A fast algorithm for computing moments of gray images based on NAM and extended shading approach

Abstract

Computing moments on images is very important in the fields of image processing and pattern recognition. The non-symmetry and anti-packing model (NAM) is a general pattern representation model that has been developed to help design some efficient image representation methods. In this paper, inspired by the idea of computing moments based on the S-Tree coding (STC) representation and by using the NAM and extended shading (NAMES) approach, we propose a fast algorithm for computing lower order moments based on the NAMES representation, which takes O(N) time where N is the number of NAM blocks. By taking three idiomatic standard gray images ‘Lena’, ‘F16’, and ‘Peppers’ in the field of image processing as typical test objects, and by comparing our proposed algorithm with the conventional algorithm and the popular STC representation algorithm for computing the lower order moments, the theoretical and experimental results presented in this paper show that the average execution time improvement ratios of the proposed NAMES approach over the STC approach, and also the conventional approach are 26.63%, and 82.57% respectively while maintaining the image quality.

Keywords

moment computation / gray image representation / Gouraud shading method / non-symmetry and anti-packing model (NAM) / S-Tree coding (STC)

References

[1] Tanaka Y, Ikehara M, Nguyen T Q. Multiresolution image representation using combined 2-D and 1-D directional filter banks. IEEE Transactions on Image Processing, 2009, 18(2): 269–280

[2] Guo J M, Wu M F. Improved block truncation coding based on the void-and-cluster dithering approach. IEEE Transactions on Image Processing, 2009, 18(1): 211–213

[3] Yang E H, Wang L. Joint optimization of run-length coding, Huffman coding, and quantization table with complete baseline JPEG decoder compatibility. IEEE Transactions on Image Processing, 2009, 18(1): 63–74

[4] Distasi R, Nappi M, Vitulano S. Image compression by B-tree triangular coding. IEEE Transactions on Communications, 1997, 45(9): 1095–1100

[5] Dejonge W, Scheuermann P, Schijf A. S+-Trees: an efficient structure for the representation of large pictures. Computer Vision and Image Understanding, 1994, 59(3): 265–280

[6] Foley J D, Dam A V, Feiner S K, Hughes J F. Computer Graphics, Principle, and Practice. 2nd ed. Reading: Addision-Wesley, 1990

[7] Chung K L, Wu J G. Improved image compression using S-tree and shading approach. IEEE Transactions on Communications, 2000, 48(5): 748–751

[8] Chen C B, Zheng Y P, Sarem M. A novel non-symmetry and anti-packing model for image representation. Chinese Journal of Electronics, 2009, 18(1): 89–94

[9] Zheng Y, Chen C. Study on a new algorithm for gray image representation. Chinese Journal of Computers, 2010, 33(12): 2397–2406

[10] Qiao Y, Wang W, Minematsu N, Liu J, Takeda M, Tang X. A theory of phase singularities for image representation and its applications to object tracking and image matching. IEEE Transactions on Image Processing, 2009, 18(10): 2153–2166

[11] Chung K L, Liu Y W, Yan W M. A hybrid gray image representation using spatial- and DCT-based approach with application to moment computation. Journal of Visual Communication and Image Representation, 2006, 17(6): 1209–1226

[12] Chung K L, Yan W M, Liao Z H. Fast computation of moments on compressed grey images using block representation. Real-Time Imaging, 2002, 8(2): 137–144

[13] Papakostas G A, Boutalis Y S, Karras D A, Mertzios B G. Fast numerically stable computation of orthogonal Fourier-Mellin moments. IET Computer Vision, 2007, 1(1): 11–16

[14] Kotoulas L, Andreadis I. Fast computation of Chebyshev moments. IEEE Transactions on Circuits and Systems for Video Technology, 2006, 16(7): 884–888

[15] Kotoulas L, Andreadis I. Accurate calculation of image moments. IEEE Transactions on Image Processing, 2007, 16(8): 2028–2037

[16] Pei S C, Liou L G. Using moments to acquire the motion parameters of a deformable object without correspondences. Image and Vision Computing, 1994, 12(8): 475–485

[17] Tsai W H. Moment-preserving thresholding: a new approach. Computer Vision Graphics and Image Processing, 1985, 29(3): 377–393

[18] Pei S C, Horng J H. A moment-based approach for deskewing rotationally symmetric shapes. IEEE Transactions on Image Processing, 1999, 8(12): 1831–1834

[19] Lin H, Si J, Abousleman G P. Orthogonal rotation-invariant moments for digital image processing. IEEE Transactions on Image Processing, 2008, 17(3): 272–282

[20] Chung K, Chen P. An efficient algorithm for computing moments on a block representation of a grey-scale image. Pattern Recognition, 2005, 38(12): 2578–2586

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg