Measuring grinding surface roughness based on singular value entropy of quaternion

Abstract Color image indices used to characterize surface roughness are more sensitive than grayscale images or spectral indices owing to the rich information contained in color images. In this paper, a method for measuring grinding surface roughness grinding based on the singular value entropy of the color image quaternion matrix is proposed. Color images captured at different levels of surface roughness are analyzed using a quaternion matrix, which is subjected to singular value decomposition from which a quaternion singular value entropy is derived as an index for evaluating roughness. Our experimental results show that this method for measuring grinding surface roughness based on quaternion singular value entropy is a more feasible roughness detection method than color difference indices because the singular value entropy is more strongly correlated with the actual roughness, with the monotonicity of the entropy decreasing more significantly as the roughness increases. Roughness prediction results obtained using a support vector machine also support the feasibility of measuring surface roughness based on the singular value entropy of the color image quaternion matrix, which can provide a reliable engineering application for the automatic measurement of surface roughness. Finally, the high degree of correspondence between the pure quaternion matrix and the image color matrix in the mathematical structure provides a broad mathematical space for the design and optimization of the color index.