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

基于色彩空间的黎曼几何特性，提出了一种新的色弱补偿算法。标准是匹配平均观察者，正常观察者和色弱观察者的颜色辨别阈值，使两组观察者具有相同的色差体验。为了将色彩空间描述为黎曼空间，我们测量了色彩弱和色彩正常观察者的色彩辨别阈值数据。在LMS空间中给出了色差的一维补偿和仿真。提出了在色度平面和全彩色空间下的二维和三维补偿和仿真方法。首先，我们展示了一个局部仿射等距，它可以由判别阈值数据定义的度量张量估计。其次，利用测地线网格建立黎曼法向坐标。通过主观评价，验证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.