Optical determination of fractal dimensions using Fourier transforms

Reyer Zwiggelaar; Christine R. Bull

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Optical determination of fractal dimensions using Fourier transforms

机译：使用傅立叶变换光学确定分形维数

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Links between the fractal Hausdorff dimension, the Fourier transform of two-dimensional scenes, and image segmentation by texture are discussed. It is shown that the fractal Hausdorff dimension can be derived by integration of the intensity in the spatial frequency domain (i.e., the Fourier plane) over a set of bandlimited spatial filters. The differences between a computational and an optical approach to determine the Hausdorff dimension are shown, and advantages of each method are discussed. Possible future directions for research and improvements are mentioned. Simulated fractal scenes are considered as test images for both the computational and the optical approach.

机译：讨论了分形的Hausdorff维数，二维场景的Fourier变换和按纹理进行图像分割之间的联系。结果表明，可以通过在一组带宽受限的空间滤波器上对空间频域（即傅立叶平面）中的强度进行积分来得出分形的Hausdorff维数。显示了确定Hausdorff尺寸的计算方法与光学方法之间的差异，并讨论了每种方法的优点。提到了可能的未来研究和改进方向。模拟的分形场景被视为计算和光学方法的测试图像。

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来源
《Optical engineering》 |1995年第5期|p.1325-1332|共8页
作者
Reyer Zwiggelaar; Christine R. Bull;
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作者单位

Silsoe Research Institute Wrest Park Silsoe, Bedford MK45 4HS, United Kingdom;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类光学仪器;
关键词
fractals; fourier transforms; image analysis; optical signal processing;

机译：分形;傅立叶变换;图像分析;光信号处理;

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5. Optical two-dimensional Fourier transform spectroscopy of semiconductors. [D] . Zhang, Tianhao. 2008

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8. Serrated Circular Apertures: Optical Fourier Transforms and Fractal Analysis. [R] . Beal, M. M. 1990

机译：锯齿形圆孔：光学傅里叶变换和分形分析。

Optical determination of fractal dimensions using Fourier transforms

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