The kriging update model and recursive space-time function estimation

Kerwin, William S.; Prince, Jerry L.

doi:10.1109/78.796430

Cited by 29 publications

(9 citation statements)

References 23 publications

(53 reference statements)

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“…In medical imaging, the technique seems to have been applied first by Stytz and Parrot [320], [321]. More recent studies related to kriging in signal and image processing include those of Kerwin and Prince [322] and Leung et al [323].…”

Section: Development Of Alternative Interpolation Methodsmentioning

confidence: 99%

A chronology of interpolation: from ancient astronomy to modern signal and image processing

Meijering

Falk²

2002

Proc. IEEE

527

252

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Section: Development Of Alternative Interpolation Methodsmentioning

confidence: 99%

A chronology of interpolation: from ancient astronomy to modern signal and image processing

Meijering

Falk²

2002

Proc. IEEE

527

252

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“…where (11) is represented by the kriging model in (8). The idea is to store representative precomputed function evaluations from the full dynamic system in the time invariant vectors X ∈ R n×d and Y ∈ R n .…”

Section: B Dynamic Mapping Krigingmentioning

confidence: 99%

“…The kriging method has been extended from its initial formulation to incorporate dynamic features by including time as an additional spatial variable in the model [6], or by building a spacetime covariance function that can handle a time dimension separately from the state-space [7]. More relevant are the applications of kriging in the systems area, for time-series theory [8] and for discrete-time nonlinear systems [9]. These examples show the potential that this technique has to be applied in dynamic modeling and control.…”

Section: Introductionmentioning

confidence: 99%

An exploratory study of discrete time state-space models using kriging

Hernandez

Gallivan

2008

2008 American Control Conference

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An exploratory study of the application of kriging as an approximated model of complex dynamic systems is presented in this paper. This technique, which has its roots in the geology community, is gaining popularity for its simplicity and ability to track the error of the reduced model, making it attractive for engineering applications. Our proposed methodology, called dynamic mapping kriging, requires the generation of representative function evaluations, and then uses them in a recursive state-space formulation to represent the evolution of the process. By demonstrating on a highly simplified model, our intention is to present the relevant elements of this methodology, focusing on the design of the function evaluations as a crucial factor in the accurate representation of the system. We illustrate the advantages that the error prediction has as a tool to improve our technique and as a measurement to bound the error dynamics, and give some final recommendations about the applications of this methodology to build approximated models.

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“…In addition, multiframe analysis is also of paramount importance for cardiac motion recovery. The temporal kinematics coherence plays key roles in achieving robust motion estimates, especially when there are uncertainties in system models and noises in input data [7,8,10]. Unfortunately, none of these multiframe works have employed the proper anisotropic and finite deformation constraints.…”

Section: Introductionmentioning

confidence: 99%

Finite Deformation Guided Nonlinear Filtering for Multiframe Cardiac Motion Analysis

Wong

Shi

2004

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004

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Abstract. In order to obtain sensible estimates of myocardial kinematics based on biomechanics constraints, one must adopt appropriate material, deformation, and temporal models. Earlier efforts, although not concurrently adopted within the same framework, have shown that it is essential to carefully consider the fibrous structure of the myocardium, the large geometric deformation of the cardiac wall movement, the multiframe observations over the cardiac cycle, and the uncertainties in the system modeling and data measurements. With the meshfree particle method providing the platform to enforce the anisotropic material property derived from the myofiber architecture, we present the first effort to perform multiframe cardiac motion analysis under finite deformation conditions, posed as a nonlinear statistical filtering process. Total Lagrangian (TL) formulation is adopted to establish the myocardial system dynamics under finite deformation, which is then used to perform nonlinear state space prediction (of the tissue displacement and velocity) at each time frame, using the Newton-Raphson iteration scheme. The system matrices of the state space equation are then derived, and the optimal estimation of the kinematic state is achieved through TL-updated recursive filtering. Results from synthetic data with ground truth and canine cardiac image sequence are presented.

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The kriging update model and recursive space-time function estimation

Cited by 29 publications

References 23 publications

A chronology of interpolation: from ancient astronomy to modern signal and image processing

A chronology of interpolation: from ancient astronomy to modern signal and image processing

An exploratory study of discrete time state-space models using kriging

Finite Deformation Guided Nonlinear Filtering for Multiframe Cardiac Motion Analysis

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