Fast Multiscale Operator Development for Hexagonal Images

  • Bryan Gardiner
  • Sonya Coleman
  • Bryan Scotney
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5748)

Abstract

For many years the concept of using hexagonal pixels for image capture has been investigated, and several advantages of such an approach have been highlighted. Recently there has been a renewed interested in using hexagonal pixel based images for various image processing tasks. Therefore, we present a design procedure for scalable hexagonal gradient operators, developed within the finite element framework, for use on hexagonal pixel based images. We highlight the efficiency of our approach, based on computing just one small neighbourhood operator and generating larger scale operators via linear additions of the small operator. We also demonstrate that scaled salient feature maps can be generated from one low level feature map without the need for application of larger operators.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allen, J.D.: Filter Banks for Images on Hexagonal Grid, Signal Solutions (2003)Google Scholar
  2. 2.
    Becker, E.B., Carey, G.F., Oden, J.T.: Finite elements: An Introduction. Prentice Hall, London (1981)MATHGoogle Scholar
  3. 3.
    Coleman, S.A., Scotney, B.W., Herron, M.G.: A Systematic Design Procedure for Scalable Near-Circular Laplacian of Gaussian Operators. In: Proceedings of the International Conference on Pattern Recognition, Cambridge, pp. 700–703 (2004)Google Scholar
  4. 4.
    Davies, E.R.: Circularity - A New Design Principle Underlying the Design of Accurate Edge Orientation Filters. Image and Vision Computing 2(3), 134–142 (1984)CrossRefGoogle Scholar
  5. 5.
    Davies, E.R.: Optimising Computation of Hexagonal Differential Gradient Edge Detector. Elect. Letters 27(17) (1991)Google Scholar
  6. 6.
    Gardiner, B., Coleman, S., Scotney, B.: A Design Procedure for Gradient Operators on Hexagonal Images. In: Irish Machine Vision & Image Processing Conference (IMVIP 2008), pp. 47–54 (2008)Google Scholar
  7. 7.
    Gardiner, B., Coleman, S., Scotney, B.: Multi-Scale Feature Extraction in a Sub-Pixel Virtual Hexagonal Environment. In: Irish Machine Vision & Image Processing Conference (IMVIP 2008), pp. 47–54 (2008)Google Scholar
  8. 8.
    He, X., Jia, W.: Hexagonal Structure for Intelligent Vision. In: Information and Communication Technologies, ICICT, pp. 52–64 (2005)Google Scholar
  9. 9.
    Huang, C.-H., Lin, C.-T.: Bio-Inspired Computer Fovea Model Based on Hexagonal-Type Cellular Neural Network. IEEE Trans Circuits and Systems 54(1), 35–47 (2007)CrossRefGoogle Scholar
  10. 10.
    Jiang, Q.: Orthogonal and Biorthogonal FIR Hexagonal Filter Banks with Sixfold Symmetry. IEEE Transactions on Signal Processing 56(12), 5861–5873 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Knaup, M., Steckmann, S., Bockenbach, O., Kachelrieb, M.: CT Image Reconstruction using Hexagonal Grids. In: Proceedings of IEEE Nuclear Science Symposium Conference Record, pp. 3074–3076 (2007)Google Scholar
  12. 12.
    Lau, D.L., Ulichney, R.: Blue-Noise Halftoning for Hexagonal Grids. IEEE Transaction on Image Processing 15(5), 1270–1284 (2006)CrossRefGoogle Scholar
  13. 13.
    Middleton, L., Sivaswamy, J.: Hexagonal Image Processing; A Practical Approach. Springer, Heidelberg (2005)MATHGoogle Scholar
  14. 14.
    Quijano, H.J., Garrido, L.: Improving Cooperative Robot Exploration Using a Hexagonal World Representation. In: Proceeding of the 4th Congress of Electronics, Robotics and Automotive Mechanics, pp. 450–455 (2007)Google Scholar
  15. 15.
    Scotney, B.W., Coleman, S.A.: Improving Angular Error via Systematically Designed Near-Circular Gaussian-based Feature Extraction Operators. In: Pattern Recognition, vol. 40(5), pp. 1451–1465. Elsevier, Amsterdam (2007)Google Scholar
  16. 16.
    Shimonomura, K., et al.: Neuromorphic binocular vision system for real-time disparity estimation. In: IEEE Int Conf on Robotics and Automation, pp. 4867–4872 (2007)Google Scholar
  17. 17.
    Takami, R., et al.: An Image Pre-processing system Employing Neuromorphic 100 x 100 Pixel Silicon Retina. In: IEEE Int. Symp. Circuits & Systems, vol. 3, pp. 2771–2774 (2005)Google Scholar
  18. 18.
    Vitulli, R.: Aliasing Effects Mitigation by Optimized Sampling Grids and Impact on Image Acquisition Chains. In: Geoscience and Remote Sensing Symposium, pp. 979–981 (2002)Google Scholar
  19. 19.
    Wu, Q., He, X., Hintz, T.: Virtual Spiral Architecture. In: Int. Conf. on Parallel and Distributed Processing Techniques and Applications, pp. 339–405 (2004)Google Scholar
  20. 20.
    Wuthrich, C.A., Stucki, P.: An Algorithmic Comparison Between Square-and Hexagonal-based Grid. In: CVGIP: Graphical Models and Image Processing, vol. 53, pp. 324–339 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Bryan Gardiner
    • 1
  • Sonya Coleman
    • 1
  • Bryan Scotney
    • 2
  1. 1.University of UlsterMageeNorthern Ireland
  2. 2.University of UlsterColeraineNorthern Ireland

Personalised recommendations