Most existing person re-identification algorithms either extract robust visual features or learn discriminative metrics for person images. However, the underlying manifold which those images reside on is rarely investigated. That raises a problem that the learned metric is not smooth with respect to the local geometry structure of the data manifold. In this paper, we study person re-identification with manifold-based affinity learning, which did not receive enough attention from this area. An unconventional manifold-preserving algorithm is proposed, which can 1) make the best use of supervision from training data, whose label information is given as pairwise constraints; 2) scale up to large repositories with low on-line time complexity; and 3) be plunged into most existing algorithms, serving as a generic postprocessing procedure to further boost the identification accuracies. Extensive experimental results on five popular person re-identification benchmarks consistently demonstrate the effectiveness of our method. Especially, on the largest CUHK03 and Market-1501, our method outperforms the state-of-the-art alternatives by a large margin with high efficiency, which is more appropriate for practical applications.
The manifold structure has been observed by several works. Motivated by the fact that pedestrian data are distributed on a highly curved manifold, a sampling strategy for training neural network called Moderate Positive Mining (MPM) is proposed in @cite_39 . However, considering the data distribution is hard to define, MPM does aim at estimating the geodesic distances along the manifold. From this point of view, SSM explicitly learns the geodesic distances between instances, which can be directly used for re-identification.
@cite_39
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A new architecture, denoted spatial pyramid matching on the semantic manifold (SPMSM), is proposed for scene recognition. SPMSM is based on a recent image representation on a semantic probability simplex, which is now augmented with a rough encoding of spatial information. A connection between the semantic simplex and a Riemmanian manifold is established, so as to equip the architecture with a similarity measure that respects the manifold structure of the semantic space. It is then argued that the closed-form geodesic distance between two manifold points is a natural measure of similarity between images. This leads to a conditionally positive definite kernel that can be used with any SVM classifier. An approximation of the geodesic distance reveals connections to the well-known Bhattacharyya kernel, and is explored to derive an explicit feature embedding for this kernel, by simple square-rooting. This enables a low-complexity SVM implementation, using a linear SVM on the embedded features. Several experiments are reported, comparing SPMSM to state-of-the-art recognition methods. SPMSM is shown to achieve the best recognition rates in the literature for two large datasets (MIT Indoor and SUN) and rates equivalent or superior to the state-of-the-art on a number of smaller datasets. In all cases, the resulting SVM also has much smaller dimensionality and requires much fewer support vectors than previous classifiers. This guarantees much smaller complexity and suggests improved generalization beyond the datasets considered. Person re-identification is challenging due to the large variations of pose, illumination, occlusion and camera view. Owing to these variations, the pedestrian data is distributed as highly-curved manifolds in the feature space, despite the current convolutional neural networks (CNN)’s capability of feature extraction. However, the distribution is unknown, so it is difficult to use the geodesic distance when comparing two samples. In practice, the current deep embedding methods use the Euclidean distance for the training and test. On the other hand, the manifold learning methods suggest to use the Euclidean distance in the local range, combining with the graphical relationship between samples, for approximating the geodesic distance. From this point of view, selecting suitable positive (i.e. intra-class) training samples within a local range is critical for training the CNN embedding, especially when the data has large intra-class variations. In this paper, we propose a novel moderate positive sample mining method to train robust CNN for person re-identification, dealing with the problem of large variation. In addition, we improve the learning by a metric weight constraint, so that the learned metric has a better generalization ability. Experiments show that these two strategies are effective in learning robust deep metrics for person re-identification, and accordingly our deep model significantly outperforms the state-of-the-art methods on several benchmarks of person re-identification. Therefore, the study presented in this paper may be useful in inspiring new designs of deep models for person re-identification. In this work we present a novel unsupervised framework for hard training example mining. The only input to the method is a collection of images relevant to the target application and a meaningful initial representation, provided e.g. by pre-trained CNN. Positive examples are distant points on a single manifold, while negative examples are nearby points on different manifolds. Both types of examples are revealed by disagreements between Euclidean and manifold similarities. The discovered examples can be used in training with any discriminative loss. The method is applied to unsupervised fine-tuning of pre-trained networks for fine-grained classification and particular object retrieval. Our models are on par or are outperforming prior models that are fully or partially supervised. In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the advantage to bring naturally a second desirable quantity when comparing shapes -- the spatial covariance -- in addition to the conventional affine-shape representation. We derive then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the manifold. Specifically, our approach involves three steps: 1) facial landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of rank 2, to build time-parameterized trajectories; 2) a temporal alignment is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; 3) finally, pairwise proximity function SVM (ppfSVM) is used to classify them, incorporating the latter (dis-)similarity measure into the kernel function. We show the effectiveness of the proposed approach on four publicly available benchmarks (CK+, MMI, Oulu-CASIA, and AFEW). The results of the proposed approach are comparable to or better than the state-of-the-art methods when involving only facial landmarks.