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This matched keypoint has the smallest Euclidean distance under the constraint of Equation 8 to the stable keypoint.
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Note that stable keypoints here refer to the SIFT keypoints for which a matched keypoint can be found in the reference audio.
A pair of keypoint mappings determines a similarity transformation T, and then it is evaluated with the induced global information that is defined to be the similarity metric between the reference image and the transformed image by T. A process is utilized that iteratively considers the pairs of keypoint mappings and searches the best reference matched keypoint for every test keypoint.
A wrong mapping here is referred to two matched keypoints that are spatially far away from each other.
In Figure 3, a 01 and a 02 are matched keypoints of a 1 and a 2, respectively.
Although we did not exploit such advantage here, it is interesting to point out that it is not always strictly necessary to completely remove all the matched keypoints.
Application for trademark registration for KeyPoint has been filed by Keygene NV.
Secondly, each such keypoint has a descriptor associated with it, as similar to a fingerprint.
Expectedly, the descriptors extracted from a cloned region are quite similar to those of the source, thus making possible to discover the manipulation by matching keypoints.
This wonderful property of 3D keypoints has been realized, the same five shape functions by Osada et al. [21] are analyzed, and it has been found that the geometric distributions of 3D keypoints are unique for individual object.
We have successfully completed this task by eliminating only the keypoints having matches across the copy-moved regions that were used to detect the manipulation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com