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首页> 外文期刊>Journal of Scientific Computing >Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
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Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing

机译：在图像处理中使用总变化最小化和振荡模式对纹理建模

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摘要

This paper is devoted to the modeling of real textured images by functional minimization and partial differential equations. Following the ideas of Yves Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, we decompose a given (possible textured) image f into a sum of two functions u + v, where u ∈ BV is a function of bounded variation (a cartoon or sketchy approximation of f), while v is a function representing the texture or noise. To model v we use the space of oscillating functions introduced by Yves Meyer, which is in some sense the dual of the BV space. The new algorithm is very simple, making use of differential equations and is easily solved in practice. Finally, we implement the method by finite differences, and we present various numerical results on real textured images, showing the obtained decomposition u + v, but we also show how the method can be used for texture discrimination and texture segmentation.
机译：本文致力于通过功能最小化和偏微分方程对真实纹理图像进行建模。遵循伊夫·迈耶（Yves Meyer）在L. Rudin，S。Osher和E. Fatemi的总变化最小化框架中的思想，我们将给定的（可能有纹理的）图像f分解为两个函数u + v的和，其中u∈BV是有界变化的函数（f的卡通近似或粗略近似），而v是表示纹理或噪声的函数。为了建模v，我们使用Yves Meyer引入的振荡函数空间，从某种意义上说，它是BV空间的对偶。新算法非常简单，利用了微分方程，在实践中很容易解决。最后，我们通过有限差分实现该方法，并在真实纹理图像上呈现各种数值结果，显示了获得的分解u + v，但同时也展示了该方法如何用于纹理识别和纹理分割。

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