Abstract
In this paper we show how statistical constraints can be incorporated into the surface integration process. This problem aims to reconstruct the surface height function from a noisy field of surface normals. We propose two methods that employ a statistical model that captures variations in surface height. The first uses a coupled model that captures the variation in a training set of face surfaces in both the surface normal and surface height domain. The second is based on finding the parameters of a surface height model directly from a field of surface normals. We present experiments on ground truth face data and compare the results of the two methods with an existing surface integration technique.
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
Smith, W.A.P., Hancock, E.R.: Recovering facial shape using a statistical model of surface normal direction. IEEE Trans. Pattern Anal. Mach. Intell. 28, 1914–1930 (2006)
Castelán, M., Hancock, E.R.: Acquiring height data from a single image of a face using local shape indicators. Comput. Vis. Image Underst. 103, 64–79 (2006)
Wu, Z., Li, L.: A line integration based method for depth recovery from surface normals. Comput. Vis. Graph. Image Process 43, 53–66 (1988)
Frankot, R.T., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988)
Wei, T., Klette, R.: Height from gradient using surface curvature and area constraints. In: Proc. ICVGIP, pp. 204–210 (2002)
Agrawal, A., Chellappa, R., Raskar, R.: An algebraic approach to surface reconstruction from gradient fields. In: Proc. ICCV 1, 174–181 (2005)
Worthington, P.L., Hancock, E.R.: New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Trans. Pattern Anal. Mach. Intell. 21, 1250–1267 (1999)
Cootes, T.F., Taylor, C.J.: Statistical models of appearance for computer vision. Technical report, Division of Imaging Science and Biomedical Engineering, University of Manchester (2001)
USF HumanID 3D Face Database, Courtesy of Sudeep. Sarkar, University of South Florida, Tampa, FL
Smith, W.A.P., Hancock, E.R.: Face recognition using 2.5d shape information. Proc. CVPR 2, 1407–1414 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Smith, W.A.P., Hancock, E.R. (2007). Statistical Methods for Surface Integration. In: Martin, R., Sabin, M., Winkler, J. (eds) Mathematics of Surfaces XII. Mathematics of Surfaces 2007. Lecture Notes in Computer Science, vol 4647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73843-5_26
Download citation
DOI: https://doi.org/10.1007/978-3-540-73843-5_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73842-8
Online ISBN: 978-3-540-73843-5
eBook Packages: Computer ScienceComputer Science (R0)