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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

Postal Subscription Code 80-970

2018 Impact Factor: 1.129

Front Comput Sci Chin    2011, Vol. 5 Issue (1) : 57-65    https://doi.org/10.1007/s11704-010-0337-3
RESEARCH ARTICLE
A fast algorithm for computing moments of gray images based on NAM and extended shading approach
Yunping ZHENG1(), Mudar SAREM2
1. School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China; 2. School of Software Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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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)     
Corresponding Author(s): ZHENG Yunping,Email:zhengyp@scut.edu.cn   
Issue Date: 05 March 2011
 Cite this article:   
Yunping ZHENG,Mudar SAREM. A fast algorithm for computing moments of gray images based on NAM and extended shading approach[J]. Front Comput Sci Chin, 2011, 5(1): 57-65.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-010-0337-3
https://academic.hep.com.cn/fcs/EN/Y2011/V5/I1/57
Fig.1  Sketch of a homogeneous block
Fig.1  Sketch of a homogeneous block
Fig.2  An example of the NAMES approach. (a) A 16 × 16 digital subimage; (b) partitioned homogenous blocks of (a)
Fig.2  An example of the NAMES approach. (a) A 16 × 16 digital subimage; (b) partitioned homogenous blocks of (a)
Fig.3  Three idiomatic standard gray images. (a) Lena; (b) F16; (c) Peppers
Fig.3  Three idiomatic standard gray images. (a) Lena; (b) F16; (c) Peppers
ImageC?Number of blocksΔN/%
STCNAMES
Lena0.99705412423620212.22
10198211737012.37
15129771068717.65
209428768618.48
257210589818.20
305676469317.32
F160.98645335792858414.88
10207251555924.93
15156981054832.81
2012594801636.35
2510321651336.90
308637535637.99
Peppers0.99885508714528710.98
1025255229029.32
15144571254013.26
2010235798421.99
258061592426.51
306616477027.90
Tab.1  Comparison of number of blocks between NAMES and STC
Conventional approachSTC approachNAMES approach
LenaF16PeppersLenaF16PeppersLenaF16Peppers
m003.25E+ 074.70E+ 072.73E+ 073.23E+ 074.68E+ 072.73E+ 073.23E+ 074.67E+ 072.72E+ 07
m108.08E+ 091.19E+ 106.77E+ 098.06E+ 091.18E+ 106.77E+ 098.06E+ 091.17E+ 106.75E+ 09
m018.70E+ 091.23E+ 107.11E+ 098.66E+ 091.23E+ 107.10E+ 098.65E+ 091.21E+ 107.08E+ 09
m112.20E+ 123.08E+ 121.69E+ 122.20E+ 123.07E+ 121.69E+ 122.19E+ 123.06E+ 121.69E+ 12
m202.71E+ 124.05E+ 122.28E+ 122.71E+ 124.04E+ 122.28E+ 122.71E+ 124.04E+ 122.27E+ 12
m023.03E+ 124.27E+ 122.44E+ 123.02E+ 124.26E+ 122.44E+ 123.02E+ 124.24E+ 122.43E+ 12
m217.45E+ 141.04E+ 155.51E+ 147.42E+ 141.04E+ 155.51E+ 147.40E+ 141.03E+ 155.50E+ 14
m127.78E+ 141.07E+ 155.64E+ 147.75E+ 141.07E+ 155.64E+ 147.74E+ 141.06E+ 155.63E+ 14
m301.03E+ 151.57E+ 158.71E+ 141.03E+ 151.56E+ 158.69E+ 141.03E+ 151.55E+ 158.67E+ 14
m031.17E+ 151.66E+ 159.43E+ 141.17E+ 151.66E+ 159.41E+ 141.16E+ 151.66E+ 159.41E+ 14
Tab.2  Accuracy comparison of moment among the three approaches
Fig.4  Performance comparisons between conventional, STC, and NAMES approaches for (a) ‘Lena’; (b) ‘F16’; (c) ‘Peppers’
Fig.4  Performance comparisons between conventional, STC, and NAMES approaches for (a) ‘Lena’; (b) ‘F16’; (c) ‘Peppers’
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