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首页> 外文期刊>Geometry, Imaging and Computing >A class of nonlocal variational problems on a vector bundle for color image local contrast reduction / enhancement
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A class of nonlocal variational problems on a vector bundle for color image local contrast reduction / enhancement

机译：向量束上一类用于彩色图像局部对比度降低/增强的非局部变分问题。

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摘要

We extend two existing variational models from the Euclidean space to a vector bundle over a Riemannian manifold. The Euclidean models, dedicated to regularize or enhance some color image features, are based on the concept of nonlocal gradient operator acting on a function of the Euclidean space. We then extend these models by generalizing this operator to a vector bundle over a Riemannian manifold with the help of the parallel transport map associated to some class of covariant derivatives. Through the dual formulations of the proposed models, we obtain the expressions of their solutions, which exhibit the functional spaces that describe the image features. Finally, for a well-chosen covariant derivative and its nonlocal extension, the proposed models perform local contrast modification (reduction or enhancement) and experiments show that they preserve more the aspect of the original image than the Euclidean models do while modifying equally its contrast.
机译：我们将两个现有的变分模型从欧式空间扩展到黎曼流形上的向量束。致力于规范化或增强某些彩色图像特征的欧几里得模型基于作用于欧几里得空间函数的非局部梯度算符的概念。然后，我们借助于与一类协变导数相关的并行传输图，将该算子推广到黎曼流形上的向量束，从而扩展这些模型。通过提出的模型的双重表述，我们获得了其解决方案的表达式，这些表达式展现了描述图像特征的功能空间。最后，对于选择良好的协变量导数及其非局部扩展，所提出的模型执行局部对比度修改（减少或增强），并且实验表明，与欧几里得模型相比，它们保留了原始图像的更多方面，同时均等地修改了其对比度。

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