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Issue No.06 - June (2010 vol.32)
pp: 961-973
Tetsuo Shima , Tokyo Institute of Technology, Tokyo
Suguru Saito , Tokyo Institute of Technology, Tokyo
Masayuki Nakajima , Tokyo Institute of Technology, Tokyo
Digital two-dimensional images are usually sampled on square lattices, while the receptors of the human eye are following a hexagonal structure. It is the main motivation for adopting hexagonal lattices. The fundamental operation in many image processing algorithms is to extract the gradient information. As such, various gradient operators have been proposed for square lattices and have been thoroughly optimized. Accurate gradient operators for hexagonal lattices have, however, not been researched well enough, while the distance between neighbor pixels is constant. We therefore derive consistent gradient operators on hexagonal lattices and compare them with the existing optimized filters on square lattices. The results show that the derived filters on hexagonal lattices achieve a better signal-to-noise ratio than those on square lattices. Results on artificial images also show that the derived filters on hexagonal lattices outperform the square ones with respect to accuracy of gradient intensity and orientation detection.
Image processing, hexagonal lattice, consistent gradient operator, gradient intensity, orientation.
Tetsuo Shima, Suguru Saito, Masayuki Nakajima, "Design and Evaluation of More Accurate Gradient Operators on Hexagonal Lattices", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.32, no. 6, pp. 961-973, June 2010, doi:10.1109/TPAMI.2009.99
[1] J.C. Russ, The Image Processing Handbook, third ed., pp. 253-268. CRC Press and IEEE Press, 1998.
[2] R.A. Kirsch, "Computer Determination of the Constituent Structure of Biological Images," Computers and Biomedical Research, vol. 4, pp. 315-328, 1971.
[3] W. Frei and C.-C. Chen, "Fast Boundary Detection: A Generalization and a New Algorithm," IEEE Trans. Computers, vol. 26, no. 10, pp. 988-998, Oct. 1977.
[4] S. Ando, "Consistent Gradient Operators," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 3, pp. 252-265, Mar. 2000.
[5] I. Her, "Geometric Transformations on the Hexagonal Grid," IEEE Trans. Image Processing, vol. 4, no. 9, pp. 1213-1222, Sept. 1995.
[6] L. Middleton, "The Co-Occurrence Matrix in Square and Hexagonal Lattices," Proc. Int'l Conf. Control, Automation, Robotics, and Vision, vol. 1, pp. 90-95, Dec. 2002.
[7] R.M. Mersereau, "The Processing of Hexagonally Sampled Two-Dimensional Signals," Proc. IEEE, vol. 67, no. 6, pp. 930-953, June 1979.
[8] A.M. Grigoryan, "Efficient Algorithms for Computing the 2-D Hexagonal Fourier Transforms," IEEE Trans. Signal Processing, vol. 50, no. 6, pp. 1438-1448, June 2002.
[9] Q. Jiang, "FIR Filter Banks for Hexagonal Data Processing," IEEE Trans. Image Processing, vol. 17, no. 9, pp. 1512-1521, Sept. 2008.
[10] D.V.D. Ville, T. Blu, M. Unser, W. Philips, I. Lemahieu, and R.V. de Walle, "Hex-Splines: A Novel Spline Family for Hexagonal Lattices," IEEE Trans. Image Processing, vol. 13, no. 6, pp. 758-772, June 2004.
[11] R. Staunton, "A One Pass Parallel Hexagonal Thinning Algorithm," Proc. Seventh Int'l Conf. Image Processing and Its Applications, vol. 2, pp. 841-845, July 1999.
[12] L. Middleton and J. Sivaswamy, Hexagonal Image Processing: A Practical Approach. Springer, 2005.
[13] I. Overington, Computer Vision: A Unified, Biologically-Inspired Approach. Elsevier Science Publishing Co., 1992.
[14] M. Balakrishnan and W.A. Pearlman, "Hexagonal Subband Image Coding with Perceptual Weighting," Optical Eng., vol. 32, no. 7, pp. 1430-1437, July 1993.
[15] J. Thiem and G. Hartmann, "Biology-Inspired Design of Digital Gabor Filters upon a Hexagonal Sampling Scheme," Proc. 15th Int'l Conf. Pattern Recognition, vol. 3, pp. 445-448, Sept. 2000.
[16] S. Chettir, M. Keefe, and J. Zimmerman, "Obtaining Centroids of Digitized Regions Using Square and Hexagonal Tilings for Photosensitive Elements," Proc. SPIE Conf. Optics, Illumination, and Image Sensing for Machine Vision IV, pp. 152-164, 1989.
[17] R.C. Staunton and N. Storey, "Comparison between Square and Hexagonal Sampling Methods for Pipeline Image Processing," Proc. SPIE Conf. Optics, Illumination, and Image Sensing for Machine Vision IV, pp. 142-151, 1989.
[18] Y. Kimuro and T. Nagata, "Image Processing on an Omni-Directional View Using a Spherical Hexagonal Pyramid: Vanishing Points Extraction and Hexagonal Chain Coding," Proc. 1995 IEEE/RSJ Int'l Conf. Intelligent Robots and Systems '95 "Human Robot Interaction and Cooperative Robots," pp. 356-361, Aug. 1995.
[19] M. Tremblay, S. Dallaire, and D. Poussart, "Low Level Segmentation Using cmos Smart Hexagonal Image Sensor," Proc. Computer Architectures for Machine Perception, pp. 21-28, Sept. 1995.
[20] K. Choi, S. Chan, and T. Ng, "A New Fast Motion Estimation Algorithm Using Hexagonal Subsampling Pattern and Multiple Candidates Search," Proc. Int'l Conf. Image Processing, vol. 1, pp. 497-500, Sept. 1996.
[21] E. Dubois, "The Sampling and Reconstruction of Time-Varying Imagery with Application in Video Systems," Proc. IEEE, vol. 73, no. 4, pp. 502-522, Apr. 1985.
[22] R. Ulichney, Digital Halftoning. MIT Press, June 1987.
[23] "Octave,", 2010.
[24] J. Allen, "Perfect Reconstruction Filter Banks for the Hexagon Grid," Proc. Fifth Int'l Conf. Information, Comm. and Signal Processing , pp. 73-76, Dec. 2005.
[25] E. Simoncelli and E. Adelson, "Non-Separable Extensions of Quadrature Mirror Filters to Multiple Dimensions," Proc. IEEE, vol. 78, no. 4, pp. 652-664, Apr. 1990.
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