“Krawtchouk and Tchebichef´s moments and their applications in digital imagery” (Review)
Keywords:
Digital imagery; orthogonal; Krawtchouk´s polynomials; Tchebichef´s polynomialsAbstract
In this article, there is an overview of Krawtchouk and Tchebichef´s orthogonal discreet polynomials, which have dissimilar on-the-job applications with digital imagery. A brief historic introduction is given, and then, the theory of these polynomials is summarized. Finally, a brief section with some of the most significant applications of these on-the-job polynomials with digital imagery is presented.
Downloads
References
Barmak, S. A. y Jan, F. (2014). Fast computation of Krawtchouk moments. Inform. Sci, vol. 288, pp. 73-86.
Bayraktar, B., Bernas, T., Robinson, J. y Rajwa, B., (2007). A numerical recipe for accurate image reconstruction from discrete orthogonal moments”. Pattern Recognition, vol. 40, pp. 659-669.
Chong, C. y Raveendran, P., (s/a). “On the computational aspects of Zernike moments. Image and Vision Computing”, vol. 25, pp. 967-980.
Chong, C., Raveendran, P. y Mukundan, R., (2003). A comparative analysis of algorithms for fast computation of Zernike moments. Pattern Recognition, vol. 36, pp. 731-742.
Dai, X. B., Shu, H. Z., Luo, L. M., Han G. N. y Coatrieux, J. L., (2010). Reconstruction of tomographic images from limited range projections using discrete Radon transform and Tchebichef moments. Pattern Recognition, vol. 43, pp. 1152-1164.
Elshoura, S. M. y Megherbi, D. B. (2013). A secure high capacity full-gray-scale-level multi-image information hiding and secret image authentication scheme via Tchebichef moments. Signal Processing: Image Communication. http://dx.doi.org/10.1016/j.image.2012.12.005.
Honarvar, B. y Flusser, J., (2014). Fast computation of Krawtchouk moments. Information Sciences, pp. 73-86.
Hu, B. y Liao, S., (2013). Local Feature Extraction Property of Krawtchouk Moment. Lecture Notes on Software Engineering, vol. 1, pp. 356-359.
Prattipati, S., Swamy, M. y Meher, P. K, (2015). A Comparison of Integer Cosine an Tchebichef Transforms for Image Compression Using Variable Quantization. Journal of Signal and Information Processing, vol. 6, pp. 203-216.
See, K. W., Loke, K. S., Lee, P. A. y Loe, K. F., (2007). Image reconstruction using various discrete orthogonal polynomials in comparison with DCT. Appl. Math. Comput, vol. 193, pp. 346-359.
Shu, H., Zhang, H., Chen, B., Haigron, P. y Luo, L. (2010). Fast Computation of Tchebichef Moments for Binary and Grayscale Images. IEEE Trans. Image Process, vol. 19, pp. 3171-3180.
Yap, P., Paramesran, R. y Ong, S. H. (2003). Image Analysis by Krawtchouk Moments. IEEE Trans. Image Process, vol. 12, pp. 1367-1377.
Wee, C., Raveendran, P. y Mukundan, R. (2010). Image quality assessment by discrete orthogonal moments. Pattern Recognition, vol. 43, pp. 4055-4068.
Wang, G. B. y Wang, S. G., (2007). Recursive computation of Tchebichef moment and its inverse transform. Pattern Recognition, vol. 39, pp. 47-56.
Zhu, H., (2007). Image representation using separable two-dimensional continuous and discrete orthogonal moments. Pattern Recognition, vol. 45, (2012), pp. 1540-1558. ISSN: 0305-0548
