<i>Numerical Recipes: The Art of Scientific Computing</i>

Press, William H.; Flannery, Brian P.; Teukolsky, Saul A.; Vetterling, William T.; Kramer, Peter B.

doi:10.1063/1.2820230

Cited by 103 publications

(98 citation statements)

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“…Again, the nodal velocity field v n−1/2 is interpolated to these locations (3) and the resulting velocity field (green vector) is used to obtain trajectories backward in time (green) for a full time step t. The nodal velocity field v n−1 (pink) saved from the previous time step is interpolated to locations (4) and its solution is, together with the velocity field evaluations at the previous locations (1)-(3), used to obtain a weighted velocity field (see fourth equation in (28)); with this velocity field, the characteristics backward in time to points X are computed, nodal temperatures T(n, j) are interpolated to points X and assigned to nodes j. Adapted to backward in time from forward Runge-Kutta-4 description in Press (1992) and Spiegelman (2004).…”

Section: Semi-lagrangian Backward Characteristics For Heat Advectionmentioning

confidence: 99%

“…We follow the approach of time step doubling presented in Press (1992) for our implementation of the adaptive time stepping routine. Its essence is to compare the computed solutions for the characteristics (3.3) when taking a trial full and two successive half time steps.…”

Section: Adaptive Runge-kutta-5 Time Steppingmentioning

confidence: 99%

“…If the accuracy is sufficient, the subsequent time step size is increased. This error control mechanism results in cancellation of the fifth-order truncation error and theoretically increases the accuracy of the Runge-Kutta scheme from fourth-to fifth-order (Press 1992).…”

Section: Adaptive Runge-kutta-5 Time Steppingmentioning

confidence: 99%

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Viscoelastic mantle convection and lithospheric stresses

Beuchert¹,

Podladchikov²

2010

Geophysical Journal International

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S U M M A R YAccurate predictions of stress distribution in the lithosphere are of major importance for approaching more realistic numerical models of the mantle-lithosphere system. Since stress fields in the lithosphere computed in convection models differ substantially between viscous and viscoelastic rheologies, it is essential to employ a viscoelastic rheology when accurate stresses are to be predicted in mantle convection models involving the lithosphere. This difference in stress distribution and magnitude has important implications for accurate modelling of stress-dependent processes like power-law creep, shear heating and plasticity. A further requirement for computation of accurate stress fields is to ensure numerically divergence-free solutions in the Boussinesq approximation. We present the technical background required for implementation of numerically incompressible solutions and for implementation of a Maxwell viscoelastic rheology in the frame of the finite element method (FEM). We employ the Jaumann invariant stress derivative in our implementation and demonstrate that the choice of the invariant stress derivative is irrelevant for geodynamic simulations. We discuss potential numerical advantages of a viscoelastic rheology when large viscosity variations are applied in thermal convection models. Due to the physical transition from effectively viscous to elastic behaviour in a viscoelastic model, the introduction of viscosity cut-offs generally applied in viscous models can be avoided.

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Section: Semi-lagrangian Backward Characteristics For Heat Advectionmentioning

confidence: 99%

Section: Adaptive Runge-kutta-5 Time Steppingmentioning

confidence: 99%

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Viscoelastic mantle convection and lithospheric stresses

Beuchert¹,

Podladchikov²

2010

Geophysical Journal International

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“…The information of 2D features and locations of 2D bodypart blobs are used to reconstruct 3D human poses, through the methodology of analysis-by-synthesis, by fitting 2D features to 3D poses. The downhill simplex algorithm [47] is applied to minimize the cost function so as to find the optimal 3D human pose for each frame. The cost function is a measure of the difference between the 2D features and the 3D model projections; it is composed of the following four scores: silhouette score, edge score, motion score, and feature point score.…”

