Geometric Loss Functions for Camera Pose Regression with Deep Learning (1704.00390v2)

Abstract: Deep learning has shown to be effective for robust and real-time monocular image relocalisation. In particular, PoseNet is a deep convolutional neural network which learns to regress the 6-DOF camera pose from a single image. It learns to localize using high level features and is robust to difficult lighting, motion blur and unknown camera intrinsics, where point based SIFT registration fails. However, it was trained using a naive loss function, with hyper-parameters which require expensive tuning. In this paper, we give the problem a more fundamental theoretical treatment. We explore a number of novel loss functions for learning camera pose which are based on geometry and scene reprojection error. Additionally we show how to automatically learn an optimal weighting to simultaneously regress position and orientation. By leveraging geometry, we demonstrate that our technique significantly improves PoseNet's performance across datasets ranging from indoor rooms to a small city.

• The paper introduces novel geometric loss functions that balance position and orientation errors automatically to improve camera pose regression.
• It leverages quaternion representations and learned uncertainty modeling to eliminate extensive manual hyper-parameter tuning.
• Experimental evaluations on multiple datasets show significant accuracy gains in both positional and rotational estimates compared to conventional methods.

Geometric Loss Functions for Camera Pose Regression with Deep Learning

The paper "Geometric loss functions for camera pose regression with deep learning" by Alex Kendall and Roberto Cipolla from the University of Cambridge explores advanced methodologies for improving the performance of deep learning-based camera pose estimation. The primary focus of this research is the enhancement of PoseNet, a convolutional neural network (CNN) architecture designed for predicting 6-DOF camera pose from a single monocular image.

Introduction

PoseNet demonstrated considerable robustness for tasks involving monocular image-based relocalisation. However, the original implementation utilized a naive loss function requiring manual hyper-parameter tuning, which did not fully leverage geometric constraints. This paper proposes a series of novel loss functions that integrate geometric insights, thereby facilitating automatic tuning of necessary parameters and improving overall accuracy.

Methodology

Pose Representation

The deep learning model estimates the 6-DOF camera pose as a combination of position (3D) and orientation (quaternion). The research emphasizes using quaternions due to their smooth, continuous representation and ease of incorporation into back-propagation frameworks. Quaternions avoid the pitfalls of gimbal lock encountered with Euler angles and provide direct normalization to unit length, facilitating robust learning of rotational quantities.

Loss Functions

The paper explores several loss functions:

1. Weighted Sum of Position and Orientation Losses: Initially, PoseNet employed a linear sum of Euclidean loss in position and orientation, balanced using a constant scaling factor. This required significant manual tuning.
2. Learned Weighting via Homoscedastic Uncertainty: This approach automatically learns the optimal weighting between position and orientation by modeling the respective homoscedastic uncertainties. It effectively balances the differential scales and units of positional and rotational errors, enhancing the accuracy of the regression task.
3. Geometric Reprojection Error: Incorporating scene geometry directly, this loss function computes the reprojection error of known 3D points onto the 2D image plane, integrating both position and orientation into a single scalar value. The approach aligns with multi-view geometry principles, automatically adjusting the pose error based on scene-specific constraints.

Experimental Results

The efficacy of the proposed loss functions was validated across several datasets, including indoor (7 Scenes) and outdoor (Cambridge Landmarks and Dubrovnik 6K) environments. Key observations include:

• The learned weighting approach significantly improves performance by reducing median positional and rotational errors compared to the original PoseNet. For instance, on the King's College dataset, it achieves errors of 0.99 meters in position and 1.06 degrees in orientation.
• The geometric reprojection loss did not converge effectively from random initializations, likely due to sensitivity to large initial pose errors. However, when fine-tuning pre-trained models, it yielded the most accurate results, especially in rotational estimates.

Discussion and Implications

The introduction of geometric constraints via reprojection error represents a significant step towards more principled, theory-grounded pose regression using deep learning. The automatic balancing of pose components through uncertainty modeling mitigates the need for extensive manual hyper-parameter tuning, enhancing practical usability. Furthermore, this work narrows the accuracy gap between deep learning approaches and traditional SIFT-based methods, which remain state-of-the-art in large-scale, feature-rich localization tasks.

Future Directions

Potential future directions highlighted by the authors include extending the architecture to handle video inputs, leveraging temporal coherence for improved pose estimates. Additionally, integrating multi-view stereo techniques could further refine localization accuracy, making these approaches viable for real-time applications in mobile robotics and augmented reality.

Conclusion

This paper significantly advances the deep learning-based camera pose regression by introducing loss functions grounded in geometric principles. These methods enhance PoseNet's robustness and accuracy, reducing the dependency on manual parameter tuning and laying the groundwork for future research in real-time, scalable visual localization systems. By integrating decades of research in multi-view geometry with modern deep learning frameworks, this work bridges the gap between theoretical rigor and practical applicability in computer vision.