Farup Ivar
Department of Computer Science, Norwegian University of Science and Technology (NTNU), 2802 Gjøvik, Norway.
J Imaging. 2021 Sep 29;7(10):196. doi: 10.3390/jimaging7100196.
Gradient-domain image processing is a technique where, instead of operating directly on the image pixel values, the gradient of the image is computed and processed. The resulting image is obtained by reintegrating the processed gradient. This is normally done by solving the Poisson equation, most often by means of a finite difference implementation of the gradient descent method. However, this technique in some cases lead to severe haloing artefacts in the resulting image. To deal with this, local or anisotropic diffusion has been added as an ad hoc modification of the Poisson equation. In this paper, we show that a version of anisotropic gradient-domain image processing can result from a more general variational formulation through the minimisation of a functional formulated in terms of the eigenvalues of the structure tensor of the differences between the processed gradient and the gradient of the original image. Example applications of linear and nonlinear local contrast enhancement and colour image Daltonisation illustrate the behaviour of the method.
梯度域图像处理是一种技术，它不是直接对图像像素值进行操作，而是计算并处理图像的梯度。通过对处理后的梯度进行重新积分来获得最终图像。这通常是通过求解泊松方程来完成的，最常见的是借助梯度下降法的有限差分实现。然而，这种技术在某些情况下会在最终图像中导致严重的光晕伪影。为了解决这个问题，局部或各向异性扩散已被作为对泊松方程的一种临时修改添加进来。在本文中，我们表明，一种各向异性梯度域图像处理版本可以通过一个更通用的变分公式得到，该公式是通过最小化一个根据处理后的梯度与原始图像梯度之间差异的结构张量的特征值来制定的泛函。线性和非线性局部对比度增强以及彩色图像色盲矫正的示例应用说明了该方法的性能。
