Exact mathematical modeling of human color perception and applications to color weak compensation and color information processsing

利用颜色空间的Riemann几何性质，提出了一种新的基于客观判据的色弱补偿算法。该判据是将普通观察者、正常观察者和弱色观察者的色弱辨别阈值匹配，使两组观察者具有相同的色差体验。为了将颜色空间描述为黎曼空间，我们测量了弱色观察者和正常观察者的辨色阈值数据，并在LMS空间的混乱线上对弱色弱进行了一维补偿和模拟。在色度平面和全色空间中通过以下两种方式进行2D和3D补偿和模拟。首先，我们给出了一个局部仿射等距，它可以从由判别阈值数据定义的度量张量中估计出来。其次，使用测地线网格建立黎曼法向坐标。主观评价结果证实了所提方法的有效性。

We proposed a novel compensation algorithm for color-weakness based on a new, objective criterion using Riemann geometric properties of color spaces.The criterion is to match the color discrimination thresholds of average, normal observers and a colorweak observer such that he two groups of observers have the same color-difference experience.In order to describe the color spaces as Riemann spaces, we measured color discrimination thresholds data for color-weak and color-normal observers.A 1D compensation and simulation of color-weakness is shown on confusion lines in the LMS space. The 2D and 3D compensations and simulations are proposed in chromaticity planes and full color spaces in the two following ways. First, we show a local affine isometry which can be estimated from the metric tensor defined by the discrimination thresholds data. Second, the Riemann normal coordinates are built using geodesics grids. Performance of the proposed methods are confirmed by subjective evaluations.