Advertisement

Optimal Difference Operator Selection

  • Peter Veelaert
  • Kristof Teelen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

Differential operators are essential in many image processing applications. Previous work has shown how to compute derivatives more accurately by examining the image locally, and by applying a difference operator which is optimal for each pixel neighborhood. The proposed technique avoids the explicit computation of fitting functions, and replaces the function fitting process by a function classification process. This paper introduces a new criterion to select the best function class and the best template size so that the optimal difference operator is applied to a given digitized function. An evaluation of the performance of the selection criterion for the computation of the Laplacian for digitized functions shows better results when compared to our previous method and the widely used Laplacian operator.

References

  1. 1.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 60(2), 91–110 (2004)CrossRefGoogle Scholar
  2. 2.
    Lindeberg, T.: Discrete Derivative Approximations with Scale-Space Properties: A Basis for Low-Level Feature Extraction. J. of Mathematical Imaging and Vision 3, 349–376 (1993)CrossRefGoogle Scholar
  3. 3.
    Lachaud, J.O., Vialard, A., de Vieilleville, F.: Analysis and Comparative Evaluation of Discrete Tangent Estimators. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 240–251. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Gunn, S.: On the discrete representation of the Laplacian of Gaussian. Pattern Recognition 32, 1463–1472 (1999)CrossRefGoogle Scholar
  5. 5.
    Demigny, D., Kamlé, T.: A Discrete Expression of Canny’s Criteria for Step Edge Detector Performances Evaluation. IEEE Trans. Patt. Anal. Mach. Intell. 19, 1199–1211 (1997)CrossRefGoogle Scholar
  6. 6.
    Veelaert, P.: Local feature detection for digital surfaces. In: Proceedings of the SPIE Conference on Vision geometry V, SPIE, vol. 2826, pp. 34–45 (1996)Google Scholar
  7. 7.
    Teelen, K., Veelaert, P.: Improving Difference Operators by Local Feature Detection. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 391–402. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Veelaert, P., Teelen, K.: Feature controlled adaptive difference operators. Discrete Applied Mathematics (preprint, submitted, 2007)Google Scholar
  9. 9.
    Oberst, U.: Multidimensional constant linear systems. Acta Appl. Math. 20, 1–175 (1990)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Oberst, U., Pauer, F.: The Constructive Solution of Linear Systems of Partial Difference and Differential Equations with Constant Coefficients. Multidim. Systems and Signal Processing 12, 253–308 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Gerdt, V., Blinkov, Y., Mozzhilkin, V.: Groebner Bases and Generation of Difference Schemes for Partial Differential Equations. Symmetry, Integrability and Geometry: Methods and Applications 2 (2006) (Paper 051, arXiv:math.RA/0605334)Google Scholar
  12. 12.
    Stoer, J., Witzgall, C.: Convexity and Optimization in Finite Dimensions I. Springer, Berlin (1970)Google Scholar
  13. 13.
    Cox, D., Little, J., O’Shea, D.: Ideals, Varieties and Algorithms: an Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, New York (1992)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Peter Veelaert
    • 1
  • Kristof Teelen
    • 1
  1. 1.University College Ghent, Engineering Sciences - Ghent University AssociationGhentBelgium

Personalised recommendations