Scale Exploiting Minimal Solvers for Relative Pose with Calibrated Cameras

We present efficient minimal solvers for the estimation of relative pose between two calibrated images. The proposed method exploits known scale ratios of feature matches which are intrinsically provided by scale invariant feature detectors with scale-space pyramids (e.g. SIFT). Since we are using scale, the number of required feature matches is reduced and consequently fewer inliers are needed. In our paper, we derive two solvers each related to one of the two possible minimal sets: Our 1+3 point algorithm estimates relative pose from four feature matches with one known scale, while our 2+1 point algorithm computes relative pose from three feature matches with two known scales. We embed the proposed methods into RANSAC with two inlier classes, and present an efficient RANSAC modification for less reliable scales. Finally, we analyze performance and robustness in synthetic data, and evaluate our RANSAC approach on real data in comparison to RANSAC based on the five point algorithm.

[1]  I HartleyRichard.  In Defense of the Eight-Point Algorithm , 1997 .

[2]  David Nistér,et al.  Preemptive RANSAC for live structure and motion estimation , 2005, Machine Vision and Applications.

[3]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[4]  Christopher Zach,et al.  The Likelihood-Ratio Test and Efficient Robust Estimation , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[5]  Davide Scaramuzza,et al.  1-Point-RANSAC Structure from Motion for Vehicle-Mounted Cameras by Exploiting Non-holonomic Constraints , 2011, International Journal of Computer Vision.

[6]  Stergios I. Roumeliotis,et al.  Two Efficient Solutions for Visual Odometry Using Directional Correspondence , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Frederik Schaffalitzky,et al.  A minimal solution for relative pose with unknown focal length , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[8]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[9]  Claus Gramkow,et al.  On Averaging Rotations , 2004, Journal of Mathematical Imaging and Vision.

[10]  Zuzana Kukelova,et al.  Automatic Generator of Minimal Problem Solvers , 2008, ECCV.

[11]  Marc Pollefeys,et al.  A 4-point algorithm for relative pose estimation of a calibrated camera with a known relative rotation angle , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[12]  W. Gellert,et al.  The VNR concise encyclopedia of mathematics , 1977 .

[13]  Jan-Michael Frahm,et al.  A new minimal solution to the relative pose of a calibrated stereo camera with small field of view overlap , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[14]  Carolina Raposo,et al.  Theory and Practice of Structure-From-Motion Using Affine Correspondences , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[15]  Jiri Matas,et al.  Randomized RANSAC with Td, d test , 2004, Image Vis. Comput..

[16]  Marc Pollefeys,et al.  Motion Estimation for Self-Driving Cars with a Generalized Camera , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[17]  Gary R. Bradski,et al.  ORB: An efficient alternative to SIFT or SURF , 2011, 2011 International Conference on Computer Vision.

[18]  Hongdong Li.  A Simple Solution to the Six-Point Two-View Focal-Length Problem , 2006, ECCV.

[19]  Jiri Matas,et al.  Epipolar Geometry from Two Correspondences , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[20]  David Nistér,et al.  An efficient solution to the five-point relative pose problem , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.