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Zero-Shot Image Feature Consensus with Deep Functional Maps (2403.12038v1)

Published 18 Mar 2024 in cs.CV

Abstract: Correspondences emerge from large-scale vision models trained for generative and discriminative tasks. This has been revealed and benchmarked by computing correspondence maps between pairs of images, using nearest neighbors on the feature grids. Existing work has attempted to improve the quality of these correspondence maps by carefully mixing features from different sources, such as by combining the features of different layers or networks. We point out that a better correspondence strategy is available, which directly imposes structure on the correspondence field: the functional map. Wielding this simple mathematical tool, we lift the correspondence problem from the pixel space to the function space and directly optimize for mappings that are globally coherent. We demonstrate that our technique yields correspondences that are not only smoother but also more accurate, with the possibility of better reflecting the knowledge embedded in the large-scale vision models that we are studying. Our approach sets a new state-of-the-art on various dense correspondence tasks. We also demonstrate our effectiveness in keypoint correspondence and affordance map transfer.

Citations (1)

Summary

  • The paper's main contribution is a novel zero-shot framework that leverages deep functional maps to enforce global coherence in image correspondences.
  • It converts pixel matching into a function space consensus process using pre-trained vision model features and Laplacian eigenfunctions to improve robustness against occlusions.
  • Experimental results show state-of-the-art performance with enhanced PCK and smoothness metrics on benchmark datasets such as TSS and SPair-71k.

Zero-Shot Image Feature Consensus with Deep Functional Maps

The paper "Zero-Shot Image Feature Consensus with Deep Functional Maps" addresses a critical challenge in mid-level computer vision tasks: constructing accurate image correspondences. Although large-scale vision models possess emergent abilities for dense correspondences, they often grapple with retaining global structure due to inherent distortions in nearest-neighbor search processes. To overcome these challenges, the paper proposes a novel methodology leveraging functional maps and feature representations from pre-trained large-scale vision models to improve the quality of image correspondence maps without additional fine-tuning or task-specific training.

Core Methodology

The authors' approach diverges from traditional pixel-space nearest neighbor queries. Instead, they propose transitioning from pixel-based correspondence problems to a function space, thereby using a structured technique that ensures global coherence. This is accomplished through functional maps, originally from computer graphics, which provide a robust alternative by viewing dense correspondences as linear mappings between function spaces. The functional maps embody a low-dimensional yet expressive representation, thus effectively incorporating global structures into the matching process.

The methodology consists of two phases: computing the Laplacian eigenfunction basis from one set of image features and optimizing the functional map with another feature set acting as a regularizer. This dual-process provides a consensus between features extracted from distinct models, for instance, DINOv2 and Stable Diffusion. The functional mapping optimizes through a consensus process in the spectral domain, influenced by refined feature sets, thus increasing robustness to partial correspondences and occlusions through a deep partial functional map framework.

Experimental Findings

Detailed evaluations show the framework sets a new benchmark on dense correspondence tasks, demonstrating strong numerical results across various datasets, such as TSS and SPair-71k. The framework outperforms existing state-of-the-art zero-shot methods in terms of percentage of correct keypoints (PCK) and smoothness metrics, showcasing its superior ability to generate point-wise accurate and globally coherent correspondences. Moreover, it demonstrates robust performance even in challenging scenarios with significant shape variations and occlusions, highlighting the efficacy of integrating structure-aware functional maps.

Theoretical and Practical Implications

The proposed framework significantly advances the current state of image correspondence research by integrating insights from functional maps in computer graphics with contemporary vision models. The theoretical implications are profound, as the method pioneers the practical application of functional maps in image correspondence, thus creating an innovative crossover between deep learning and computer vision.

Practically, the paper presents a substantial leap for various applications, such as image editing and composition, by affording accurate correspondences without the need for supervised training. Moreover, this approach can be instrumental in tasks requiring robust feature alignment across different domains, such as medical imaging or augmented reality.

Future Directions and Speculation

The work opens several avenues for future research. Integrating this approach with generative models could further enhance the quality of image synthesis and manipulation tasks. Additionally, its application to more complex scene compositions, beyond object-centric images, could be explored by incorporating advanced segmentation algorithms. Finally, scaling to larger datasets and extending this consensus framework to video data represent promising directions for expanding its applicability.

In summary, the proposed use of deep functional maps in zero-shot feature consensus sets a high bar in image correspondence, effectively leveraging the global structure of pre-trained model features. Its ability to enhance both the accuracy and coherence of correspondences without direct supervision marks a significant advancement in the field, inspiring future research towards more generalized and robust image correspondence methods.