## Abstract

We show that the Hough transform filter can be obtained easily by
use of rotational multiplexing. To demonstrate our method
experimentally, we recorded the Hough transform filter for 18 discrete
projection angles and compared experimental transform results with
simulated ones for a few input patterns.

© 1998 Optical Society of America

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### Equations (5)

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(1)
$${c}_{i}\left(x,y\right)=\int \int {h}_{i}*\left(u-x,v-y\right)f\left(u,v\right)\mathrm{d}u\mathrm{d}v,$$
(2)
$${c}_{i}\left(x,y\right)=\int \int \mathrm{\delta}\left(xcos{\mathrm{\theta}}_{i}+ysin{\mathrm{\theta}}_{i}-ucos{\mathrm{\theta}}_{i}-vsin{\mathrm{\theta}}_{i}\right)f\left(u,v\right)\mathrm{d}u\mathrm{d}v,$$
(3)
$${c}_{i}\left(\mathrm{\rho},{\mathrm{\theta}}_{i}\right)=\int \int \mathrm{\delta}\left(\mathrm{\rho}-ucos{\mathrm{\theta}}_{i}-vsin{\mathrm{\theta}}_{i}\right)f\left(u,v\right)\mathrm{d}u\mathrm{d}v.$$
(4)
$$|{c}_{i}\prime \left(\mathrm{\rho},{\mathrm{\theta}}_{i}\right){|}^{2}={\left[{\mathrm{\alpha}}_{i}|{\mathrm{\beta}}_{i}\left(\mathrm{\rho}\right){|}^{2}\right]}^{-1}|{c}_{i}\left(\mathrm{\rho},{\mathrm{\theta}}_{i}\right){|}^{2}.$$
(5)
$${F}_{i}\left(a,b,{r}_{i}\right)=\int \int \mathrm{\delta}\left[{\left(x-a\right)}^{2}+{\left(y-b\right)}^{2}-r_{i}{}^{2}\right]\times f\left(x,y\right)\mathrm{d}x\mathrm{d}y,$$