Relationship between Saturation and Brightness Value in HSV Color Space

The quantitative relationship between saturation and brightness value of color images had not been determined yet.According to Weber-Fechner law,the relationship equation is proposed.In the gradient field of logarithm value,the saturation and brightness value of a group of color images is analyzed by means of hypothesis-testing.The hypothesis value of slope is set based on the probability distribution.Then the intercepts and the lines' equations are got.The termination of the algorithm depends on the error between bright value and the value obtained by the saturation and the equations.The results show that the saturation and brightness' logarithm values subject to a group of parallel lines with independence from devices.The dimension of pixel vectors of color images could be decreased to two.The proposed model of saturation and brightness value will play very active and important effect of understanding and analysis of color images.And it will have a great influence on the optimal design of image sensors.