influence of each eigenmode in the modified field of surface normals. This graph-spectral method is illustrated with surface normals extracted from a face. Experiments are carried with local affinity functions that convey both the intrinsic and extrinsic geometry of the surface, and an information-theoretic definition of affinity.
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
Agrawal, A., Chellappa, R.: An algebraic approach to surface reconstruction from gradient fields. In: Proceedings of ICCV 2005, pp. 23–114 (2005)
Chung, F.R.K.: Spectral Graph Theory. AMS (1997)
Do Carmo, M.: Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs (1976)
Fraile, R., Hancock, E.R.: Combinatorial surface integration. In: International Conference on Pattern Recognition, vol. I, pp. 59–62 (2006)
Frankot, R.T., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. IEEE Trans. Pattern Analysis and Machine Intelligence 10(4), 439–451 (1988)
Gibbons, A.: Algorithmic Graph Theory. Cambridge University Press, Cambridge (1985)
Kondor, R.I., Lafferty, J.: Diffusion kernels on graphs and other discrete structures. In: ICML 2002 (2002)
Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)
Rissanen, J.: A universal prior for integers and estimation by minimum description length. Annals of Statistics 11(2), 416–431 (1983)
Robles-Kelly, A., Hancock, E.R.: A graph-spectral approach to shape-from-shading. IEEE Transactions on Image Processing 13(7), 912–926 (2004)
Robles-Kelly, A.: Graph-spectral methods for Computer Vision. PhD thesis, The University of York (September 2003)
Sarkar, S., Boyer, K.L.: Quantitative measures of change based on feature organization: Eigenvalues and eigenvectors. Computer Vision and Image Understanding 71(1), 110–136 (1998)
Sclaroff, S., Pentland, A.: Modal matching for correspondence and recognition. IEEE PAMI 17(6), 545–561 (1995)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)
Smith, W.A.P., Hancock, E.R.: Recovering facial shape using a statistical model of surface normal direction. IEEE Trans. Pattern Analysis and Machine Intelligence 28(12), 1914–1930 (2006)
Smith, W.A.P., Hancock, E.R.: Face recognition using 2.5D shape information. In: CVPR, pp. 1407–1414. IEEE Computer Society, Los Alamitos (2006)
Widder, D.V.: The Heat Equation. Academic Press, London (1975)
Worthington, P.L., Hancock, E.R.: New constraints on data-closeness and needle map consistency for shape-from-shading. PAMI 21(12), 1250–1267 (1999)
Zhang, F., Qiu, H., Hancock, E.R.: Evolving spanning trees using the heat equation. In: Gagalowicz, A., Philips, W. (eds.) CAIP 2005. LNCS, vol. 3691, pp. 272–279. Springer, Heidelberg (2005)
Zhang, R., Tsai, P.-S., Cryer, J.E., Shah, M.: Shape-from-shading: a survey. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(8), 690–706 (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Fraile, R., Hancock, E.R. (2007). Spectral Modes of Facial Needle-Maps. In: MartÃ, J., BenedÃ, J.M., Mendonça, A.M., Serrat, J. (eds) Pattern Recognition and Image Analysis. IbPRIA 2007. Lecture Notes in Computer Science, vol 4477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72847-4_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-72847-4_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72846-7
Online ISBN: 978-3-540-72847-4
eBook Packages: Computer ScienceComputer Science (R0)