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.
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References
Allen, J.D.: Filter Banks for Images on Hexagonal Grid, Signal Solutions (2003)
Becker, E.B., Carey, G.F., Oden, J.T.: Finite elements: An Introduction. Prentice Hall, London (1981)
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)
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)
Davies, E.R.: Optimising Computation of Hexagonal Differential Gradient Edge Detector. Elect. Letters 27(17) (1991)
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)
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)
He, X., Jia, W.: Hexagonal Structure for Intelligent Vision. In: Information and Communication Technologies, ICICT, pp. 52–64 (2005)
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)
Jiang, Q.: Orthogonal and Biorthogonal FIR Hexagonal Filter Banks with Sixfold Symmetry. IEEE Transactions on Signal Processing 56(12), 5861–5873 (2008)
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)
Lau, D.L., Ulichney, R.: Blue-Noise Halftoning for Hexagonal Grids. IEEE Transaction on Image Processing 15(5), 1270–1284 (2006)
Middleton, L., Sivaswamy, J.: Hexagonal Image Processing; A Practical Approach. Springer, Heidelberg (2005)
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)
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)
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)
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)
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)
Wu, Q., He, X., Hintz, T.: Virtual Spiral Architecture. In: Int. Conf. on Parallel and Distributed Processing Techniques and Applications, pp. 339–405 (2004)
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)
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Gardiner, B., Coleman, S., Scotney, B. (2009). Fast Multiscale Operator Development for Hexagonal Images. In: Denzler, J., Notni, G., Süße, H. (eds) Pattern Recognition. DAGM 2009. Lecture Notes in Computer Science, vol 5748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03798-6_29
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DOI: https://doi.org/10.1007/978-3-642-03798-6_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03797-9
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