Image Acquisitionand Proces

Image Analysis 169
( T00 ¥ S00 ) + ( T10 ¥ S10 ) + ( T20 ¥ S20
) +
( T00 ¥ S10 ) + ( T10 ¥ S20 ) + ( T20 ¥ S30
) +
( T00 ¥ Sa0 ) + ( T10 ¥ Sa+ 1, 0 ) + ( T20 ¥ Sa+
2,
0 ) +
( T01 ¥ S01) + ( T11 ¥ S11) + ( T21 ¥ S21) +
( T02 ¥ S02 ) + ( T12 ¥ S12 ) + ( T22 ¥ S22
)
( T01 ¥ S11) + ( T11 ¥ S21) + ( T21 ¥ S31) +
( T02 ¥ S12 ) + ( T12 ¥ S22 ) + ( T22 ¥ S32
)
•••
( T01 ¥ Sa 1) + ( T11 ¥ Sa+ 1, 1) + ( T21 ¥ Sa+
2,
1) +
( T02 ¥ Sa2 ) + ( T12 ¥ Sa+ 1, 2 ) + ( T22 ¥ Sa+
2,
2 )
( T00 ¥ S01) + ( T10 ¥ S11) + ( T20 ¥ S21) +
( T00 ¥ Sa 1) + ( T10 ¥ Sa+ 1, 1) + ( T20 ¥ Sa+
2,
1) +
( T01 ¥ S02 ) + ( T11 ¥ S12 ) + ( T21 ¥ S22
) +
( T02 ¥ S03 ) + ( T12 ¥ S13 ) + ( T22 ¥ S23
)
•••
•••
( T01 ¥ Sa2 ) + ( T11 ¥ Sa+ 1, 2 ) + ( T21 ¥ Sa+
2,
2 ) +
( T02 ¥ Sa3 ) + ( T12 ¥ Sa+ 1, 3 ) + ( T22 ¥ Sa+
2,
3 )
••• ••• ••• •••
( T00 ¥ S0 b) + ( T10 ¥ S1 b) + ( T20 ¥ S2
b) +
( T00 ¥ Sab ) + ( T10 ¥ Sa + 1, b ) + ( T20 ¥ Sa + 2,
b ) +
( T01 ¥ S0, b+ 1) + ( T11 ¥ S1 , b+ 1) + ( T21 ¥ S2,
b+
1) +
( T02 ¥ S0, b+ 2 ) + ( T12 ¥ S1 , b+ 2 ) + ( T22 ¥ S2,
b+
2 )
•••
•••
( T01 ¥ Sab , + 1) + ( T11 ¥ Sa+ 1, b+ 1) + ( T21 ¥ Sa+ 2,
b+
1) +
( T02 ¥ Sab , + 2 ) + ( T12 ¥ Sa+ 1, b+ 2) + ( T22 ¥ Sa+ 2,
b+
2)
issue is to be overcome, the template needs to be rescanned over the source image
using different rotations and sizes (variances in both x and y). This can be extremely
time consuming; consider performing a cross correlation 360 times just to perform
a rotation-invariant match — and that is without subdegree accuracy.
Several techniques exist that can assist in speeding up scale and rotation invariant
matching. The most important method is to scan only for variations that are likely to
exist. If your part is always the same size, and no spatial distortion exists, then do not
scan for size variations. Similarly for rotation variance, if your part will be repeatedly
placed at the same orientation, then you do not need to rescan the source image using
a range of different angles (cross correlation can typically detect object rotations of
around ±5∞ without rescanning). If you predict that spatial distortions may exist, only
scan for those that are likely, as removing scans that are unlikely to occur will decrease
the processing time required to complete a search. When objects may be rotated, it is
common to place a small coordinate marker on the object that can be easily found and
extract the rotation angle from it. Then with the template rotated to the new angle,
perform a standard cross correlation.
7.1.2.3 Pyramidal Matching
Although the accuracy of cross correlation is quite good, it is a very slow technique
to use. Pyramidal matching uses a similar searching technique, but subsamples both
the source image and template to smaller spatial resolutions, effectively reducing
the amount of data to be searched by up to 75%. As the resolutions are lower, more
care must be taken in deÞning what is a potential match, as the search is performed