Error propagation in monocular navigation for Z∞ compared to eightpoint algorithm

Efficient visual pose estimation plays an important role for a variety of applications. To improve the quality, the measurements from different sensors can be fused. However, a reliable fusion requires the knowledge of the uncertainty of each estimate. In this work, we provide an error analysis for the Z ∞ algorithm. Furthermore, we extend the existing first-order error propagation for the 8-point algorithm to allow for feature normalization, as proposed by Hartley or Mühlich, and the rotation matrix based decomposition. Both methods are efficient visual odometry techniques which allow high frame-rates and, thus, dynamic motions in unbounded workspaces. Finally, we provide experiments which validate the accuracy of the error propagation and which enable a brief comparison, showing that the Z ∞ significantly outperforms the 8-point algorithm. We also discuss the influence of the number of features, the aperture angle, and the image resolution on the accuracy of the pose estimation.

Authors

• Elmar Mair
• Michael Suppa
• Darius Burschka

Keywords

• Estimation
• Vectors
• Covariance matrices
• Matrix decomposition
• Accuracy
• Cameras
• Motion estimation
• Error Propagation
• Monocular
• Eight-point Algorithm
• Pose Estimation
• High Frame Rate
• Accuracy Of Pose Estimation
• Estimation Error
• Field Of View
• Covariance Matrix
• Image Features
• Efficient Algorithm
• Singular Value
• Point Cloud
• Focal Length
• Corresponding Points
• Frobenius Norm
• Tracking Accuracy
• Upper Triangular
• Landmark Localization
• Root Mean Square Error Of Cross-validation
• Translation Vector
• Frobenius Norm Of A Matrix
• Isotropic Scaling
• Rotation Error
• Sensor Information
• Angular Resolution
• Measurement Uncertainty
• Errors In Order
• Coordinate Frame