![](bg8.png)
If the real peak is still within proximity to the first es-
timation, the refined estimation can still recover it. If
the rough estimation is very imprecise, an unavoid-
able error will occur in the refined determination. To
improve the algorithm in this respect, the rough esti-
mation can be refined by using a higher upsampling
factor or to enlarge image region for the refined esti-
mation. For this reason, it must be clarified whether
the gain in accuracy is worth the increase in runtime.
The upsampling factor is a tool to achieve higher
accuracy. For a factor κ translation can be determined
by
1
κ
of a pixel. Results have shown that this factor
is limited to 100. Higher factors don’t achieve higher
accuracy. Additionally, a higher upsampling results in
a longer runtime, because there are more data points
to be processed. For low factors the increase in run-
time isn’t significant, because it’s just a slight increase
of data. However, for large factors like 1000 run-
time increases rapidly. This property was observed
for all algorithms. Finally an upsampling factor of
κ = 100 is a suitable choice, because best accuracy
can be achieved without rapid increase of runtime.
The combination algorithm is limited to determine
translation between images. Therefore, our evalua-
tion only focuses on paraxial translation between im-
ages. For most image registration problems, rotation
and scaling has to be considered as additional trans-
formations between images. In order to generalize our
algorithm it can be extended to determine also other
transformations: The Fourier-Mellin-Transformation
can be used for computing rotation and scaling, and
afterwards determining the translation (Tong et al.,
2019).
5 CONCLUSIONS
This paper presents an efficient algorithm for image
registration with subpixel accuracy. More precisely,
we propose a hybrid approach consisting of a coarse
to fine strategy. For the first rough estimation image
projections are used, while for the refined estimation
the method of matrix multiplication is performed only
on a small region around the first estimation center.
Experimental results have shown that the algorithm
is very accurate and computationally highly efficient.
The MAE can be reduced by over 70 % compared to
the IP approach and runtime by over 75 % compared
to the MM approach. It is robust with respect to noise
and can handle large images. To improve the algo-
rithm in further work, it can be extended to consider
generalized transformation models, such as including
rotation and scaling.
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