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 develope...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 tile 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.展开更多
We propose a novel binary image representation algorithm using the non-symmetry and anti-packing model and the coordinate encoding procedure （NAMCEP）. By tak- ing some idiomatic standard binary images in the field o...We propose a novel binary image representation algorithm using the non-symmetry and anti-packing model and the coordinate encoding procedure （NAMCEP）. By tak- ing some idiomatic standard binary images in the field of image processing as typical test objects, and by comparing our proposed NAMCEP representation with linear quadtree （LQT）, binary tree （Bintree）, non-symmetry and anti-packing model （NAM） with K-lines （NAMK）, and NAM representa- tions, we show that NAMCEP can not only reduce the aver- age node, but also simultaneously improve the average com- pression. We also present a novel NAMCEP-based algorithm for area calculation and show experimentally that our algo- rithm offers significant improvements.展开更多
Let 0<λ_1,λ_2<1 and 1-λ_1-λ_2≥max｛λ_1,λ_2｝.Let ~K(λ_1,λ_2) be the attractor of the iterated function system ｛φ_1,φ_2｝on the line,where φ_1(x)=λ_1x and φ_2(x)=1-λ_2+λ_2x,x∈R.~K(λ_1,λ_2) is ...Let 0<λ_1,λ_2<1 and 1-λ_1-λ_2≥max｛λ_1,λ_2｝.Let ~K(λ_1,λ_2) be the attractor of the iterated function system ｛φ_1,φ_2｝on the line,where φ_1(x)=λ_1x and φ_2(x)=1-λ_2+λ_2x,x∈R.~K(λ_1,λ_2) is called a non-symmetry Cantor set. In this paper,it is proved that the exact Hausdorff centred measure of K(λ_1,λ_2) equals 2s(1-λ)s,where λ=max｛λ_1,λ_2｝ and s is the Hausdorff dimension of K(λ_1,λ_2).展开更多
文摘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 tile 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.
基金We thank the anonymous reviewers and editors for their valuable comments on improving this paper. This work was supported by the National Natural Science Foundation of China （Grant No. 61300134）, the Research Fund for the Doctoral Program of Higher Education of China （20120172120036）, the Natural Science Foundation of Guangdong Province of China （S2011040005815 and S2013010012515）, the Foundation for Dis- tinguished Young Talents in Higher Education of Guangdong of China （LYM11015）, and the Fundamental Research Funds for the Central Universities of China （2011ZM0074 and 2013ZZ0050）.
文摘We propose a novel binary image representation algorithm using the non-symmetry and anti-packing model and the coordinate encoding procedure （NAMCEP）. By tak- ing some idiomatic standard binary images in the field of image processing as typical test objects, and by comparing our proposed NAMCEP representation with linear quadtree （LQT）, binary tree （Bintree）, non-symmetry and anti-packing model （NAM） with K-lines （NAMK）, and NAM representa- tions, we show that NAMCEP can not only reduce the aver- age node, but also simultaneously improve the average com- pression. We also present a novel NAMCEP-based algorithm for area calculation and show experimentally that our algo- rithm offers significant improvements.
文摘Let 0<λ_1,λ_2<1 and 1-λ_1-λ_2≥max｛λ_1,λ_2｝.Let ~K(λ_1,λ_2) be the attractor of the iterated function system ｛φ_1,φ_2｝on the line,where φ_1(x)=λ_1x and φ_2(x)=1-λ_2+λ_2x,x∈R.~K(λ_1,λ_2) is called a non-symmetry Cantor set. In this paper,it is proved that the exact Hausdorff centred measure of K(λ_1,λ_2) equals 2s(1-λ)s,where λ=max｛λ_1,λ_2｝ and s is the Hausdorff dimension of K(λ_1,λ_2).
