欧拉方程及运动补偿中泛函最小值的迹线性质

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/ipi.2021072

R. March, G. Riey

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引用次数: 0

摘要

我们计算了一个函数的欧拉方程，该函数可用于同时进行视频绘制和运动估计，该函数是在[17]中得到的，作为[16]中提出的函数的修改版本的松弛。泛函是在有界变分的向量函数上定义的，因此我们也得到了在极小值的奇异集上成立的欧拉方程，特别强调了跳跃集的条件。这些条件是用几何上有意义的向量场的轨迹来表示的，并以轴平行于跳跃集的单位法线的圆柱体上的平均值的点向极限来表征。

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Euler equations and trace properties of minimizers of a functional for motion compensated inpainting

We compute the Euler equations of a functional useful for simultaneous video inpainting and motion estimation, which was obtained in [17] as the relaxation of a modified version of the functional proposed in [16]. The functional is defined on vectorial functions of bounded variations, therefore we also get the Euler equations holding on the singular sets of minimizers, highlighting in particular the conditions on the jump sets. Such conditions are expressed by means of traces of geometrically meaningful vector fields and characterized as pointwise limits of averages on cylinders with axes parallel to the unit normals to the jump sets.

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.