数码照相颜色数值与物质浓度辨识的数学模型
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摘要
在一定的环境条件下,可以认为一种物质溶液的浓度确定了该溶液的颜色,因此可以根据溶液的颜色来判断物质溶液的浓度.根据观测数据,应用SPSS软件对二氧化硫的浓度和数码照片颜色RGB读数进行了相关性分析.在此基础上建立了二氧化硫溶液浓度与颜色的RGB读数的多元二次多项式回归模型,并用MATLAB软件对模型求解.进一步地,还深刻分析了RGB变量对物质浓度的判断的交叉影响,并建立了完全的二次多项式模型.最后在残差分析的基础上,引入相对残差的概念对所得模型进行了误差分析.结果显示,完全二次多项式回归模型具有更高的相关系数和更小的残差方差,并且所得到的模型非常简洁.
In general, it can be considered that the concentration of a solution determines its color. Therefore, we can estimate the concentration of a material solution by the color of its solution, which is known as the colorimetry. In this paper, we analyze the correlation between the concentration of sulfur dioxide solution and the RGB values of color of this solution according to the observational data by applying SPSS. Based on this, a quadratic polynomial regression model for the concentration of sulfur dioxide solution and RGB values of the digital photo is established, and we solve the model by using MATLAB. Furthermore,we consider the cross-effects of the BGR variables on the determination of the concentration of solution in depth and give a complete quadratic polynomial model. At last, the concept of relative residual was introduced to analyze the error of these models. The results show that the complete quadratic polynomial regression model has a bigger correlation coefficient,a smaller residual variance, and a more concise form.
In general, it can be considered that the concentration of a solution determines its color. Therefore, we can estimate the concentration of a material solution by the color of its solution, which is known as the colorimetry. In this paper, we analyze the correlation between the concentration of sulfur dioxide solution and the RGB values of color of this solution according to the observational data by applying SPSS. Based on this, a quadratic polynomial regression model for the concentration of sulfur dioxide solution and RGB values of the digital photo is established, and we solve the model by using MATLAB. Furthermore,we consider the cross-effects of the BGR variables on the determination of the concentration of solution in depth and give a complete quadratic polynomial model. At last, the concept of relative residual was introduced to analyze the error of these models. The results show that the complete quadratic polynomial regression model has a bigger correlation coefficient,a smaller residual variance, and a more concise form.
引文
[1]胡卫军.RGB图像颜色检测的Cd(Ⅱ)浓度测量研究[J].传感器与微系统,2016(10):17-19.
[2]李俊峰.基于RGB色彩空间自然场景统计的无参考图像质量评价[J].自动化学报,2015, 41(9):1601-1615.
[3] Chatterjee S,Hadi A. Regression Analysis by Example[M].北京,机械工业出版社,2013.
[4]姜启源,谢金星,叶俊.数学模型(第4版)[M].北京:高等教育出版社,2011.
[5]薛毅.“电池剩余放电时间预测”问题解析[J].数学建模及其应用,2016, 4(5):41-49.
[2]李俊峰.基于RGB色彩空间自然场景统计的无参考图像质量评价[J].自动化学报,2015, 41(9):1601-1615.
[3] Chatterjee S,Hadi A. Regression Analysis by Example[M].北京,机械工业出版社,2013.
[4]姜启源,谢金星,叶俊.数学模型(第4版)[M].北京:高等教育出版社,2011.
[5]薛毅.“电池剩余放电时间预测”问题解析[J].数学建模及其应用,2016, 4(5):41-49.