鄭國揚臺灣大學：資訊工程學研究所張晃維Chang, Huang-WeiHuang-WeiChang2007-11-262018-07-052007-11-262018-07-052005http://ntur.lib.ntu.edu.tw//handle/246246/53644We propose a spatio-temporal embedding framework for better modeling image sequences, known as dynamic textures, that exhibit certain stationarity in the appearance and the dynamics. Our method can characterize more types of data than those by the existing techniques established on linear dynamical systems (LDS). The algorithm finds a low-dimensional representation for the original data without discarding the critical time-dependent information. It then directly deals with the nonlinear dynamics through an integration of Gaussian process with time delay embedding. In addition, the possible nonlinearity in the appearance space is also appropriately addressed by our use of multiple local analyzers. Consequently, the framework is flexible enough for handling various applications, including prediction and smoothing. Results on prediction and smoothing are provided to demonstrate the advantages of our approach.1 Introduction 1 1.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Physics-Based Approaches . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Image-Based Approaches . . . . . . . . . . . . . . . . . . . . . 3 1.2 Our Approach and Contributions . . . . . . . . . . . . . . . . . . . . 6 2 Modeling Dynamic Textures via Dynamical Systems 9 2.1 Introduction to Dynamical Systems . . . . . . . . . . . . . . . . . . . 9 2.2 Dynamic Textures as Dynamical Systems . . . . . . . . . . . . . . . . 12 2.2.1 Learning the LDS Parameters . . . . . . . . . . . . . . . . . . 13 2.3 A Sub-Optimal LDS Solution . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 The Solution and Algorithms . . . . . . . . . . . . . . . . . . 15 2.3.2 Analysis of the LDS modeling . . . . . . . . . . . . . . . . . . 19 2.4 A Closed-Loop Dynamical System Modeling . . . . . . . . . . . . . . 23 3 Spatio-Temporal Embeddings for Dynamic Textures 27 3.1 Time Delay Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . 29 i 3.2 Gaussian Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Learning Spatio-Temporal Embeddings for Dynamic Textures . . . . 36 3.3.1 Linear Latent Model . . . . . . . . . . . . . . . . . . . . . . . 37 3.3.2 Multiple Local Linear Models . . . . . . . . . . . . . . . . . . 39 4 Experimental Results 43 5 Conclusions 49 A EM algorithm for Linear Dynamical Systems 53 A.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 A.2 E-step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 A.3 M-step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 B Mixtures of Probabilistic Principal Component Analyzers 59 B.1 Probabilistic Principal Component Analysis . . . . . . . . . . . . . . 60 B.2 The Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621108238 bytesapplication/pdfen-US高斯過程動態影像動態系統Dynamic TexturesGaussian ProcessesSpatio-temporalEmbeddingDynamical Systemthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53644/1/ntu-94-R92922059-1.pdf