Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 3) DYNAMIC TEXTURE METHODS <s> A dynamic texture is a linear dynamical system used to model a single video as a sample from a spatio-temporal stochastic process. In this work, we introduce the mixture of dynamic textures, which models a collection of videos consisting of different visual processes as samples from a set of dynamic textures. We derive the EM algorithm for learning a mixture of dynamic textures, and relate the learning algorithm and the dynamic texture mixture model to previous works. Finally, we demonstrate the applicability of the proposed model to problems that have traditionally been challenging for computer vision. <s> BIB001 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 3) DYNAMIC TEXTURE METHODS <s> A dynamic texture is a spatio-temporal generative model for video, which represents video sequences as observations from a linear dynamical system. This work studies the mixture of dynamic textures, a statistical model for an ensemble of video sequences that is sampled from a finite collection of visual processes, each of which is a dynamic texture. An expectation-maximization (EM) algorithm is derived for learning the parameters of the model, and the model is related to previous works in linear systems, machine learning, time- series clustering, control theory, and computer vision. Through experimentation, it is shown that the mixture of dynamic textures is a suitable representation for both the appearance and dynamics of a variety of visual processes that have traditionally been challenging for computer vision (for example, fire, steam, water, vehicle and pedestrian traffic, and so forth). When compared with state-of-the-art methods in motion segmentation, including both temporal texture methods and traditional representations (for example, optical flow or other localized motion representations), the mixture of dynamic textures achieves superior performance in the problems of clustering and segmenting video of such processes. <s> BIB002 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 3) DYNAMIC TEXTURE METHODS <s> This paper examines the problem of moving object detection. More precisely, it addresses the difficult scenarios where background scene textures in the video might change over time. In this paper, we formulate the problem mathematically as minimizing a constrained risk functional motivated from the large margin principle. It is a generalization of the one class support vector machines (1-SVMs) [17] to accommodate spatial interactions, which is further incorporated into an online learning framework to track temporal changes. As a result it yields a closed-form update formula, a central component of the proposed algorithm to enable prompt adaptation to spatio-temporal changes. We also analyze the mistake bound and discuss issues such as dealing with non-stationary distributions, making use of kernels and efficient inference by a variant of dynamic programming. By exploiting the inherently concurrent structure, the proposed approach is designed to work with the highly parallel graphics processors (GPUs) to facilitate realtime analysis. Our empirical study demonstrates that the proposed approach works in realtime (over 80 frames per second) and at the same time performs competitively against state-of-the-art offline and quasi-realtime methods. <s> BIB003 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 3) DYNAMIC TEXTURE METHODS <s> The layered dynamic texture (LDT) is a generative model, which represents video as a collection of stochastic layers of different appearance and dynamics. Each layer is modeled as a temporal texture sampled from a different linear dynamical system, with regions of the video assigned to a layer using a Markov random field. Model parameters are learned from training video using the EM algorithm. However, exact inference for the E-step is intractable. In this paper, we propose a variational approximation for the LDT that enables efficient learning of the model. We also propose a temporally-switching LDT (TS-LDT), which allows the layer shape to change over time, along with the associated EM algorithm and variational approximation. The ability of the LDT to segment video into layers of coherent appearance and dynamics is also extensively evaluated, on both synthetic and natural video. These experiments show that the model possesses an ability to group regions of globally homogeneous, but locally heterogeneous, stochastic dynamics currently unparalleled in the literature. <s> BIB004 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 3) DYNAMIC TEXTURE METHODS <s> NA <s> BIB005 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 3) DYNAMIC TEXTURE METHODS <s> In this paper, we propose a novel framework for dynamical texture modeling based on chaos theory. Our method first extracts features from dynamical texutre and concatenate the features to a feature vector. A video is then represented by a feature matrix. The mean shift clustering algorithm is used to cluster the feature vector which achieves segmenting videos into different motion patterns. The earth mover s distance(EMD) is employed to compute the feature cluster similarities and classify the dynamic textures. Experimental results indicate that: 1) The segmentation algorithm can cluster different motion patterns in videos; 2) The feature vector proposed in this paper can effectively characterize the dynamical texture; 3) The proposed algorithm can classify dynamical texture accurately. In addition, the algorithm is robust to video noise. <s> BIB006
The aforementioned camera motion compensation based methods or object motion segmentation based methods are mainly developed for dynamic scenarios with homogeneous background motions. For example, the background motion is generated by moving camera. However, there is another type of visual processes composed of ensembles of particles which are subject to stochastic motion BIB001 , BIB002 . The particles can be macroscopic (e.g. leaves and vegetation blowing in the wind), microscopic (e.g. plumes of smoke), or even objects (e.g. a traffic jam, a human crowd, a bee hive or a flock of birds). Because of chaotic heterogeneous background motions, the segmentation of objects from these visual processes are highly challenging for traditional motion segmentation methods such as parametric methods, which assume a piecewise planar scenario, dense optical flow based methods, which requires some degree of motion homogeneous, or feature trajectory clustering based methods, which tend to be impractical especially with a large number of subjects interacting with each other. To solve this problem, recently, there has been an effort to advance toward this kind of holistic modeling by treating such video sequences as 'dynamic textures'. Dynamic texture is defined as a spatio-temporal generative model for image sequences (or videos), which represents image sequences as observations from a linear dynamical system BIB001 , BIB002 . The dynamic texture based methods have shown great potential in motion segmentation with dynamic backgrounds BIB001 -  , BIB006 . For example, Chan and Vasconcelos BIB001 introduced a mixture of dynamic textures to model a set of videos consisting of variant visual processes as samples from a collection of dynamic textures fro the foreground segmentation. Update version of this work is presented in BIB002 , where an improved expectation-maximization (EM) algorithm is derived for learning the model parameters for clustering and segmenting videos. Cheng and Gong BIB003 proposed a background subtraction method in dynamic scenes using dynamic texture for moving object segmentation. Later, Chan and Vasconcelos BIB004 developed a variational layered dynamic texture method, where each layer is constructed as a temporal texture sampled from a different liner dynamic system. And the regions of the video are assigned to a layer using a Markov random field BIB004 . Forouzanfar et al. BIB005 proposed an analytical approach for segmentation of dynamic textures using linear predictive coding. Recently, Xia and Luo  developed a dynamic texture based motion segmentation and background estimation method for moving object segmentation in complex scenes.