Dynamic textures exist in various forms, e.g., fire, smoke, and traffic jams, but recognizing dynamic texture is challenging due to the complex temporal variations. In this paper, we present a novel approach stemmed from slow feature analysis (SFA) for dynamic texture recognition. SFA extracts slowly varying features from fast varying signals. Fortunately, SFA is capable to leach invariant representations from dynamic textures. However, complex temporal variations require high-level semantic representations to fully achieve temporal slowness, and thus it is impractical to learn a high-level representation from dynamic textures directly by SFA. In order to learn a robust low-level feature to resolve the complexity of dynamic textures, we propose manifold regularized SFA (MR-SFA) by exploring the neighbor relationship of the initial state of each temporal transition and retaining the locality of their variations. Therefore, the learned features are not only slowly varying, but also partly predictable. MR-SFA for dynamic texture recognition is proposed in the following steps: 1) learning feature extraction functions as convolution filters by MR-SFA, 2) extracting local features by convolution and pooling, and 3) employing Fisher vectors to form a video-level representation for classification. Experimental results on dynamic texture and dynamic scene recognition datasets validate the effectiveness of the proposed approach.
A linear dynamical systems (LDS) approach for dynamic texture recognition was proposed assuming that dynamic textures are stationary stochastic processes @cite_22 . LDS is a statistical generative model. It can be further used for dynamic texture synthesis @cite_30 . The recognition is performed by comparing the parameters of LDS. Some kernel methods and distance learning approaches were then proposed to improve the comparison @cite_47 @cite_17 ; however, their results are still limited by LDS-based features, which cannot handle different viewpoints, scales, or other aspects. A bag-of-words model based on LDS features was proposed to improve conventional LDS-based approaches @cite_46 . Then, the bag-of-system-trees was further proposed for better efficiency @cite_37 . Extreme learning machine (ELM) was applied to construct the codebook of LDS features while preserving the spatial and temporal characteristics of dynamic textures @cite_18 . A hierarchical expectation maximization algorithm was proposed to cluster dynamic textures using LDS features @cite_48 . The mixture of LDS was also exploited for modeling, clustering and segmenting dynamic textures @cite_31 . Although LDS is reasonable and intuitive, it tends to suffer from complex temporal variations in the sequential process.
@cite_30 @cite_37 @cite_18 @cite_31 @cite_22 @cite_46 @cite_48 @cite_47 @cite_17
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We consider the problem of categorizing video sequences of dynamic textures, i.e., nonrigid dynamical objects such as fire, water, steam, flags, etc. This problem is extremely challenging because the shape and appearance of a dynamic texture continuously change as a function of time. State-of-the-art dynamic texture categorization methods have been successful at classifying videos taken from the same viewpoint and scale by using a Linear Dynamical System (LDS) to model each video, and using distances or kernels in the space of LDSs to classify the videos. However, these methods perform poorly when the video sequences are taken under a different viewpoint or scale. In this paper, we propose a novel dynamic texture categorization framework that can handle such changes. We model each video sequence with a collection of LDSs, each one describing a small spatiotemporal patch extracted from the video. This Bag-of-Systems (BoS) representation is analogous to the Bag-of-Features (BoF) representation for object recognition, except that we use LDSs as feature descriptors. This choice poses several technical challenges in adopting the traditional BoF approach. Most notably, the space of LDSs is not euclidean; hence, novel methods for clustering LDSs and computing codewords of LDSs need to be developed. We propose a framework that makes use of nonlinear dimensionality reduction and clustering techniques combined with the Martin distance for LDSs to tackle these issues. Our experiments compare the proposed BoS approach to existing dynamic texture categorization methods and show that it can be used for recognizing dynamic textures in challenging scenarios which could not be handled by existing methods. System theoretic approaches to action recognition model the dynamics of a scene with linear dynamical systems (LDSs) and perform classification using metrics on the space of LDSs, e.g. Binet-Cauchy kernels. However, such approaches are only applicable to time series data living in a Euclidean space, e.g. joint trajectories extracted from motion capture data or feature point trajectories extracted from video. Much of the success of recent object recognition techniques relies on the use of more complex feature descriptors, such as SIFT descriptors or HOG descriptors, which are essentially histograms. Since histograms live in a non-Euclidean space, we can no longer model their temporal evolution with LDSs, nor can we classify them using a metric for LDSs. In this paper, we propose to represent each frame of a video using a histogram of oriented optical flow (HOOF) and to recognize human actions by classifying HOOF time-series. For this purpose, we propose a generalization of the Binet-Cauchy kernels to nonlinear dynamical systems (NLDS) whose output lives in a non-Euclidean space, e.g. the space of histograms. This can be achieved by using kernels defined on the original non-Euclidean space, leading to a well-defined metric for NLDSs. We use these kernels for the classification of actions in video sequences using (HOOF) as the output of the NLDS. We evaluate our approach to recognition of human actions in several scenarios and achieve encouraging results. Abstract: We propose local distributional smoothness (LDS), a new notion of smoothness for statistical model that can be used as a regularization term to promote the smoothness of the model distribution. We named the LDS based regularization as virtual adversarial training (VAT). The LDS of a model at an input datapoint is defined as the KL-divergence based robustness of the model distribution against local perturbation around the datapoint. VAT resembles adversarial training, but distinguishes itself in that it determines the adversarial direction from the model distribution alone without using the label information, making it applicable to semi-supervised learning. The computational cost for VAT is relatively low. For neural network, the approximated gradient of the LDS can be computed with no more than three pairs of forward and back propagations. When we applied our technique to supervised and semi-supervised learning for the MNIST dataset, it outperformed all the training methods other than the current state of the art method, which is based on a highly advanced generative model. We also applied our method to SVHN and NORB, and confirmed our method's superior performance over the current state of the art semi-supervised method applied to these datasets. In this paper we present a novel approach for representing trajectories using sequenced linear dynamical systems. This method uses a closed-form least-squares procedure to fit a single linear dynamical system (LDS) to a simple trajectory. These LDS estimates form the elemental building blocks used to describe complicated trajectories through an automatic segmentation procedure that can represent complicated trajectories with high accuracy. Each estimated LDS induces a control law, mapping current state to desired state, that encodes the target trajectory in a generative manner. We provide a proof of stability of the control law and show how multiple trajectories can be incorporated to improve the generalization ability of the system.