1. EPL 443
joint transform correlator
&
rotational INVARIANT OPTICAL
CORRELATION USING MELLIN TRANSFORMS
Presented by :
Ajay Singh
2010PH10821

2. JTC
The field transmitted through the front focal plane is given by
In the rear focal plane of the lens we find the Fourier transform of this field

3. We are interested in third and forth terms so we can write :
and
Both of these expressions are crosscorrelations of the functions g and h. One output is
centered at coordinates (0, - Y) and the other at coordinates (0, Y). The second output
is a mirror reflection of the first about the optical axis.

4. Rotational invariance
When the outcome is invariant w.r.t. rotation at any angle, the
phenomenon is known as rotational invariance.
When sub images are well resolved , pattern recognition can
be achieved .
 A circular harmonic expansion filter is real value implemented
in a joint transform correlator architecture to perform rotation
invariant pattern recognition.
When two input are equal ( f = g ) we get intensity maxima.
It was found that by using single simple harmonics fk(r,α) as a
complex reference function , the intensity of the correlation Centre
is independent of rotation angle.

8. Fig. 1. (a) Input consists of a number of characters A in various orientations, (b) each
character A produces a correlation spot regardless of its orientation.

9. REF:
 Francis T. S. Yu, Xiaoyang Li, Eddy Tarn, Suganda Jutamulia, and Don A.
Gregory , Rotation invariant pattern recognition with a programmable
joint transform correlator “ 15 November 1989 / Vol. 28, No. 22 /
APPLIED OPTICS ”
 Suganda Jutamulia and Toshimitsu Asakura , Rotation-invariant joint
transform correlator “APPLIED OPTICS / Vol. 33, No. 2 3 / 1 0 August 1994 ”
 Introduction to Fourier optics by Joseph W. Goodman .