Depth estimation from single monocular images is a key component of scene understanding and has benefited largely from deep convolutional neural networks (CNN) recently. In this article, we take advantage of the recent deep residual networks and propose a simple yet effective approach to this problem. We formulate depth estimation as a pixel-wise classification task. Specifically, we first discretize the continuous depth values into multiple bins and label the bins according to their depth range. Then we train fully convolutional deep residual networks to predict the depth label of each pixel. Performing discrete depth label classification instead of continuous depth value regression allows us to predict a confidence in the form of probability distribution. We further apply fully-connected conditional random fields (CRF) as a post processing step to enforce local smoothness interactions, which improves the results. We evaluate our approach on both indoor and outdoor datasets and achieve state-of-the-art performance.
Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57 error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28 relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation. 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. This paper addresses the problem of estimating the depth map of a scene given a single RGB image. We propose a fully convolutional architecture, encompassing residual learning, to model the ambiguous mapping between monocular images and depth maps. In order to improve the output resolution, we present a novel way to efficiently learn feature map up-sampling within the network. For optimization, we introduce the reverse Huber loss that is particularly suited for the task at hand and driven by the value distributions commonly present in depth maps. Our model is composed of a single architecture that is trained end-to-end and does not rely on post-processing techniques, such as CRFs or other additional refinement steps. As a result, it runs in real-time on images or videos. In the evaluation, we show that the proposed model contains fewer parameters and requires fewer training data than the current state of the art, while outperforming all approaches on depth estimation. Code and models are publicly available.