Section: D Pose Estimationmentioning

confidence: 99%

Human Action Recognition Based on 3D Human Modeling and Cyclic HMMs

Thuc

Hwang

et al. 2014

ETRI J

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Human action recognition is used in areas such as surveillance, entertainment, and healthcare. This paper proposes a system to recognize both single and continuous human actions from monocular video sequences, based on 3D human modeling and cyclic hidden Markov models (CHMMs). First, for each frame in a monocular video sequence, the 3D coordinates of joints belonging to a human object, through actions of multiple cycles, are extracted using 3D human modeling techniques. The 3D coordinates are then converted into a set of geometrical relational features (GRFs) for dimensionality reduction and discrimination increase. For further dimensionality reduction, k-means clustering is applied to the GRFs to generate clustered feature vectors. These vectors are used to train CHMMs separately for different types of actions, based on the Baum-Welch re-estimation algorithm. For recognition of continuous actions that are concatenated from several distinct types of actions, a designed graphical model is used to systematically concatenate different separately trained CHMMs. The experimental results show the effective performance of our proposed system in both single and continuous action recognition problems. Keywords I. IntroductionHuman action recognition is a growing topic in video analysis and understanding -one of the most popular areas in the community of computer vision -thanks to its applications in surveillance, entertainment, and healthcare. In surveillance, human action recognition can be used in conjunction with video camera footage to help with the recognition and analysis of human actions. In entertainment, human-computer interaction can be helped to appear more natural via human action recognition, which in turn can help increase the entertainment experience. In healthcare, human action recognition can help detect abnormal gaits or assist in a patient's rehabilitation through an analysis of their actions.However, it is challenging to recognize various human actions due to the high number of degrees of freedom associated with the average human body -namely, variations in human poses; variations in the colors of a person's clothing; changes in lighting and illumination; variations in viewpoints; and frequent self-occlusion. Moreover, the use of monocular video sequences further increases the difficulty for human action recognition.Generally, the two main stages in human action recognition are: the feature extraction and representation stage and the classification stage.In the feature extraction and representation stage, the features or characteristics of video frames, such as silhouette, shape, color, and motion, are extracted and represented in a systematic and efficient way. consists of stacking segmented silhouettes (frame by frame) to form a 3D spatial-temporal shape. In a similar way, Ke and others [2] build STVs, for shape-based matching, from image features that are based on the consecutive silhouettes of objects along a time axis, including spatial-temporal region extraction and region matching. Kim and oth...

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“…Note here that there are six degrees of freedom for controlling a virtual camera: a translational vector Tx,Ty,Tz, and rotational angle Rx,Ry,Rz. To adjust these parameters, we employ iterative calculations of a Simplex method 18 . We employ a coarse incremental step initially, and then gradually reduce the step size when the minimization of E with a step size reaches an oscillatory mode.…”

Section: Figure 10: Erroneous Correspondencementioning

confidence: 99%

Efficient and Handy Texture Mapping on 3D Surfaces

Matsushita

Kaneko

1999

Computer Graphics Forum

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There has been a rapid technical progress in three‐dimensional (3D) computer graphics. But gathering surface and texture data is yet a laborious task. This paper addresses the problem of mapping photographic images on the surface of a 3D object whose geometric data are already known. We propose an efficient and handy method for acquiring textures and mapping them precisely on the surface, employing a digital camera alone. We describe an algorithm for selecting a minimal number of camera positions that can cover the entire surface of a given object and also an algorithm to determine camera’s position and direction for each photograph taken so as to paste it to the corresponding surfaces precisely. We obtained a matching accuracy within a pixel on a surface through three experimental examples, by which the practicability of our method is demonstrated.

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Numerical Recipes: The Art of Scientific Computing

Cited by 103 publications

References 0 publications

Viscoelastic mantle convection and lithospheric stresses

Viscoelastic mantle convection and lithospheric stresses

Human Action Recognition Based on 3D Human Modeling and Cyclic HMMs

Efficient and Handy Texture Mapping on 3D Surfaces

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