IEEE Trans Image Process. 2014 Jan;23(1):9-18. doi: 10.1109/TIP.2013.2277775. Epub 2013 Aug 8.
Vector-valued images such as RGB color images or multimodal medical images show a strong interchannel correlation, which is not exploited by most image processing tools. We propose a new notion of treating vector-valued images which is based on the angle between the spatial gradients of their channels. Through minimizing a cost functional that penalizes large angles, images with parallel level sets can be obtained. After formally introducing this idea and the corresponding cost functionals, we discuss their Gâteaux derivatives that lead to a diffusion-like gradient descent scheme. We illustrate the properties of this cost functional by several examples in denoising and demosaicking of RGB color images. They show that parallel level sets are a suitable concept for color image enhancement. Demosaicking with parallel level sets gives visually perfect results for low noise levels. Furthermore, the proposed functional yields sharper images than the other approaches in comparison.
向量值图像，如 RGB 彩色图像或多模态医学图像，显示出很强的通道间相关性，但大多数图像处理工具都没有利用这一点。我们提出了一种新的处理向量值图像的概念，该概念基于它们通道的空间梯度之间的角度。通过最小化惩罚大角度的代价函数，可以得到具有平行水平集的图像。在正式引入这个想法和相应的代价函数之后，我们讨论了它们的 Gâteaux 导数，这导致了一种类似于扩散的梯度下降方案。我们通过 RGB 彩色图像的去噪和去马赛克的几个例子来说明这个代价函数的性质。结果表明，平行水平集是一种适合彩色图像增强的概念。对于低噪声水平，使用平行水平集进行去马赛克可以得到视觉完美的结果。此外，与其他方法相比，所提出的函数产生的图像更清晰。
