Solving the Blind Perspective-n-Point Problem End-To-End With Robust Differentiable Geometric Optimization (2007.14628v2)

Abstract: Blind Perspective-n-Point (PnP) is the problem of estimating the position and orientation of a camera relative to a scene, given 2D image points and 3D scene points, without prior knowledge of the 2D-3D correspondences. Solving for pose and correspondences simultaneously is extremely challenging since the search space is very large. Fortunately it is a coupled problem: the pose can be found easily given the correspondences and vice versa. Existing approaches assume that noisy correspondences are provided, that a good pose prior is available, or that the problem size is small. We instead propose the first fully end-to-end trainable network for solving the blind PnP problem efficiently and globally, that is, without the need for pose priors. We make use of recent results in differentiating optimization problems to incorporate geometric model fitting into an end-to-end learning framework, including Sinkhorn, RANSAC and PnP algorithms. Our proposed approach significantly outperforms other methods on synthetic and real data.

• The paper introduces a novel end-to-end network that leverages differentiable geometric optimization to resolve camera pose estimation and 2D-3D correspondence simultaneously.
• It employs advanced methods like Sinkhorn matching, RANSAC, and nonlinear PnP solvers, significantly enhancing accuracy and computational efficiency over traditional techniques.
• The integration of declarative layers within the neural network opens new avenues for applications in augmented reality, visual localization, and autonomous navigation.

Solving the Blind Perspective-n-Point Problem End-To-End With Robust Differentiable Geometric Optimization

In camera pose estimation, the blind Perspective-n-Point (PnP) problem represents an advanced task of determining the orientation and position of a camera relative to a given scene, using 2D image points and 3D scene points, absent any prior knowledge about the correspondences between these points. This problem is particularly formidable due to its expansive search space and the intrinsic challenge of simultaneously solving for pose and correspondences. Addressing this problem, Campbell et al. introduce a novel, fully end-to-end trainable network integrating robust geometric optimization techniques with deep learning architectures, promising a comprehensive solution without requiring pose priors.

Technical Overview

The proposed approach leverages recent advances in differentiable optimization, specifically embedding geometric model fitting and robust estimation algorithms such as Sinkhorn, RANSAC, and PnP into a neural network framework. This integration is made possible through the adoption of deep declarative networks, which allow complex optimization problems to be encapsulated as differentiable layers. Unlike traditional techniques which rely heavily on iterative and non-differentiable processes, this method facilitates seamless back-propagation through the optimization stages, allowing them to become part of the learning process.

Core Components

1. Feature Extraction and Matching: The initial stage of the network involves extracting point-wise features from 2D and 3D coordinates using conventional network layers. These features are then matched using the Sinkhorn algorithm to create a joint probability matrix representing potential 2D--3D correspondences effectively.
2. Optimization Framework: Employing RANSAC for robust initial estimates, the network refines these estimates using a nonlinear PnP solver, optimizing a probability-weighted objective function. This sequence significantly outperforms traditional methods in terms of accuracy and computational efficiency.
3. Declarative Layers: This work demonstrates the novel incorporation of mathematical optimization procedures as declarative layers within a neural network. Declarative layers enable the network to manage non-differentiable steps internally, maintaining end-to-end differentiability. The efficacy of this novel approach is evident in its superior performance metrics compared to existing solutions.

Implications and Future Directions

The implications of this research are manifold, providing a potent tool for computer vision applications such as augmented reality and visual localization without visual information. The use of geometric rather than visual features enhances generalizability across variable conditions, such as changing weather or lighting. The results from benchmarks on synthetic and real datasets affirm the network's capacity to surpass traditional boundaries, solving the blind PnP problem efficiently and accurately on large-scale tasks previously thought intractable.

Looking ahead, the potential to fine-tune this network in an unsupervised manner using scene-specific test data could offer pivotal advancements in AI and robotics, particularly in autonomous navigation and multi-modal localization tasks. Further exploration into refining the architecture and enabling broader applications beyond pose estimation could substantially impact a range of sectors reliant on spatial awareness and scene understanding.

In conclusion, Campbell et al.'s proposed methodology marks a significant step forward in camera pose estimation, showcasing the potential of combining differentiable geometric optimization with deep learning. This fusion opens avenues for robust, scalable solutions in complex, real-world environments, pushing the envelope of what is possible in AI-driven scene understanding.