Abstract
This paper analyzes four explicit, two implicit and four semi-implicit finite difference algorithms for the linear shape from shading problem. Comparisons of accuracy, solvability, stability and convergence of these schemes indicate that the weighted semi-implicit scheme and the box scheme are better than the other ones because they can be calculated more easily, they are more accurate, faster in convergence and unconditionally stable.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Horn, B.K.P.: Robot Vision. McGraw-Hill, New York, Cambridge M.A. (1986)
Horn, B.K.P., Brooks, M.J.: The variational approach to shape from shading. Computer Vision, Graphics, and Image Processing 33 (1986) 174–208
Horn, B.K.P.: Height and gradient from shading. International Journal of Computer Vision 5 (1990) 37–75
Kimmel, R., Bruckstein, A.M.: Tracking level sets by level sets: a method for solving the shape from shading problem. Computer Vision and Image Understanding 62 (1995) 47–58
Klette, R., K. Schlüns, Koschan, A.: Computer Vision-Three-dimensional Data from Images. Springer, Singapore (1998)
Kozera, R.: Existence and uniqueness on photometric stereo. Applied Mathematics and Computation 44 (1991) 1–104
Kozera, R., Klette, R.: Finite difference based algorithms in linear shape from shading. Machine Graphics and Vision, 2 (1997) 157–201
Kozera, R., Klette, R.: Criteria for differential equations in computer vision. CITR-TR-27, The University of Auckland, Tamaki Campus (Aug 1998)
Lee, K.M., Kuo, C.J.: Shape from shading with a linear triangular element surface model. IEEE Transactions on Pattern Analysis and Machine Intelligence 15 (1993) 815–822
Oliensis, J.: Uniqueness in shape from shading. International Journal of Computer Vision 6 (1991) 75–104
Pentland, A.P.: Linear shape from shading. International Journal of Computer Vision 4 (1991) 153–162
Strikwerda, J.C.: Finite Difference Schemes and Partial Differential Equations. Wordsworth & Brooks/Cole Advanced Books & Software. Pacific Grove, California (1989)
Tsai, P.S., Shah, M.: Shape from shading using linear approximation. Image and Vision Computing 12 (1994) 487–498
Ulich, G.: Provably convergent methods for the linear and nonlinear shape from shading problem. Journal of Mathematical Imaging and Vision 9 (1998) 69–82
T. Wei and R. Klette: Analysis of finite difference algorithms for linear shape from shading. CITR-TR-70, Tamaki Campus, The University of Auckland (Oct 2000)
Zhang, R., Tsai, P.S., Cryer, J.E., Shah, M.: Shape from shading: a survey. IEEE Trans. Pattern Analysis and Machine Intelligence 21 (1999) 690–706
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wei, T., Klette, R. (2001). Theoretical Analysis of Finite Difference Algorithms for Linear Shape from Shading. In: Skarbek, W. (eds) Computer Analysis of Images and Patterns. CAIP 2001. Lecture Notes in Computer Science, vol 2124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44692-3_77
Download citation
DOI: https://doi.org/10.1007/3-540-44692-3_77
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42513-7
Online ISBN: 978-3-540-44692-7
eBook Packages: Springer Book Archive