论文标题
使用光纤束颜色空间将图像向前和向后映射到2D矢量场
Forward and backward mapping of image to 2D vector field using fiber bundle color space
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We introduce the concept of a fiber bundle color space, which acts according to the psychophysiological rules of trichromacy perception of colors by a human. The image resides in the fiber bundle base space and the fiber color space contains color vectors. Further we propose the decomposition of color vectors into spectral and achromatic parts. A homomorphism of a color image and constructed two-dimensional vector field is demonstrated that allows us to apply well-known advanced methods of vector analysis to a color image, i.e. ultimately give new numerical characteristics of the image. Appropriate image to vector field forward mapping is constructed. The proposed backward mapping algorithm converts a two-dimensional vector field to color image. The type of image filter is described using sequential forward and backward mapping algorithms. An example of the color image formation on the base of two-dimensional magnetic vector field scattered by a typical pipe line defect is given.
