Age estimation from facial images is typically cast as a nonlinear regression problem. The main challenge of this problem is the facial feature space w.r.t. ages is heterogeneous, due to the large variation in facial appearance across different persons of the same age and the non-stationary property of aging patterns. In this paper, we propose Deep Regression Forests (DRFs), an end-to-end model, for age estimation. DRFs connect the split nodes to a fully connected layer of a convolutional neural network (CNN) and deal with heterogeneous data by jointly learning input-dependant data partitions at the split nodes and data abstractions at the leaf nodes. This joint learning follows an alternating strategy: First, by fixing the leaf nodes, the split nodes as well as the CNN parameters are optimized by Back-propagation; Then, by fixing the split nodes, the leaf nodes are optimized by iterating a step-size free and fast-converging update rule derived from Variational Bounding. We verify the proposed DRFs on three standard age estimation benchmarks and achieve state-of-the-art results on all of them.
 In this paper, we propose an ordinal hyperplane ranking algorithm called OHRank, which estimates human ages via facial images. The design of the algorithm is based on the relative order information among the age labels in a database. Each ordinal hyperplane separates all the facial images into two groups according to the relative order, and a cost-sensitive property is exploited to find better hyperplanes based on the classification costs. Human ages are inferred by aggregating a set of preferences from the ordinal hyperplanes with their cost sensitivities. Our experimental results demonstrate that the proposed approach outperforms conventional multiclass-based and regression-based approaches as well as recently developed ranking-based age estimation approaches. Although multi-label learning can deal with many problems with label ambiguity, it does not fit some real applications well where the overall distribution of the importance of the labels matters. This paper proposes a novel learning paradigm named label distribution learning (LDL) for such kind of applications. The label distribution covers a certain number of labels, representing the degree to which each label describes the instance. LDL is a more general learning framework which includes both single-label and multi-label learning as its special cases. This paper proposes six working LDL algorithms in three ways: problem transformation, algorithm adaptation, and specialized algorithm design. In order to compare the performance of the LDL algorithms, six representative and diverse evaluation measures are selected via a clustering analysis, and the first batch of label distribution datasets are collected and made publicly available. Experimental results on one artificial and 15 real-world datasets show clear advantages of the specialized algorithms, which indicates the importance of special design for the characteristics of the LDL problem. Nonlinear regression is a common statistical tool to solve many computer vision problems (e.g., age estimation, pose estimation). Existing approaches to nonlinear regression fall into two main categories: (1) The universal approach provides an implicit or explicit homogeneous feature mapping (e.g., kernel ridge regression, Gaussian process regression, neural networks). These approaches may fail when data is heterogeneous or discontinuous. (2) Divide-and-conquer approaches partition a heterogeneous input feature space and learn multiple local regressors. However, existing divide-and-conquer approaches fail to deal with discontinuities between partitions (e.g., Gaussian mixture of regressions) and they cannot guarantee that the partitioned input space will be homogeneously modeled by local regressors (e.g., ordinal regression). To address these issues, this paper proposes Soft-Margin Mixture of Regressions (SMMR), a method that directly learns homogeneous partitions of the input space and is able to deal with discontinuities. SMMR outperforms the state-of-the-art methods on three popular computer vision tasks: age estimation, crowd counting and viewpoint estimation from images.  One of the main difficulties in facial age estimation is that the learning algorithms cannot expect sufficient and complete training data. Fortunately, the faces at close ages look quite similar since aging is a slow and smooth process. Inspired by this observation, instead of considering each face image as an instance with one label (age), this paper regards each face image as an instance associated with a label distribution. The label distribution covers a certain number of class labels, representing the degree that each label describes the instance. Through this way, one face image can contribute to not only the learning of its chronological age, but also the learning of its adjacent ages. Two algorithms, named IIS-LLD and CPNN, are proposed to learn from such label distributions. Experimental results on two aging face databases show remarkable advantages of the proposed label distribution learning algorithms over the compared single-label learning algorithms, either specially designed for age estimation or for general purpose. By observing that the faces at close ages are similar, some Label Distribution Learning (LDL) methods have been proposed to solve age estimation tasks that they treat age distributions as the training targets. However, these existent LDL methods are limited because they can hardly extract enough useful information from complex image features. In this paper, Sparsity Conditional Energy Label Distribution Learning (SCE-LDL) is proposed to solve this problem. In the proposed SCE-LDL, age distributions are used as the training targets and energy function is utilized to define the age distribution. By assigning a suitable energy function, SCE-LDL can learn distributed representations, which provides the model with strong expressiveness for capturing enough of the complexity of interest from image features. The sparsity constraints are also incorporated to ameliorate the model. Experiment results in two age datasets show remarkable advantages of the proposed SCE-LDL model over the previous proposed age estimation methods. 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.  Human age is considered an important biometric trait for human identification or search. Recent research shows that the aging features deeply learned from large-scale data lead to significant performance improvement on facial image-based age estimation. However, age-related ordinal information is totally ignored in these approaches. In this paper, we propose a novel Convolutional Neural Network (CNN)-based framework, ranking-CNN, for age estimation. Ranking-CNN contains a series of basic CNNs, each of which is trained with ordinal age labels. Then, their binary outputs are aggregated for the final age prediction. We theoretically obtain a much tighter error bound for ranking-based age estimation. Moreover, we rigorously prove that ranking-CNN is more likely to get smaller estimation errors when compared with multi-class classification approaches. Through extensive experiments, we show that statistically, ranking-CNN significantly outperforms other state-of-the-art age estimation models on benchmark datasets.