An improved corner dealiasing and recognition algorithm for 2D Wadell roundness computation

This paper optimizes the 2D Wadell roundness calculation of particles based on digital image processing methods. An algorithm for grouping corner key points is proposed to distinguish each independent corner. Additionally, the cyclic midpoint filtering method is introduced for corner dealiasing, aiming to mitigate aliasing issues effectively. The relationships between the number of corner pixels (m), the central angle of the corner (α) and the parameter of the dealiasing degree (n) are established. The Krumbein chart and a sandstone thin section image were used as examples to calculate the 2D Wadell roundness. A set of regular shapes is calculated, and the error of this method is discussed. When α ≥ 30°, the maximum error of Wadell roundness for regular shapes is 5.21%; when 12° ≤ α < 30°, the maximum error increases. By applying interpolation to increase the corner pixels to the minimum number (m₀) within the allowable range of error, based on the α-m₀ relational expression obtained in this study, the error of the corner circle can be minimized. The results indicate that as the value of m increases, the optimal range interval for n also widens. Additionally, a higher value of α leads to a lower dependence on m. The study's results can be applied to dealiasing and shape analysis of complex closed contours.