New method for feature extraction based on fractal behavior - IDRBT
New method for feature extraction based on fractal behavior - IDRBT
New method for feature extraction based on fractal behavior - IDRBT
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
1080 Y.Y. Tang et al. / Pattern Recogniti<strong>on</strong> 35 (2002) 1071–1081<br />
Fig. 6. An example of handwritten signature vericati<strong>on</strong>.<br />
dimensi<strong>on</strong> tells us much about geometrical properties,<br />
such as the projecti<strong>on</strong> of sets, andwe have seen something<br />
of the problems associatedwith calculating the<br />
<strong>fractal</strong> dimensi<strong>on</strong>s. Clearly, dimensi<strong>on</strong>s are intimately<br />
relatedto the study of <strong>fractal</strong> geometry. However, the<br />
experiment results show that this approach allows us<br />
to obtain new andinteresting descripti<strong>on</strong>s of complex<br />
patterns. In some situati<strong>on</strong>s, it has even already yielded<br />
better results than “classical” <str<strong>on</strong>g>method</str<strong>on</strong>g>s. For all the cases,<br />
dierences in <strong>fractal</strong> dimensi<strong>on</strong> can be found the signicative<br />
values. We expect that the proposed<strong>fractal</strong><br />
<str<strong>on</strong>g>method</str<strong>on</strong>g>can also be used<str<strong>on</strong>g>for</str<strong>on</strong>g> improving the <str<strong>on</strong>g>extracti<strong>on</strong></str<strong>on</strong>g> and<br />
classicati<strong>on</strong> of <str<strong>on</strong>g>feature</str<strong>on</strong>g>s in a pattern recogniti<strong>on</strong> system.<br />
Acknowledgements<br />
This work was supportedby research grants received<br />
from the Research Grant Council (RGC) of H<strong>on</strong>g K<strong>on</strong>g<br />
anda Faculty Research Grant (FRG) from H<strong>on</strong>g K<strong>on</strong>g<br />
Baptist University.<br />
References<br />
[1] B.B. Mandelbrot, Fractals: Form, Chance and Dimensi<strong>on</strong>s,<br />
Freeman, San Francisco, CA, 1977.<br />
[2] M.Bald<strong>on</strong>i, C. Baroglio, D. Cavagnino, L. Saitta, Towards<br />
automatic <strong>fractal</strong> <str<strong>on</strong>g>feature</str<strong>on</strong>g> <str<strong>on</strong>g>extracti<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>for</str<strong>on</strong>g> image recogniti<strong>on</strong>,<br />
in: Huan Liu, Hiroshi Motoda (Eds.), Feature Extracti<strong>on</strong>,<br />
C<strong>on</strong>structi<strong>on</strong> andSelecti<strong>on</strong>: a Data Mining Perspective,<br />
Kluwer Academic Publishers, Dordrecht, 1998, pp.<br />
356–373.<br />
[3] B.B. Chaudhuri, N. Sarkar, Texture segmentati<strong>on</strong> using<br />
<strong>fractal</strong> dimensi<strong>on</strong>, IEEE Trans. Pattern Anal. Mach. Intell.<br />
17 (1995) 72–77.<br />
[4] B.B. Chaudhuri, N. Sarkar, Multi<strong>fractal</strong> approach to<br />
textural analysis, in: Fractals andBey<strong>on</strong>dComplexities<br />
in the Sciences, WorldScientic, Singapore, 1998, pp.<br />
161–171.<br />
[5] Y.Y. Tang, J. Liu, H. Ma, B.Li, Two-dimensi<strong>on</strong>al<br />
wavelet trans<str<strong>on</strong>g>for</str<strong>on</strong>g>m in document analysis, in Proceedings<br />
of the First Internati<strong>on</strong>al C<strong>on</strong>ference <strong>on</strong> Multimodal<br />
Interface, Beijing, China, October 15–17, 1996, pp.<br />
274–279.<br />
[6] P. Kube, A. Pentland, On the imaging of <strong>fractal</strong> surfaces,<br />
IEEE Trans. Pattern Anal. Mach. Intell. 10 (5) (1988)<br />
704–707.<br />
[7] S.G. Mallat, A theory <str<strong>on</strong>g>for</str<strong>on</strong>g> multiresoluti<strong>on</strong> signal decompositi<strong>on</strong>:<br />
the wavelet representati<strong>on</strong>, IEEE Trans. Pattern<br />
Anal. Mach. Intell. 11 (1989) 674–693.<br />
[8] A. Pentland, Fractal-<str<strong>on</strong>g>based</str<strong>on</strong>g> descripti<strong>on</strong> of nature scenes,<br />
IEEE Trans. Pattern Anal. Mach. Intell. 6 (1984)<br />
661–674.<br />
[9] A.J. Hurd, D.A. Weitz, B.B. Mandelbrot, Fractal Aspects<br />
of Materials: Disordered Systems, Materials Research<br />
Society, 1987.<br />
[10] B.B. Mandelbrot, The Fractal Geometry of Nature,<br />
Freeman, <str<strong>on</strong>g>New</str<strong>on</strong>g> York, 1983.<br />
[11] G.A. Edgar, Measure, Topology and Fractal Geometry,<br />
Springer, <str<strong>on</strong>g>New</str<strong>on</strong>g> York, USA, 1990.<br />
[12] K. Falc<strong>on</strong>er, Fractal Geometry: Mathematical Foundati<strong>on</strong><br />
andApplicati<strong>on</strong>s, Wiley, <str<strong>on</strong>g>New</str<strong>on</strong>g> York, USA, 1990.<br />
[13] S. Peleg, J. Naor, R. Hartley, D. Avnir, Multiple resoluti<strong>on</strong><br />
texture analysis andclassicati<strong>on</strong>, IEEE Trans. Pattern<br />
Anal. Mach. Intell. 6 (4) (1984) 518–523.<br />
[14] Y.Y. Tang, Y. Tao, <str<strong>on</strong>g>New</str<strong>on</strong>g> <str<strong>on</strong>g>method</str<strong>on</strong>g>of feture <str<strong>on</strong>g>extracti<strong>on</strong></str<strong>on</strong>g> using<br />
<strong>fractal</strong> andwavelet, in: D. P. Casasent, T.-H. Chao (Eds.),<br />
Optical Pattern Recogniti<strong>on</strong> X, Proceedings of SPIE, Vol.<br />
3715, 1999, pp. 248–258.