Background Removal
B.3 Two-Image Alignment
There are many applications of image alignment for photographic images, for example, object tracing, image stitching, and panoramic photography [64]. Fig . B.1 shows an example of the stitching of two images.
Given an image I, and a transformation function T with a parameter vector u, the transformed image I0 is derived by the following equation.
I0(x) = I(T (x)). (B.14)
Given two images, IA and IB, the two-image alignment problem is that searching a u to transform the location of all pixels in IA, such that the similarity of IA and IB is maximum. The simplest solution for two-image alignment problem is the brute force method that tests all possible u. However, this method is impracticable when the images are large or the dimension of u is greater than two, for example, a transformation includes
Figure B.1: The image alignment. (a) IA. (b) IB. (c) The alignment result of IA and IB.
shift, rotation, and scaling. The level-of-detail method (LOD) is a more efficient method than the brute force method. However, LOD could find a false solution although it can be easily implemented. The most popular alignment method is the LucasKanade method (LKM) [67]. The fundamental of LKM is that it iteratively find the increase of u by the LevenbergMarquardt algorithm such that the SSE between two images is minimum.
However, because the LKM is based on SSE, the alignment results of LKM could be failed if the images are taken from different imaging environments.
The mutual information can also solve the two-image alignment problem. Viola [51]
proposed an alignment method by maximizing the mutual information of two images.
Dowson and Bowden combined the mutual information and LKM to devise an efficient alignment algorithm.
Another alignment method based on the analysis in frequency domain has been pro-posed. Frank used the cross-correlation (Eq. B.5) to estimate the transformation from the frequency domain of images [38]. As the LKM, this method could not align the images taken by different imaging modalities.
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