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In computer vision, many algorithms have been developed for image registration based on image pattern matching.
However, there might be no universal method for all applications because of their advantages and disadvantages.
Therefore, we have to select the best method suited for each task. A representative sub-pixel registration method uses
one dimensional parabola fitting over the similarity measurements at three positions. The parabola fitting method could
be applied to two dimensional, assuming that horizontal and vertical displacements are independent. Although this
method has been widely used because of their simplicity and practical usability, large errors are involved. To avoid
these errors depending on the spatial structure of image pattern, "two-dimensional simultaneous sub-pixel estimation"
was proposed. However, it needs conditional branching control procedures such as scan field expansion and exception.
The conditional branching control procedures make estimation instable and disturb the speed of processing. Therefore,
the authors employ a paraboloid fitting: by using the least square method, a paraboloid is fitted with the image similarity
values at nine points and the best matching point is obtained with sub-pixel order. It is robust against the image pattern
and enables speed-up, but it still has error margin. The authors analyzed the error characteristics of the sub-pixel
estimation using the paraboloid fitting. The error can be characterized by "a bias; a systematic error" and "dispersion; a
random error." It was found that the magnitude of each error was different according to the sub-pixel values of the best
matching positions. In this paper, based on the analysis, the authors proposed a novel accurate algorithm for 2D subpixel
matching. The method does not need any iteration processes and any exception processes on runtime. Therefore,
it is easy to implement the method on software and hardware. Experimental results demonstrated the advantage of the
proposed algorithm.
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