Deep Convolutional Neural Fields for Depth Estimation from a Single Image (1411.6387v2)

Abstract: We consider the problem of depth estimation from a single monocular image in this work. It is a challenging task as no reliable depth cues are available, e.g., stereo correspondences, motions, etc. Previous efforts have been focusing on exploiting geometric priors or additional sources of information, with all using hand-crafted features. Recently, there is mounting evidence that features from deep convolutional neural networks (CNN) are setting new records for various vision applications. On the other hand, considering the continuous characteristic of the depth values, depth estimations can be naturally formulated into a continuous conditional random field (CRF) learning problem. Therefore, we in this paper present a deep convolutional neural field model for estimating depths from a single image, aiming to jointly explore the capacity of deep CNN and continuous CRF. Specifically, we propose a deep structured learning scheme which learns the unary and pairwise potentials of continuous CRF in a unified deep CNN framework. The proposed method can be used for depth estimations of general scenes with no geometric priors nor any extra information injected. In our case, the integral of the partition function can be analytically calculated, thus we can exactly solve the log-likelihood optimization. Moreover, solving the MAP problem for predicting depths of a new image is highly efficient as closed-form solutions exist. We experimentally demonstrate that the proposed method outperforms state-of-the-art depth estimation methods on both indoor and outdoor scene datasets.

• The paper introduces a unified framework that fuses CNN feature extraction with CRF-based structured prediction to estimate depth from monocular images.
• It jointly learns unary and pairwise potentials, enabling exact log-likelihood optimization and efficient MAP inference.
• Experiments on NYU Depth v2 and Make3D show significant improvements in RMS and relative errors across diverse indoor and outdoor scenes.

Deep Convolutional Neural Fields for Depth Estimation from a Single Image

The paper "Deep Convolutional Neural Fields for Depth Estimation from a Single Image" by Fayao Liu, Chunhua Shen, and Guosheng Lin presents a sophisticated approach to predicting depth from monocular images by integrating Deep Convolutional Neural Networks (CNNs) with Continuous Conditional Random Fields (CRFs). This integration uniquely leverages both the feature extraction capabilities of CNNs and the structured prediction strengths of CRFs.

Overview of the Contribution

The authors tackle the longstanding problem of depth estimation without relying on geometric priors or additional information like stereo correspondences or motion data. Monocular depth estimation is inherently challenging due to its ill-posed nature, and previous techniques have depended largely on hand-crafted features or have required geometric assumptions that limit their applicability to general scenes.

To address these challenges, the authors propose a unified framework that marries CNNs with continuous CRFs, termed as Deep Convolutional Neural Fields (DCNF). Specifically, they develop a deep structured learning scheme that concurrently learns unary and pairwise potentials within the continuous CRF model, utilizing the robust feature extraction capabilities of CNNs. This method allows for efficient depth estimation across diverse scenes.

Technical Details and Architecture

The model's architecture comprises three main components:

1. Unary Potential: Extracted using a CNN from segmented superpixels. The CNN includes five convolutional layers and four fully-connected layers. The output for each superpixel is a scalar depth value.
2. Pairwise Potential: Derived from various similarity metrics between neighboring superpixels, considering factors like color difference, color histogram difference, and texture disparity.
3. CRF Loss Layer: Jointly optimizes the unary and pairwise potentials, minimizing the negative log-likelihood of depth predictions using back propagation.

Key to the authors' approach is the ability to compute the integral of the partition function analytically, thereby allowing exact log-likelihood optimization without approximation. Solving the Maximum A Posteriori (MAP) problem, therefore, becomes efficient as it boils down to simple closed-form solutions.

Experimental Results

The authors demonstrate the efficacy of their model on two datasets: NYU Depth v2 (indoor scenes) and Make3D (outdoor scenes). The results reveal that their approach outperforms contemporary state-of-the-art methods:

• NYU v2: The method achieved significant performance improvements in root mean square (RMS) error and average relative error when compared with previous methods, including those relying on large annotated datasets for training.
• Make3D: The proposed method outperformed other advanced approaches, especially in terms of RMS error under both criteria (C1 and C2), indicating superior performance in diverse and complex outdoor scenes.

Notably, the authors' method achieves competitive results even without additional training data, which some other methods require to avoid overfitting. This underlines the strength of their integration of CNN and CRF in a deep learning framework.

Practical Implications

From a practical standpoint, the approach proposed in this paper offers significant advantages for applications requiring robust depth estimation from a single image. The method's efficiency in both training and inference, combined with its superior accuracy, makes it a valuable tool for various computer vision tasks, such as 3D modeling, scene understanding, and robotics.

Theoretical Implications and Future Directions

The exploration of combining CNNs with continuous CRFs opens new avenues for structured learning problems that extend beyond depth estimation. This pioneering model can inspire further research into hybrid architectures that exploit the strengths of multiple machine learning paradigms for structured prediction tasks.

Future work could explore extending this approach to other domains, such as image denoising and super-resolution, where structured outputs are essential. Additionally, exploring more advanced architectures for the pairwise component and incorporating more complex learned similarity metrics could further enhance performance.

In conclusion, this paper presents a robust and efficient method for monocular depth estimation, setting a new benchmark in the field by integrating deep convolutional neural networks with continuous conditional random fields. The results achieved on benchmark datasets underscore the potential of this approach to generalize across varied scenes and applications.