Image Processing Reference
In-Depth Information
I 20 ( x j ,y j )=
l
( f )( x j + x l ,y j + y l ) w 20 ( x l ,y l )
=
l
exp[ i 2 θ ( x j + x l ,y j + y l )
i 2 φ ( x l ,y l )]
(11.71)
The latter assumes that the same unitary gradient of the image and the unitary gra-
dient of the prototype as those used in the computation of A are employed to obtain
( f )( x j ,y j ) and w 20 ( x j ,y j ), via Eq. (11.61), and Eq. (11.62). Consistent with Eq.
(11.70), θ = i
whenever it is not defined, i.e., when a pixel position does not rep-
resent an edge pixel position, the vote contribution of that point to I 20
is reduced
to 0. While A ( x j ,y j ) is the count of the positive matches only,
is the positive
matching score adjusted downwards with the amount of negative matches. At the
reference point, when the image is the same as the prototype itself, we obtain the
maximum match with both of the techniques:
|
I 20 |
A = L,
I 20 = L,
(11.72)
where L represents the number of edge pixels in the prototype. When 100% of the
edge directions mismatch maximally i.e., when all prototype directions are orthogo-
nal to the image directions, we obtain:
A =0
I 20 =
L
(11.73)
while if 50% of the edge directions match perfectly and 50% mismatch maximally
we obtain,
A = L
2 ,
I 20 =0 .
(11.74)
In computing I 20 ( x j ,y j ) the scores of the positions with contradictory gradient di-
rections will be reduced compared to the GHT scores, A ( x j ,y j ). The GHT is with-
out score reduction since a score of A ( x j ,y j ) is only allowed to increase (in case
of gradient direction match) or it is unchanged (in case of mismatch). For GHT this
is a necessity, because negative scores would not be meaningful in case they were
given to empty accumulators, while in the case of I 20 this is allowed as this sim-
ply corresponds to a vote for a pattern which is locally orthogonal to the prototype,
antiprototype. Clearly, the computation of I 20
is a voting process in which not only
negative but also complex votes are allowed.
Formally, nonprototype ILST images can be generated by a phase shift of the
prototype ILST image:
exp[ 0 ) exp( i 2tan 1 ( ξ x j , ξ y j )]
(11.75)
But to which real patterns ϕ 0
=0corresponds, as this new ILST image is a purely
synthetic construct, is not obvious. This is because a phase shift of the prototype
ILST may result in tangent fields that are not always imaginable or intelligible by
visual inspection of Eq. (11.75). To give every ϕ 0
an exact meaning, i.e., to find a
ξ j , an estimation should be made by numerical methods. For
ξ j that approximates
Search WWH ::




Custom Search