Monocular depth estimation, which plays a crucial role in understanding 3D scene geometry, is an ill-posed problem. Recent methods have gained significant improvement by exploring image-level information and hierarchical features from deep convolutional neural networks (DCNNs). These methods model depth estimation as a regression problem and train the regression networks by minimizing mean squared error, which suffers from slow convergence and unsatisfactory local solutions. Besides, existing depth estimation networks employ repeated spatial pooling operations, resulting in undesirable low-resolution feature maps. To obtain high-resolution depth maps, skip-connections or multilayer deconvolution networks are required, which complicates network training and consumes much more computations. To eliminate or at least largely reduce these problems, we introduce a spacing-increasing discretization (SID) strategy to discretize depth and recast depth network learning as an ordinal regression problem. By training the network using an ordinary regression loss, our method achieves much higher accuracy and faster convergence in synch. Furthermore, we adopt a multi-scale network structure which avoids unnecessary spatial pooling and captures multi-scale information in parallel. The proposed deep ordinal regression network (DORN) achieves state-of-the-art results on three challenging benchmarks, i.e., KITTI [16], Make3D [49], and NYU Depth v2 [41], and outperforms existing methods by a large margin.
@cite_45 @cite_65 aims to learn a rule to predict labels from an ordinal scale. Most literatures modify well-studied classification algorithms to address ordinal regression algorithms. For example, Shashua and Levin @cite_23 handled multiple thresholds by developing a new SVM. Cammer and Singer @cite_51 generalized the online perceptron algorithms with multiple thresholds to do ordinal regression. Another way is to formulate ordinal regression as a set of binary classification subproblems. For instance, Frank and Hall @cite_25 applied some decision trees as binary classifiers for ordinal regression. In computer vision, ordinal regression has been combined with DCNNs to address the age estimation problem @cite_28 .
@cite_28 @cite_65 @cite_45 @cite_23 @cite_51 @cite_25
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We present a reduction framework from ordinal regression to binary classification based on extended examples. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and constructing a ranking rule from the binary classifier. A weighted 0 1 loss of the binary classifier would then bound the mislabeling cost of the ranking rule. Our framework allows not only to design good ordinal regression algorithms based on well-tuned binary classification approaches, but also to derive new generalization bounds for ordinal regression from known bounds for binary classification. In addition, our framework unifies many existing ordinal regression algorithms, such as perceptron ranking and support vector ordinal regression. When compared empirically on benchmark data sets, some of our newly designed algorithms enjoy advantages in terms of both training speed and generalization performance over existing algorithms, which demonstrates the usefulness of our framework. To address the non-stationary property of aging patterns, age estimation can be cast as an ordinal regression problem. However, the processes of extracting features and learning a regression model are often separated and optimized independently in previous work. In this paper, we propose an End-to-End learning approach to address ordinal regression problems using deep Convolutional Neural Network, which could simultaneously conduct feature learning and regression modeling. In particular, an ordinal regression problem is transformed into a series of binary classification sub-problems. And we propose a multiple output CNN learning algorithm to collectively solve these classification sub-problems, so that the correlation between these tasks could be explored. In addition, we publish an Asian Face Age Dataset (AFAD) containing more than 160K facial images with precise age ground-truths, which is the largest public age dataset to date. To the best of our knowledge, this is the first work to address ordinal regression problems by using CNN, and achieves the state-of-the-art performance on both the MORPH and AFAD datasets. In this letter, we propose two new support vector approaches for ordinal regression, which optimize multiple thresholds to define parallel discriminant hyperplanes for the ordinal scales. Both approaches guarantee that the thresholds are properly ordered at the optimal solution. The size of these optimization problems is linear in the number of training samples. The sequential minimal optimization algorithm is adapted for the resulting optimization problems; it is extremely easy to implement and scales efficiently as a quadratic function of the number of examples. The results of numerical experiments on some benchmark and real-world data sets, including applications of ordinal regression to information retrieval, verify the usefulness of these approaches. We investigate the problem of predicting variables of ordinal scale. This task is referred to as ordinal regression and is complementary to the standard machine learning tasks of classification and metric regression. In contrast to statistical models we present a distribution independent formulation of the problem together with uniform bounds of the risk functional. The approach presented is based on a mapping from objects to scalar utility values. Similar to support vector methods we derive a new learning algorithm for the task of ordinal regression based on large margin rank boundaries. We give experimental results for an information retrieval task: learning the order of documents with respect to an initial query. Experimental results indicate that the presented algorithm outperforms more naive approaches to ordinal regression such as support vector classification and support vector regression in the case of more than two ranks.