Because of the regularizer of optical ow, estimated motion accuracy around unreliable regions such as occlusions decreases. We propose a reliability measurement of the regions and an adaptive weight control of the regularizer based on the reliability for optical ow estimation.

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Apparent motion estimation and obstructive objects removal technique on a video are closely related and important techniques for video editing. We consider a basic removal technique based on the motion estimation under obstructive objects and evaluate its basic performance.

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We previously proposed a method to estimate optical flow based on corresponding region detection using bidirectional motions (forward and backward optical flows). In this paper, we improve the estimation accuracy by performing the detection even in upper level of the multiresolution processing for the optical flow estimation.

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Optical flow is estimated by imposing invariant conditions of brightness and its gradient. However, it is difficult to adjust the weights of these conditions due to the convenience of numerical calculation. In this paper, we consider the adjustment of the weights based on the estimation method that guarantees numerical stability.

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ストラトノヴィチ型確率微分方程式に対する弱い1次スキームのについて述べる.強い1次の近似スキームにミルシュテイン・スキームとプラーテン・スキームがあるが,これらのスキームは弱い収束次数1をもつ.本論文では,ミルシュテイン簡易スキームと最適なプラーテン簡易スキームを取り上げる.そして,各スキームに対して2種類の近似正規乱数を用いた場合のを調べ,比較する.

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映像上の動きの算出にはオプティカルフロー推定が用いられているが，奥行き方向の速度は分からない．シーンフローは，ステレオ法とオプティカルフロー推定の拡張版から算出するステレオ映像上のベクトル場であり，奥行き方向の速度を復元できる．シーンフローにより被写体とカメラの3次元的な運動が推定でき，障害物検出や自己位置推定などに利用できる．従来のシーンフロー推定法では，シーンフローの正則条件による過平滑を防ぐために非線型方程式の数値計算が必要であった．さらに，そのが画像と正則条件の係数に依存していたため，適切な係数の探索も不可能であった．本稿では，従来のアルゴリズムをまとめ直して単純化し，数値的安定条件の導出により，任意の計算条件で計算できる手法を提案する．これにより，適切な正則条件の係数の探索が可能になる．さらに，誤差解析により，提案法の数値解の精度向上を実証する．

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We analyze the numerical stability of Finite Difference Lattice Boltzmann Method (FDLBM) by means of von Neumann stability analysis. A FDLBM is proposed to ensure the numerical stability by relaxing the Lagragian particle convection and by satlsfylng CFL condition. The stability boundary of FDLBM depends on the BGK relaxation time, the CFL number, the mean flow velocity, and the wavenumber. We show that stability regions, as a function of the relaxation time and of the CFL number, drastically change as varying the difference method, which discretizes the kinetic equation. With the centerered difference, FDLBM has characteristics opposite to the conventional LBM, that is, as the BGK relaxation time is increased, stability region of the FDLBM is decreased. We also analyze the numerical stability of FDLBM capable of simulating multi-phase flow by additional fictitious forcing terms. The use of semi-implicit schemes improves numerical stability. With semi-implicit upwind difference, though CFL number equals to unity, we can simulate phase transition without encountering any numerical stability problem.

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Numerical stability of a one-dimensional one-pressure steady two-fluid model was analyzed under a wide range of flow conditions. The stability was evaluated by making use of a minimum relaxation distance, which was deduced from linearized differential equations of the two-fluid model. It was confirmed by numerical experiments that the obtained minimum relaxation distance corresponds to a maximum step size for stable numerical integration of the two-fluid model. Two types of constitutive equations for the interfacial drag force and three correlations for the virtual mass force were incorporated into the model to examine effects of interfacial momentum transfer on the numerical stability. It was found that the stability is improved not only by the virtual mass force but also by changing the functional form of the interfacial drag force. Furthermore, the effects of volumetric fluxes, pressure, pipe diameter and physical properties on the stability were also clarified by the stability analysis.

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確率微分方程式の陽的な数値解法に確率ホイン法がある.本論文では確率ホイン法に修正を加えた解法を提案し,修正ホイン法と呼ぶことにする.修正ホイン法は,スカラーの確率微分方程式に対して強い収束次数1をもち,の面で確率ホイン法より優れていることを示す.

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Since numerical stability and accuracy of solutions are much affected by difference methods for convection terms of transport equations, many methods have been proposed to solve fluid flows efficiently. In recent years, higher-order upstream difference methods have been recognized as accurate methods for solving high Reynolds number flows. There is however little information on the conditions for the occurrence of numerical instability or numerical oscillation when the higher-order difference methods are adopted. In the present study, spectral radii and spectral norms of difference operators were examined analytically or numerically·to make the stability conditions of four higher-order difference methods clear. For the one-dimentional linear transport equation under various boundary conditions, the necessary and sufficient conditions of the stability defined by Lax & Richtmyer were derived using the spectral norms, and those of the stability defined by the boundedness of the solution as time nears infinity were obtained using the spectral radii. It was also shown by examination of eigenvalues of the spatial difference operators that the higher-order difference methods are subject to numerical oscillation when the cell Reynolds number exceeds a value of about two.

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特異値計算のアルゴリズムとして,近年,商差(qd)法系統のものが見直され,実用的解法としてdqds法が注目されている.dqds法はに優れているが,その収束を加速するためにシフト量を適切に設定する必要がある.本報告では,比較的単純で,かつ,超2次収束性が理論的に証明されるシフト戦略を提案する.さらに,超2次収束性を裏付ける数値実験の結果についても報告する.

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By means of a von Neumann linearized stability analysis, we analyze the numerical stability of thermal Lattice Boltzmann Methods for a 13 velocity hexagonal lattice and for 13 velocity square lattice. The LBM stability depends on the flow mean velocity, the temperature, the relaxation time, and the wavenumber. The stability boundaries are computed for varying the mean flow velocity, the temperature, and the relaxation time. Results common to these lattices are that as the relaxation time is increased, the maximum stable parameters increase monotonically until some fixed values. We also analyze the influence of a fictitious forcing term on numerical stability of the LBMs. The maximum values of stable forcing terms are shown as function of the BGK relaxation time for a 7 velocity hexagonal, a 13 velocity hexagonal, and a 13 velocity square lattices. In terms of numerical stability, we recommend that researchers use the thermal LB models in the region where the mean flow velocity is around 0.00 and the temperature is between 0.60 and 0.80.

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