
%* Last edited: Sep 25 17:11 1995 (misha)

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\begin{document}


The widely used Marr-Hildreth edge detection algorithm consists of
filtering the image with a Gaussian filter, computing the Laplacian of the
filtered image, and locating the zero crossings of the result.  Convolution
with a Gaussian can be approximated by repeated convolution with a
triangular filter, with weights $\frac{1}{4}$, $\frac{1}{2}$, and
$\frac{1}{4}$, requiring only arithmetic shifts and accumulates. Since the
Gaussian filter is separable, it can be implemented by two one-dimensional
convolutions.  Further, since zero crossings are independent of absolute
magnitude, the expensive scaling operation of the Laplacian kernel is not
required.




\begin{figure}[htbp]
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  \put(20,10){\fbox{\epsffile{/homes/misha/abacus/PS/flow1.ps}}}
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  \put(35,0){(a)}
  \put(105,0){(b)}
  \end{picture}
\caption[Optical Flow Example]{Optical flow calculation with maximum 
displacement of 2 pixels and a 5 \by 5 summation region. (a) original
image.  (b) displaced image.  The top shape moved up by one pixel and
partially off the image; the right shape moved down by one pixel and the
lower shape moved three units down and one to the left. }
\label{fig:optflow}
\end{figure}


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