Page 309 - Introduction to Information Optics

294 5. Transformation with Optics

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F'ig. 5.9. A coherent optical system to perform the Hough transform.

and performs a one-dimensional Fourier transform in the vertical and the
horizontal directions by means of two cylindrical lenses, respectively. Thus, by
picking up the zero-order Fourier spectrum with a CCD camera, a line of
Hough transform can be obtained for a given value of 9. By rotating the Dove
prism, 9 can be scanned angularly, so that the Hough transformation can be
picked up by the linear CCD detector array at the scanning rate [35].
Although optical implementation for straight-line mappings with Hough
transforms works well to some extent, the space variance of the Hough
transform may create serious problems for generalized transformation. More-
over, the usefulness of the Hough transform depends on the accuracy of
mapping, and the performance of the optical system depends on the input
signal-to-noise ratio and clutter; there is also the multiobject problem. Most
Hough transforms have been performed in digital image processing.

REFERENCES

P. M. Duffieux, The Fourier Transform and Its Applications to Optics, John Wiley & Sons,
New York, second edition, 1983.
Ernst Abbe, 1873, "Archiv Mikroskopische," Anat., vol. 9, 413,
Load Rayleigh, 1896, "On the Theory of Optical image, with Special References to the
Microscope," Phil. Mag. 5, 43, 167.
Andre Marechal, and Maurice Francon, Diffraction Structure des Images, Masson & Cie
Eeiteurs, Paris, 1970.
E. L. O'Neill, 1956, "Spatial Filtering in Optics," IRE Trans. Inform. Theory, 1T-2, 56-65.
Emmett N. Leith, James A. Roth, 1977, "White light optical processing and holography."
Applied Optics, Vol. 16, no. 9, 2565.
A. B. VanderLugt, Optical Signal Processing, John Wiley & Sons, New York, 1992.
B. E. A. Saleh and M. O. Freeman, "Optical Transformations," in Optical Signal Processing,
J. Homer, ed., Academic, New York, 1987.
F. T. S. Yu, Optical Information Processing, Wiley-Interscience, New York, 1983.