Abstract: Most of the evaluation indices used in measuring surface roughness by machine vision were statistical analyzed based on gray scale image information， while some evaluation indices based on color information did not provide reasonable mathematical structure expression in current studies.Aiming at these problems， a detection method was proposed based on singular value entropy of color images to evaluate the roughness of ground surfaces.According to the differences of the energy distribution of the virtual image formed by the color-block on the surfaces with different levels of roughness， a pure quaternion data structure was used to characterize a color image and the data was analyzed. The singular value entropy was extracted as the evaluation index， and the feasibility of evaluating ground surface roughness was demonstrated based on singular value entropy index.The experimental results show that the singular value entropy of color images is a reasonable and feasible surface roughness evaluation index， and has a reasonable data structure expression in a mathematical sense. The comparative analysis of relevant index proves that the correlation and applicability of the index with surface roughness are stronger than that of the color difference index， and the regression prediction results are relatively accurate and have the potential to be extended to the field of engineering applications.

Key words: surface roughness, machine vision measurement, quaternion, singular value entropy, color information

摘要： 机器视觉测量表面粗糙度所采用的评价指标大多是根据灰度图像进行统计分析的，而当前研究的一些基于颜色信息的评价指标并未给出合理的数理结构表达。针对此问题，提出了一种基于彩色图像奇异值熵评价磨削表面粗糙度的检测方法。根据色块在不同等级粗糙度表面所形成的虚像能量分布差异，通过纯四元数的数据结构来表征一幅彩色图像，并对其进行数据分析，抽取奇异值熵作为评价指标，论证基于奇异值熵指标评价磨削表面粗糙度的可行性。实验结果表明，彩色图像奇异值熵不仅是一种合理可行的表面粗糙度评价指标，而且该指标在数学意义上具有合理的数据结构表达方式。相关指标的对比分析证明了该指标与表面粗糙度的相关性和适用性相对色差指标更优，回归预测结果也相对较为精准，具备向工程应用领域推广的潜力。

关键词: 表面粗糙度, 机器视觉测量, 四元数, 奇异值熵, 颜色信息