Learning Depth from Single Monocular Images Using Deep Convolutional Neural Fields (1502.07411v6)

Abstract: In this article, we tackle the problem of depth estimation from single monocular images. Compared with depth estimation using multiple images such as stereo depth perception, depth from monocular images is much more challenging. Prior work typically focuses on exploiting geometric priors or additional sources of information, most using hand-crafted features. Recently, there is mounting evidence that features from deep convolutional neural networks (CNN) set new records for various vision applications. On the other hand, considering the continuous characteristic of the depth values, depth estimations can be naturally formulated as a continuous conditional random field (CRF) learning problem. Therefore, here we present a deep convolutional neural field model for estimating depths from single monocular images, aiming to jointly explore the capacity of deep CNN and continuous CRF. In particular, we propose a deep structured learning scheme which learns the unary and pairwise potentials of continuous CRF in a unified deep CNN framework. We then further propose an equally effective model based on fully convolutional networks and a novel superpixel pooling method, which is $\sim 10$ times faster, to speedup the patch-wise convolutions in the deep model. With this more efficient model, we are able to design deeper networks to pursue better performance. Experiments on both indoor and outdoor scene datasets demonstrate that the proposed method outperforms state-of-the-art depth estimation approaches.

• The paper proposes a unified DCNF model that learns unary and pairwise potentials from deep CNN features to accurately regress depth values.
• It integrates a fully convolutional network with superpixel pooling, significantly reducing computational overhead during training and prediction.
• Experimental results on NYU v2 and Make3D datasets show marked improvements in relative and RMS errors compared to existing state-of-the-art methods.

Essay on "Learning Depth from Single Monocular Images Using Deep Convolutional Neural Fields"

Introduction

The problem of estimating depth from single monocular images occupies a prominent role in computer vision, facilitating advances in areas such as semantic labeling and pose estimation. Traditional approaches generally rely on multi-image depth estimation techniques such as stereo vision. However, depth estimation from a single image is profoundly more challenging due to the ill-posed nature of the problem, where one image can correspond to multiple real-world scene configurations.

Research Contribution

This paper advances the field by introducing a novel method that leverages the strengths of Deep Convolutional Neural Networks (CNNs) and Continuous Conditional Random Fields (CRFs) to form a Deep Convolutional Neural Field (DCNF). Specifically, the method frames the depth estimation task within a unified CRF framework, where unary and pairwise potentials are learned simultaneously using a deep CNN, optimized via backpropagation.

Model Architecture and Innovations

The proposed DCNF model utilizes deep structured learning to unify the learning of unary and pairwise potentials within a deep CNN, bypassing the need for geometric priors and additional information. Further, the method includes an advanced variant—DCNF with Fully Convolutional Networks and Superpixel Pooling (DCNF-FCSP)—designed to expedite training and prediction processes. This variant performs convolution operations over the entire image once and employs superpixel pooling to associate convolution outputs with superpixels, drastically reducing computational overhead.

Methodological Details

1. Unary Potentials:
   • Constructed from deep CNN features with a least squares loss, the unary potentials aim to regress depth values for individual superpixels.
   • A network incorporating five convolutional layers and four fully connected layers extracts rich features which encode depth information.
2. Pairwise Potentials:
   • Modeled to enforce smoothness, these potentials consider multiple types of superpixel similarities (e.g., color differences, texture disparities).
   • The model employs a fully connected layer to output similarity measures for neighboring superpixels, integrated into the CRF to refine depth predictions.
3. Optimization:
   • The negative log-likelihood is minimized using stochastic gradient descent (SGD), facilitating efficient end-to-end learning.
   • Closed-form solutions to Maximum a Posteriori (MAP) problems ensure rapid depth prediction from new images.

Experimental Results

Experiments on the NYU v2 and Make3D datasets demonstrate that the DCNF model surpasses state-of-the-art methods. The adoption of deeper networks via the DCNF-FCSP further solidifies its performance enhancements. Measured against established benchmarks, the model attests to its superior capabilities in terms of relative error, RMS error, log10 error, and threshold accuracy.

Practical and Theoretical Implications

From a practical perspective, the unified approach simplifies depth estimation pipelines, obviating the need for secondary processing steps such as image retrieval or explicit geometric modeling. Theoretically, the formulation of depth estimation as a continuous CRF problem opens avenues for further research in structured regression tasks within computer vision. The robust performance underlines the potent synergy of CNNs and CRFs in handling continuous variable predictions.

Future Developments

Future research can exploit the flexibility of the proposed method in other computer vision applications such as image denoising and deblurring. Additionally, integrating geometric priors or other contextual information could refine the depth estimation further. Given the method’s efficiency, a real-time implementation could significantly impact applications in autonomous driving and augmented reality.

Conclusion

This paper presents a compelling case for the DCNF model in addressing the intricacies of monocular depth estimation. By leveraging deep convolutional architectures and structured continuous fields, it not only advances the state-of-the-art in depth prediction but also sets a framework that can be extended to other complex estimation tasks in computer vision. The combination of deep learning and probabilistic graphical models heralds a new direction for embedding structured learning within convolutional networks.