Image Processing Reference

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where and are 2 × 2 matrix formed by Fourier coeicients

on some fixed index
k
and
U
* is the
U
complex conjugate.

Computation of the shift value
l
0

Let's consider

and

(13)

where
k
1
and
k
2
are two fixed index and arg(
U
) is the complex argument of
U
.

Computation of the matrix
A
's parameters

are going to estimate affine matrix
A
parameters. Lets
O
1
, O
2
be two curves and
U
f
,
U
h
, respect-

(14)

Using matrix, we have the following formula:

(15)

So we have to estimate
a
1
,
a
2
,
a
3
, and
a
4
. This system can be represented as following:

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