Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials (1210.5644v1)

Abstract: Most state-of-the-art techniques for multi-class image segmentation and labeling use conditional random fields defined over pixels or image regions. While region-level models often feature dense pairwise connectivity, pixel-level models are considerably larger and have only permitted sparse graph structures. In this paper, we consider fully connected CRF models defined on the complete set of pixels in an image. The resulting graphs have billions of edges, making traditional inference algorithms impractical. Our main contribution is a highly efficient approximate inference algorithm for fully connected CRF models in which the pairwise edge potentials are defined by a linear combination of Gaussian kernels. Our experiments demonstrate that dense connectivity at the pixel level substantially improves segmentation and labeling accuracy.

• The paper proposes a mean field approximation that leverages Gaussian filtering for efficient inference in fully connected CRFs.
• It demonstrates significant improvements by reducing inference time to 0.2 seconds versus hours with traditional MCMC methods.
• The method enhances multi-class image segmentation performance, achieving notable accuracy gains on datasets like MSRC-21 and PASCAL VOC 2010.

Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials

Introduction

The paper "Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials" by Philipp Krahenbuhl and Vladlen Koltun addresses significant limitations in the current state-of-the-art techniques for multi-class image segmentation and labeling. Traditional CRF models, generally defined over pixels or image regions, have been restricted in their efficacy due to sparse graph structures and the inherent complexity of inference in fully connected models.

Core Contribution

The core contribution of this paper is the development of a highly efficient inference algorithm for fully connected CRF models where the pairwise edge potentials are expressed as a linear combination of Gaussian kernels. The innovation lies in utilizing a mean field approximation, iteratively optimized via message passing steps that employ Gaussian filtering in feature space to drastically reduce computational complexity.

Methodology

In this model, a random field $X$ over variables $\{X_1, \ldots, X_N\}$ assigns labels to each pixel, while another random field $I$ represents the input image. The CRF’s Gibbs energy integrates unary potentials, computed independently for each pixel, and pairwise potentials, represented as Gaussian kernels in arbitrary feature spaces.

The algorithm leverages mean field approximation to infer the CRF distribution efficiently. The primary computational challenge is addressed by reducing the quadratic complexity of message passing to linear by high-dimensional Gaussian filtering, specifically using a permutohedral lattice, which ensures the process is computationally feasible even for large, fully connected CRFs.

Results

Quantitative evaluations are conducted on the MSRC-21 and PASCAL VOC 2010 datasets. For the MSRC-21 dataset, the fully connected CRF model yields a global classification accuracy improvement to 86.0% compared to 84.6% for the grid CRF and 84.9% for the Robust P CRF. Similar enhancements are observed when using carefully annotated ground truth, particularly evaluating boundary accuracy through the trimap metric. The average class accuracy on PASCAL VOC 2010 is increased to 30.2% from the 27.6% achieved using unary potentials alone.

A striking result presented in the paper is the dramatic reduction in inference time. Where MCMC-based inference methods require up to 36 hours for an incomplete convergence, the proposed method achieves high-accuracy pixel labeling in merely 0.2 seconds on a single-threaded CPU implementation.

Implications

This research has substantial implications both theoretically and practically:

• Theoretical Implications: It demonstrates that efficient inference is achievable in fully connected CRF models through algorithmic innovations, challenging the traditionally limiting assumptions on model connectivity in image segmentation tasks.
• Practical Implications: The reduction in computational cost enables the deployment of these models in real-time applications, like autonomous vehicles and robotic vision systems, where quick and accurate segmentation is critical.

Future Directions

Potential future research directions include:

1. Parallelization: Exploiting GPU architectures and parallel processing to further reduce inference time.
2. Extended Feature Spaces: Investigating the integration of additional feature spaces beyond the color and position to enhance segmentation robustness.
3. Adaptation to Video: Applying these techniques to video segmentation tasks, which requires handling temporal coherence alongside spatial accuracy.

Conclusion

The paper provides a compelling advancement in the field of multi-class image segmentation through efficient inference in fully connected CRFs with Gaussian edge potentials. This has paved the way for future work to further explore the boundaries of CRF utility in high-dimensional and densely connected graph structures, fundamentally altering the landscape of image segmentation techniques.