Shape representation using cosine transforms
View Patent ↗A method of approximating the inner or outer boundary of an iris comprises generating an approximate boundary representation ( 20 ) comprising a least squares approximation by a cosine transform series of a function of the angle (θ) about a fixed point (A) of the distance of measured points ( 10 ) on the boundary from the fixed point (A). More broadly, the method may be used to approximate the shape of any two-dimensional curve or figure.
1. A method of approximating an iris boundary, comprising the steps of:
acquiring an image of an eye, including an iris boundary;
noting a plurality of unequally spaced boundary points on the boundary of the image;
selecting a fixed reference point in the image; and
generating an approximate boundary representation comprising a least squares approximation by a discrete cosine transform series as a function
d
(
θ
)
=
C
0
2
+
∑
n
=
1
N
-
1
C
n
cos
n
(
θ
2
+
π
2
N
)
of angle θ i about said fixed point of the distance of said boundary points in the image from said fixed point;
the spaced boundary points being not all equally spaced in θ i , and in which said least-squares approximation minimizes the sum of squares of errors in the distances taken over the boundary points.
2. A method as claimed in claim 1 in which the approximate boundary representation is generated by numerically solving the system of linear equations
PC=S
or a mathematical equivalent thereof, for the unknown matrix C, where:
C
=
[
C
0
C
1
⋮
C
N
]
and
S
=
[
S
0
S
1
⋮
S
N
]
where
S
k
=
∑
i
=
0
M
r
i
cos
k
(
θ
i
2
+
π
2
N
)
and where P in an N by N matrix given by
P
k
,
0
=
1
2
and
P
k
,
n
=
∑
i
=
1
M
C
n
cos
n
(
θ
i
2
+
π
2
N
)
cos
k
(
θ
i
2
+
π
2
N
)
for
k
=
0
…
N
-
1
and
n
=
1
…
N
-
1.
3. A method as claimed in claim 1 in which the boundary is the pupil/iris boundary.
4. A method as claimed in claim 1 in which the boundary is the outer iris boundary.
5. A method as claimed in claim 1 in which the fixed reference point is in the approximate center of the iris boundary.
6. A method as claimed in claim 1 in which, following the generating step any boundary points which lie more than a selected distance from the boundary representation are excluded, and the generating step is then repeated.