V.R. Krasheninnikov, A.D. Kadeev, M.A. Potapov

To solve many practical problems it is often required to task the image coinciding problem. In the case of mutual interframe geometric transformation (GT) model of the two images is given the task of coinciding reduces to the estimation of parameters of the model. Most well-known algorithms require accurate initial parameters estimation as the initial approximation. Thus, it is needed to obtain a rough estimate of GT parameters. The algorithm of rough estimation of the GT parameters based on finding a fixed point of transformation is suitable. In this paper the GT assumes shifting, rotation, and scaling of the two-dimensional image which is the most common model of GT. Let two images with unknown parameters of this type transformation you want to evaluate. To do this, auxiliary GT transformation of one of the images is performed and searching for a fixed point after that. Coordinates of this point are used for calculating of required GT parameters estimation. In the case where images are only shifted, the absolute value of the difference of images after extra turn has a central symmetry around fixed point. So this point could be determined by using statistics that compares opposite points in some range near the candidate point. The minimal value of the statistics is most likely to be a fixed one. If transformation rotation is small this method gives almost exact coordinates of the fixed point. In the case of transformation with a significant rotation value is fined by a number of additional turns of one image with a certain step. The method of fixed point finding by processing its trajectory for a set of transformations is proposed. The desired trajectory is a straight line and after finding it the parameters of the initial GT can be estimated. Fixed point method forms a class of algorithms that estimate the parameters of GT in a large range. Thus, this class of algorithms is suitable for an initial approximation for more precise algorithms.

 

1. Krasheninnikov V.R. Ocenka parametrov geometricheskojj transformacii izobrazhenijj metodom nepodvizhnojj tochki  // Trudy RNTO REHS im. A.S. Popova. Ser. Nauchnaja sessija, posvjashhennaja Dnju radio. Vyp. LXIII. M. 2008. S. 381-383.
2. Krasheninnikov V.R., Potapov M.A. Nakhozhdenie nepodvizhnykh tochek dlja ocenki parametrov geometricheskojj transformacii // Trudy RNTO REHS im. A.S. Popova. Ser. Nauchnaja sessija, posvjashhennaja Dnju radio. Vyp. LXIV. M. 2009. S. 315-317.
3. Krasheninnikov V.R., Potapov M.A. Detection of Rectilinear Path of a Fixed Point for the Geometrical Transformation Parameters Estimation of Three-Dimensional Images  // 10th International Conference - Pattern Recognition and Image Analysis: New information Technologies?. December 5-12. 2010. P. 219-222.
4. Krasheninnikov V.R., Potapov M.A. A Way to Detect the Straight Line Trajectory of an Immovable Point for Estimating Parameters of Geometrical Transformation of 3D Images  // Pattern Recognition and Image Analysis. 2011. V. 21. №2. P. 280-284.
5. Krasheninnikov V.R., Potapov M.A. Estimation of Parameters of Geometric Transformation of Images by Fixed Point Method  // Pattern Recognition and Image Analysis. 2012. V. 22. №2. P. 303-317.
6. Krasheninnikov V.R., Kadeev A.D. Nakhozhdenie nepodvizhnykh tochek preobrazovanijj koordinat pri ocenivanii parametrov geometricheskojj transformacii izobrazhenijj // Radiotekhnika. ZHurnal v zhurnale: Radiosistemy. Matematicheskoe modelirovanie infokommunikacionnykh sistem. 2012. Vyp. 175. S. 68-71.