Rotation Estimation: A Closed-Form Solution Using Spherical Moments †

Photometric moments are global descriptors of an image that can be used to recover motion information. This paper uses spherical photometric moments for a closed form estimation of 3D rotations from images. Since the used descriptors are global and not of the geometrical kind, they allow to avoid image processing as features extraction, matching, and tracking. The proposed scheme based on spherical projection can be used for the different vision sensors obeying the central unified model: conventional, fisheye, and catadioptric. Experimental results using both synthetic data and real images in different scenarios are provided to show the efficiency of the proposed method.

[1]  James R. Bergen,et al.  Visual odometry , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[2]  Philippe Martinet,et al.  Catadioptric Visual Servoing From 3-D Straight Lines , 2008, IEEE Transactions on Robotics.

[3]  Philippe Martinet,et al.  A generic fisheye camera model for robotic applications , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[4]  P. Schönemann,et al.  A generalized solution of the orthogonal procrustes problem , 1966 .

[5]  Fabio Morbidi,et al.  Phase Correlation for Dense Visual Compass From Omnidirectional Camera-Robot Images , 2017, IEEE Robotics and Automation Letters.

[6]  Helder Araújo,et al.  Robust image-based visual servoing using invariant visual information , 2013, Robotics Auton. Syst..

[7]  Peter I. Corke,et al.  Generic decoupled image-based visual servoing for cameras obeying the unified projection model , 2009, 2009 IEEE International Conference on Robotics and Automation.

[8]  P. Martinet,et al.  Decoupled visual servoing based on the spherical projection of points , 2009, ICRA 2009.

[9]  Éric Marchand,et al.  Experiments with robust estimation techniques in real-time robot vision , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Kostas Daniilidis,et al.  Rotation recovery from spherical images without correspondences , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Cédric Demonceaux,et al.  Visual Servoing Based on Shifted Moments , 2015, IEEE Transactions on Robotics.

[12]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[13]  M. Teague.  Image analysis via the general theory of moments , 1980 .

[14]  Mohammad H. Mahoor,et al.  A Robust Method for Rotation Estimation Using Spherical Harmonics Representation , 2013, IEEE Transactions on Image Processing.

[15]  Demetri Psaltis,et al.  Image Normalization by Complex Moments , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Omar Tahri,et al.  Closed form solution for Rotation Estimation using Photometric Spherical Moments , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[17]  Tomás Pajdla,et al.  Structure from motion with wide circular field of view cameras , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  François Chaumette,et al.  Complex Objects Pose Estimation based on Image Moment Invariants , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[19]  Helder Araújo,et al.  Efficient decoupled pose estimation from a set of points , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[20]  C. Morandi,et al.  Registration of Translated and Rotated Images Using Finite Fourier Transforms , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Nick Barnes,et al.  Estimating Relative Camera Motion from the Antipodal-Epipolar Constraint , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Pascal Vasseur,et al.  Rotation estimation and vanishing point extraction by omnidirectional vision in urban environment , 2012, Int. J. Robotics Res..

[23]  Romeo Tatsambon Fomena.  Asservissement visuel par projection sphérique , 2008 .

[24]  Omar Tahri,et al.  A Direct Dense Visual Servoing Approach Using Photometric Moments , 2018, IEEE Transactions on robotics.

[25]  François Chaumette,et al.  Distance-Based and Orientation-Based Visual Servoing From Three Points , 2011, IEEE Transactions on Robotics.

[26]  Shree K. Nayar,et al.  Ego-motion and omnidirectional cameras , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[27]  E. Malis,et al.  Spherical Image Processing for Accurate Visual Odometry with Omnidirectional Cameras , 2008 .

[28]  Kurt Konolige,et al.  Real-time Localization in Outdoor Environments using Stereo Vision and Inexpensive GPS , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[29]  Hicham Hadj-Abdelkader,et al.  Direct method for rotation estimation from spherical images using 3D mesh surfaces with SPHARM representation , 2016, J. Vis. Commun. Image Represent..

[30]  Beno Benhabib,et al.  Three-dimensional location estimation of circular features for machine vision , 1992, IEEE Trans. Robotics Autom..