Interference is an important phenomenon that plays a key role in understanding the properties of light. However, novice students have difficulties with optical interference experiments because fringe-pattern processing algorithms are not a topic of optics courses. The difficulty increases taking into account that the phase shift is usually induced manually and advanced phase-shifting algorithms must be applied. In this paper, the fundamental principles behind seven well-established phase-shifting algorithms are presented. First, five basic algorithms are analyzed: the three-, four-, and n-steps as well as two least-squares algorithms. Then, the advanced iterative algorithm and the generalized phase-shifting are studied. The operation of the algorithms is illustrated by a typical experiment on the Michelson interferometer. This work could be useful as an introductory lesson to the optics laboratory.
Existing feature-based methods for homography estimation require several point correspondences in two images of a planar scene captured from different perspectives. These methods are sensitive to outliers, and their effectiveness depends strongly on the number and accuracy of the specified points. This work presents an iterative method for homography estimation that requires only a single-point correspondence. The homography parameters are estimated by solving a search problem using particle swarm optimization, by maximizing a match score between a projective transformed fragment of the input image using the estimated homography and a matched filter constructed from the reference image, while minimizing the reprojection error. The proposed method can estimate accurately a homography from a single-point correspondence, in contrast to existing methods, which require at least four points. The effectiveness of the proposed method is tested and discussed in terms of objective measures by processing several synthetic and experimental projective transformed images.
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