Abstract
The 2-dimensional Hilbert scan (HS) is a one-to-one mapping between 2-dimensional (2-D) space and one-dimensional (1-D) space along the 2-D Hilbert curve. Because Hilbert curve can preserve the spatial relationships of the patterns effectively, 2-D HS has been studied in digital image processing actively, such as compressing image data, pattern recognition, clustering an image, etc. However, the existing HS algorithms have some strict restrictions when they are implemented. For example, the most algorithms use recursive function to generate the Hilbert curve, which makes the algorithms complex and takes time to compute the one-to-one correspondence. And some even request the sides of the scanned rectangle region must be a power of two, that limits the application scope of HS greatly. Thus, in order to improve HS to be proper to real-time processing and general application, we proposed a Pseudo-Hilbert scan (PHS) based on the look-up table method for arbitrarily-sized arrays in this paper. Experimental results for both HS and PHS indicate that the proposed generalized Hilbert scan algorithm also reserves the good property of HS that the curve preserves point neighborhoods as much as possible, and gives competitive performance in comparison with Raster scan.
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References
Biswas, S.: Hilbert Scan and Image Compression. In: Proc. of IEEE Int. Conf. on Pattern Recognition, pp. 201–210 (2000)
Moon, B., Jagadish, H.V., Faloutsos, C.: Analysis of the Clustering Properties of the Hilbert Space-Filling Curve. IEEE Trans. Knowledge and Data Engineering 13(1), 124–141 (2001)
Kamata, S., Bandoh, Y., et al.: An Address Generator of a Pseudo-Hilbert Scan in a Rectangle Region. In: Proc. of IEEE Int. Conf. on Image processing, pp. 707–710 (1997)
Kamata, S., Eason, R.O., Bandou, Y.: A New Algorithm for N-Dimensional Hilbert Scanning. IEEE Trans. Image Processing 8(7), 964–973 (1999)
Agui, T., Nagae, T., Nakajima, M.: Generalized Peano scans for arbitrary-sized arrays. IEICE Trans. Info. and Syst. E74(5), 1337–1342 (1991)
Quinqueton, J., Berthod, M.: A locally adaptive Peano scanning algorithm. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3(4), 409–412 (1981)
Hilbert, D.: Uber die stetige Abbildung einer Linie auf ein Flachenstuck. Mathematische Annalen 38, 459–460 (1891)
Melnikov, G., Katsaggelos, A.K.: A Jointly Optimal Fractal/DCT Compression Scheme. IEEE Trans. Multimedia 4(4), 413–422 (2002)
Jagadish, H.V.: Linear Clustering of Objects with Mutiple Atributes. In: Int. Conf. on Management of Data, pp. 332–342 (1990)
Jose, C., Michael, G., Ronald, D., Avelino, G.: Data-Partitioning using the Hilbert Space Filling Curves: Effect on the Speed of Convergence of Fuzzy ARTMAP for Large Database Problems. Neural Networks 18(7), 967–984 (2004)
Tian, L., Kamata, S., Tsuneyoshi, K., Tang, H.J.: A Fast and Accurate Algorithm for Matching Images using Hilbert Scanning Distance with Threshold Elimination Function. IEICE Trans. E89-D(1), 290–297 (2006)
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© 2006 Springer-Verlag Berlin Heidelberg
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Zhang, J., Kamata, Si., Ueshige, Y. (2006). A Pseudo-hilbert Scan Algorithm for Arbitrarily-Sized Rectangle Region. In: Zheng, N., Jiang, X., Lan, X. (eds) Advances in Machine Vision, Image Processing, and Pattern Analysis. IWICPAS 2006. Lecture Notes in Computer Science, vol 4153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821045_31
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DOI: https://doi.org/10.1007/11821045_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37597-5
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