Estimation of parameters and recognition of images of three-dimensional objects with disordered samples

Estimation of rotation parameters of three-dimensional images by spherical harmonics analysis

“…The results show that the method proposed provides a comparable quality of surface approximation. Figure 4: Comparison of the results of approximation, a) test three-dimensional object [16]; b), c) the results of designing the approximated surface, respectively, when L=1 and L=2 [16];d), e) a pointcloud and the results of approximation using the proposed parametrization method when L=1 and L=2; f) g) the result of the surface visualization…”

“…The fi rst approach is based on the preliminary identifi cation of marks within the structure of the reference and observable three-dimensional objects. Thus, if we have at least three identifi ed marks, we can calculate the rotation matrix.This approach can beappliedin astro-orientation systems [14], insystems for highlightobjectrecognition in radar images by means of iterative angular matching of rotation parameters of 3D objects in context of a priori uncertainty of the angular parameters [15][16][17], and in order to process images of polyhedron [18]. In the case when the identifi cation of marks is not feasible, or it has been executed with errors, the problem of estimating rotation parameters on the basis of this approach is either not solved, or solved with errors.…”

Researching methods of reconstruction of threedimensional crystal lattice from images of projections

“…Metric quaternion signals have been analyzed in addition to the Hausdorff metric [13]. The metric is based on finding polynomial coefficients, which are polynomial function of a hyper variable.…”

“…The coefficients of the polynomial m a can be found by using the least squares method. By solving the problem of minimizing the total error of the approximation, we obtain a system of linear quaternion equations, which can be solved directly using the Gauss method or reduced to solving a system of equations with real coefficients [13].…”