ESTIMATION OF ROTATION PARAMETERS OF THREE-DIMENSIONAL IMAGES BY SPHERICAL HARMONICS ANALYSIS
Abstract
The article describes a method for estimating the rotational parameters of three-dimensional objects defined as a cloud of points in three-dimensional space, which is less complex compared to other methods and it can ensure a single-valued solution. The authors propose an approach of vector-field models to parametrize images of complex three-dimensional objects. The paper discusses the ways for calculating the expansion coefficients in the basis of spherical harmonics for images of three-dimensional point cloud objects. The authors offer an approach that provides the possibility of estimating the rotation parameters of three-dimensional objects from the values of the expansion coefficients in the basis of spherical harmonics.
Keywords
Acknowledgements
The work is executed at financial support of the Ministry of education and science of Russian Federation, project RFMEFI577170254 "System intraoperative navigation technology to support augmented reality-based virtual 3D models of organs obtained from the results of CT diagnostics, minimally invasive surgeries".
References
1. Rzazewska K., & Luckner M., (2014). 3D model reconstruction and evaluation using a collection of points extracted from the series of photographs. U: the 2014 Federated Conference on Computer Science and Information Systems, 2014, Warsaw, Poland. 669-677.
2. Sakai K. & Yasumura Y., (2018). Three-dimensional shape reconstruction from a single image based on feature learning. U: International Workshop on Advanced Image Technology 2018 (IWAIT 2018), 2018, Chiang Mai, Thailand.
3. Valgma L., (2016). 3D reconstruction using Kinect v2 camera. Tartu: University of Tartu.
4. Lawin F. J., (2015). Depth data processing and 3D reconstruction using the Kinect v2. Linkoping University.
5. Buriy A.S., & Mikhailov S.N., (1994). Methods for identifying astro marks to navigate the spacecraft from images of the starry sky. Foreign Radio Electronics, 7-8, 44-52.
6. Furman Ya.A., Egoshina I.L., , & Eruslanov R.V., . Matching Angular and Vector Descriptions of Three-Dimensional Group Point Objects. Avtometriya, 48(6), 3-17.
7. Egoshina I.L., (2013). Methods, models and algorithms for processing group point objects under conditions of a priori uncertainty of angular parameters.
8. Furman Ya.A., Eruslanov R.V., & Egoshina I.L., (2013). Iterative algorithm for angular matching of group point objects with a priori uncertainty of parameters. Pattern Recognition and Image Analysis, 23(3), 381-388.
9. Furman Ya.A., & Eruslanov R.V., (2011). Contour analysis of the task of the coordinate restoration of 3d object points by the series images of its shades. Nonlinear World, 8, 482-486.
10. Anisimov B.V., (1993). Recognition and digital image processing. Moscow: Visshaya shkola.
11. Ballard, D. (1981). Generalizing the Hough transform to detect arbitrary shapes. Pattern Recognition, 13(2), 111-122.
12. Khoshelham, K. (2007). Extending general Hough transform to detect 3D object in laser range data. U: ISPRS Workshop on Laser Scanning 2007 and SilviLaser 2007, 2007, Espoo, Finland. 206-211.
13. Oliver, J.W. (2011). Demisting the Hough Tnsform for 3D Shape Recognition and registration. U: British Machine Vision Conference 2011, 2011, Dundee, Scotland. 1-11.
14. Pham, M., Woodford, O.J., Perbet, F., Maki, A., Stenger, B., & Cipolla, R. (2011). A new distance for scale-invariant 3D shape recognition and registration. U: 2011 International Conference on Computer Vision, 2011, Barcelona, Spain. 145-152.
15. Chen S., & Jiang H., (2011). Accelerating the hough transform with CUDA on graphics processing units. U: International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA), 2011, Las Vegas, USA.
16. Rozhentsov, A.A., Baev, A.A.,& Naumov A.S., (2010). Estimation of Parameters and Recognition of Images of Three-Dimensional Objects with Disordered Samples. Avtometriya, 46, 57-69.
17. Huang H., Shen L., Zhang R., Makedon F., Hettleman B.,& Pearlman J., (2005). Surface alignment of 3D spherical harmonic models: application to cardiac MRI analysis. Med Image Comput Comput Assist Interv, 8(1), 67-74.
18. Ritchie D., & Kemp G., (1999). Fast Computation, Rotation and Comparison of Low Resolution Spherical Harmonic Molecular Surfaces. Journal of Computational Chemistry, 20(4), 383-395.
19. Buhmann M.D., (2004). Radial Basis Functions: Theory and Implementations. Cambridge: Cambridge University.
20. Titov V.S., Rozhentsov A.A., & Khafi zov R.G., (2014). Modern approaches to representation and processing of three-dimensional object images. Vestnik of Mari State Technical University. Series «Radio Engineering and Infocommunication Systems», 2, 44-54.
21. Brechbühler Ch., Gerig G., & Kübler O., (1995). Parametrization of Closed Surfaces for 3-D Shape Description. Computer Vision and Image Understanding, 61(2), 154-170.
22. Tikhonov A.N., & Arsent’ev V.Ya., (1979). Methods for solving ill-posed problems. Moscow: Nauka.