GOCor: Bringing Globally Optimized Correspondence Volumes into Your Neural Network (2009.07823v4)

Abstract: The feature correlation layer serves as a key neural network module in numerous computer vision problems that involve dense correspondences between image pairs. It predicts a correspondence volume by evaluating dense scalar products between feature vectors extracted from pairs of locations in two images. However, this point-to-point feature comparison is insufficient when disambiguating multiple similar regions in an image, severely affecting the performance of the end task. We propose GOCor, a fully differentiable dense matching module, acting as a direct replacement to the feature correlation layer. The correspondence volume generated by our module is the result of an internal optimization procedure that explicitly accounts for similar regions in the scene. Moreover, our approach is capable of effectively learning spatial matching priors to resolve further matching ambiguities. We analyze our GOCor module in extensive ablative experiments. When integrated into state-of-the-art networks, our approach significantly outperforms the feature correlation layer for the tasks of geometric matching, optical flow, and dense semantic matching. The code and trained models will be made available at github.com/PruneTruong/GOCor.

• The paper introduces GOCor, a novel neural network module that uses an internal optimization framework to generate more robust correspondence volumes than traditional correlation layers.
• GOCor minimizes a learnable objective function during inference, integrating spatial priors and constraints to effectively disambiguate repeated patterns and improve matching.
• Empirical results demonstrate that integrating GOCor into state-of-the-art networks significantly improves accuracy and robustness across various dense matching tasks and datasets bond the standard techniques.

An Analytical Overview of GOCor: Optimization-Based Correspondence Volumes for Enhanced Neural Networks

In the landscape of computer vision, accurately determining dense correspondences between image pairs remains a pivotal challenge, significantly impacting tasks such as optical flow, geometric matching, and dense semantic matching. The established method to achieve dense matching involves using feature correlation layers, which measure pairwise similarities between deep feature maps from two images. While this approach is prevalent, it encounters substantial limitations, particularly when dealing with repetitive patterns or low-textured regions in imagery. The paper "GOCor: Bringing Globally Optimized Correspondence Volumes into Your Neural Network" proposes an innovative neural network module, termed GOCor, that confronts these limitations by enhancing the feature correlation operation through an internal optimization framework.

Contributions of the GOCor Module

The development of the GOCor module introduces key improvements to the feature correlation paradigm. Notably, it is formulated to minimize an objective function during inference, consisting of explicit and learnable matching constraints. This function accounts for both similar regions within an image and spatial matching priors, addressing the inherent ambiguity in matching multiple similar regions. The paper highlights several important aspects:

1. Internal Optimization Procedure: GOCor leverages an optimization approach that minimizes a customizable matching objective during inference, which inherently integrates spatial priors and constraints.
2. Robust Correspondence Volume Generation: The optimization approach adopted allows the generation of a correspondence volume that effectively disambiguates repeated patterns by utilizing global information.
3. Utilization of Reference and Query Information: The module incorporates prior knowledge and information from both reference and query frames, enhancing the accuracy of the matching process.
4. Optimization Strategy with Efficient Training and Inference: The GOCor module employs steepest descent optimization, complemented with effective initialization, maintaining end-to-end differentiability and ensuring feasible computational overhead.
5. Wide Applicability and Performance Lift: Empirical evaluations show that when integrated into state-of-the-art architectures like GLU-Net and PWC-Net, GOCor markedly improves performance in terms of accuracy and robustness across varied tasks and datasets.

Methodology: From Correlation to Optimization

The methodological pivot from traditional feature correlation to GOCor's optimization-based perspective signifies a conceptual leap. The GOCor module consists of a learnable objective function that is minimized inside the network during inference. This setup allows the network to adjust its internal representations actively. GOCor applies a steepest descent method where the filter map, instead of merely relying on feature vector point correlations, is optimized to down-weight non-distinctive regions. The objective function comprises three terms: a referential term that emphasizes correct spatial locations, a matching constraint derived from the query, and regularization on the filter map itself.

Particularly, GOCor’s implementation embraces robust non-linear least squares objectives that weight positive and negative correlation contributions differently—focusing on suppressing non-matching positive correlations that could mislead the matching task.

Experimental Validation and Insights

The GOCor module's efficacy is validated across tasks involving geometric matching on HPatches and ETH3D, optical flow on KITTI and Sintel, and even semantic matching on TSS. On HPatches, GOCor demonstrated superior domain generalization, handling large inter-frame viewpoint changes effectively. For optical flow, improvements in metrics such as AEPE and F1-score confirmed its advantage over conventional feature correlation layers.

Furthermore, maintenance of robustness across various datasets signifies GOCor's enhanced generalization capabilities, a desirable feature considering the varied nature of real-world image content and motion patterns—factors often leading to domain shifts that undermine more static approaches.

Future Prospects and Broader Implications

The introduction of GOCor paves the way for future advancements in leveraging internal optimization strategies within neural architectures to better handle disparities and ambiguities inherent in visual correspondence tasks. It hints at a broader implication where optimization-driven approaches might replace several neural network heuristics, leading to more adaptable and theoretically grounded modules.

While the primary focus was to address limitations in spatial correspondence, the methodology embodies a general philosophy beneficial to other domains reliant on dense matching or alignment, such as 3D reconstruction, structure-from-motion, and even areas beyond computer vision like bioinformatics where motif matching is relevant.

Conclusion

GOCor's novel incorporation of globally optimized correspondence volumes into neural networks provides a vital enhancement to current computer vision methodologies. By fundamentally improving the handling of spatial ambiguities through robust optimization, it advances the frontier of what can be achieved with deep learning in dense matching tasks, heralding a shift toward more robust and adaptable neural network components. The paper succeeds in presenting a convincing case for this transition, backed by comprehensive experiments and promising results.