School of Computing Sciences, University of East Anglia, Norwich, U.K.
IEEE Trans Image Process. 2013 Oct;22(10):4072-85. doi: 10.1109/TIP.2013.2270108. Epub 2013 Jun 19.
To overcome the difficulties in applying gradient-based operators to color images, Di Zenzo introduced the color tensor, an operator that provides a gradient field for multichannel images. An elegant application for this operator was developed in the domain of multichannel image visualization: Socolinsky and Wolff proposed to reintegrate Di Zenzo's gradient by solving a Poisson equation, yielding a greyscale representation of the multispectral contrast of the input image. Di Zenzo's gradients are, however, generally not integrable and some approximation must be introduced. Thus, the resulting image can suffer from artifacts such as the smearing of edges. In this paper, we focus on the integrability of Di Zenzo's gradients. We show that the integrability of the obtained field can be improved dramatically through a simple desaturation of the color image (as in the HSV color space). This result can be readily extended to multispectral images by defining an analogue to saturation. We present several results explaining what happens to color tensors as the saturation changes. Significantly we show that small changes of the saturation in the linear image space can result in large improvements in the integrability of tensor gradients calculated in logarithmic color space. This result is important for two reasons. 1) Log-differences are more perceptually meaningful. 2) In log-space we can operate with retinex algorithms, which are well known techniques for contrast enhancement. We propose that they can be used to "put back" any contrast that might be lost in the desaturation step and, more importantly, they can enhance contrast at the same time as reintegrating the gradient field because of their relation to partial differential equations. Finally, we evaluate our method psychophysically. Compared with other commonly used image fusion methods, experiments show that our data fusion using the Di Zenzo color tensor after desaturating the image and where a simple contrast boost is applied is strongly preferred.
为了克服将基于梯度的算子应用于彩色图像的困难，Di Zenzo 引入了颜色张量，这是一种为多通道图像提供梯度场的算子。这个算子在多通道图像可视化领域有一个优雅的应用：Socolinsky 和 Wolff 提出通过求解泊松方程来重新整合 Di Zenzo 的梯度，从而得到输入图像多光谱对比度的灰度表示。然而，Di Zenzo 的梯度通常不可积，因此必须引入一些近似。因此，得到的图像可能会出现边缘模糊等伪影。在本文中，我们专注于 Di Zenzo 梯度的可积性。我们表明，通过对彩色图像进行简单的去饱和（如在 HSV 颜色空间中），可以显著提高获得的场的可积性。通过定义饱和度的类似物，这个结果可以很容易地扩展到多光谱图像。我们提出了几个结果，解释了当饱和度变化时颜色张量会发生什么。重要的是，我们表明在线性图像空间中饱和度的微小变化可以导致在对数颜色空间中计算的张量梯度的可积性的显著提高。这个结果有两个重要原因。1）对数差异在感知上更有意义。2）在对数空间中，我们可以使用 Retinex 算法，这是一种众所周知的对比度增强技术。我们提出它们可以用来“恢复”在去饱和步骤中可能丢失的任何对比度，更重要的是，它们可以在重新整合梯度场的同时增强对比度，因为它们与偏微分方程有关。最后，我们从心理物理学的角度评估了我们的方法。与其他常用的图像融合方法相比，实验表明，我们使用去饱和图像后的 Di Zenzo 颜色张量进行数据融合，并应用简单的对比度增强的方法得到了强烈的偏好。
