Balanced Approximation of Stochastic Systems

Arun, K. S.; Kung, Sun‐Yuan

doi:10.1137/0611003

Cited by 61 publications

(28 citation statements)

References 28 publications

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“…The problem can be tackled by using information-theoretic or minimum description length criteria [20,21]. Following [22], we automate the selection by looking at the normalized energy encoded in the singular values of Σ and Σ v , and choose n(s) and k(s) so that we retain a given percentage of energy.…”

Section: Methodsmentioning

confidence: 99%

Spatially Homogeneous Dynamic Textures

Doretto

Jones

Soatto

2004

Lecture Notes in Computer Science

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Abstract. We address the problem of modeling the spatial and temporal second-order statistics of video sequences that exhibit both spatial and temporal regularity, intended in a statistical sense. We model such sequences as dynamic multiscale autoregressive models, and introduce an efficient algorithm to learn the model parameters. We then show how the model can be used to synthesize novel sequences that extend the original ones in both space and time, and illustrate the power, and limitations, of the models we propose with a number of real image sequences.

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Section: Methodsmentioning

confidence: 99%

Spatially Homogeneous Dynamic Textures

Doretto

Jones

Soatto

2004

Lecture Notes in Computer Science

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“…In practice, this needs to be inferred from the data. Following Arun and Kung (1990), we propose to determine the model order empirically from the singular values σ 1 , σ 2 , . .…”

Section: Closed-form Solutionmentioning

confidence: 99%

Editable dynamic textures

Doretto¹,

Soatto²

2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings.

143

270

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Abstract. Dynamic textures are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include sea-waves, smoke, foliage, whirlwind etc. We present a characterization of dynamic textures that poses the problems of modeling, learning, recognizing and synthesizing dynamic textures on a firm analytical footing. We borrow tools from system identification to capture the "essence" of dynamic textures; we do so by learning (i.e. identifying) models that are optimal in the sense of maximum likelihood or minimum prediction error variance. For the special case of second-order stationary processes, we identify the model sub-optimally in closed-form. Once learned, a model has predictive power and can be used for extrapolating synthetic sequences to infinite length with negligible computational cost. We present experimental evidence that, within our framework, even low-dimensional models can capture very complex visual phenomena.

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“…Following the methodology for identifying balanced stochastic systems in [3] we can use the tools described in this section to identify generalizations to the dynamic texture models originally presented in [23]. Such generalizations are appropriate for video data that exhibits nonlinear behavior or mode switching which can be modeled by a piecewise affine [61] dynamic texture.…”

Section: Extensions To Dynamic Texture Modelsmentioning

confidence: 99%

Design of Beneficial Wave Dynamics for Engine Life and Operability Enhancement

Hagen¹

2010

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Summary of AccomplishmentsThe accomplishments of this research program emphasized the more promising directions of points (2) and (3) listed above, where the uncertainty management called out in point (1) was implicitly accommodated in the analysis. A particular emphasis of this research was the identification of nonlinear models based on high-speed video of flame dynamics. This is a key component of the thermo-acoustic feedback model studied extensively in previous AFOSR-sponsored research programs at UTRC. These results are presented in section 1.1.These concepts were extended to nonlinear model reduction based on tangent space approximations. Here local gramians are empirically computed based on perturbation trajectories. Key components of this research were the development and application of algorithms for approximating the nonlinear manifold for which a data set belongs, and identification of the nonlinear dynamics on the particular manifold. This lead to the concept of a hybrid (switching) locally affine dynamic texture model, based on the local tangent space approximation of the manifold. These results are presented in section 1.2. ^oUo^wvn Stability Analysis of Systems with Symmetry-Breaking is presented in section 1.3. Here, sufficient conditions are established for a nonlinear PDE model of thermo-acoustics with wave-speed mistuning. In investigating a new approach to stability analysis of the nonlinear thermo-acoustic model we developed the concept of continued fraction convergence as a condition for stability. Initial results are presented for a string of oscillators and the concepts are extended to the application of subsystems connected in a ring structure.The results of the current research are summarized in 7 journal papers (1 published, 1 accepted, 5 in preparation), 9 conference papers, and another 2 conference papers currently in preparation.

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Balanced Approximation of Stochastic Systems

Cited by 61 publications

References 28 publications

Spatially Homogeneous Dynamic Textures

Spatially Homogeneous Dynamic Textures

Editable dynamic textures

Design of Beneficial Wave Dynamics for Engine Life and Operability Enhancement

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