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  5. Method for determining the projective transformation parameters of a mosaic stochastic marker without taking into account additional a priori information

Method for determining the projective transformation parameters of a mosaic stochastic marker without taking into account additional a priori information

O. Makoveychuk
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Description: The subject matter of the article is the method of parameters of projective transformation in the image. The goal is to develop a "blind" method for finding the four anchor points using an optimization algorithm. The tasks are: analyze the factors that influence the ability to solve the problem and select the fitness function for optimization. There are two main approaches to this task: direct search of the system of lines passing through each cell; search for transformation parameters to obtain a rectangular cell system, the task of binding in this case is to find a system of mutually perpendicular lines that are parallel to the sides of the image. The following results were obtained. The efficiency of using the index method instead of the coordinate method is shown, the method of initial initialization is chosen, in which the algorithm quickly matches. An fitness function is analyzed and selected. The method of finding the four anchor points using the optimization algorithm is developed. The method is proposed that builds on two basic ideas that differentiate it from existing ideas. At first, the transition instead of the coordinate space in the index, that is, instead of directly specifying the coordinates on the image, we will set the cell indices (whereby the order of indexing can be arbitrary), and the coordinates will be found as a function of the set of points of the cell, such as their centroid (center of mass). The second, the choice of a target function that takes acute extrema for a rectangular point system. Conclusions. The scientific novelty of the obtained results is as follows. The appearance of this fitness function, which takes the minimum value for correctly transformed binary images, is set. The method, which using an iterative algorithm, has been developed that allows the blind to find, without additional a priori information, the parameters of the desired projective transformation. Further theoretical and experimental studies in this area are particularly interesting, in particular the applicability of the fitness function for solving other computer vision problems. Separate consideration requires the question of determining the minimum number of neighbors to find the reference points sufficient for the convergence of the algorithm.

Keywords: AR-marker, binary images, projective transformation, optimization algorithm, a priori information.


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 Makoveichuk, O.M. (2019), “Metod vyznachennia parametriv proektyvnoho peretvorennia mozaichnoho stokhastychnoho markera bez vrakhuvannia dodatkovoi apriornoi informatsii” [Method for determining the projective transformation parameters of a mosaic stochastic marker without taking into account additional a priori information], Information Processing Systems, Vol. 4(159), pp. 36-43. https://doi.org/10.30748/soi.2019.159.04.