一种葡萄果穗凸包体积的近似计算方法

An Approximate Method for Calculating the Volume of the Convex Hull of Grape Spikes

摘要: 果穗紧实度是评价葡萄外观、葡萄酒品质形成的一个重要指标，是反应果实颗粒之间松紧程度的一个抽象指标。由于葡萄颗粒之间缝隙变化，其凸包体积难以准确计算。本文从三个视角120˚来拍摄葡萄果穗，采用图像处理分割，获取果穗区域参数，以投影面积法、横切面累加法来分别近似计算果穗的凸包体积。结果表明，采用投影面积法得到的凸包体积偏差在1%~7%之间，而横切面累加法得到的凸包体积偏差分布较小，在0.76%~5.86%，且平均偏差仅为2.48%。因此，横切面积累加法可以为后续果穗紧实度的凸包体积计算提供了一种可行的参考方法。

Abstract: The compactness of grape clusters is an important indicator for evaluating grape appearance and the formation of wine quality, reflecting an abstract measure of the tightness between fruit particles. Due to variations in the gaps between grape particles, accurately calculating their convex hull volume is challenging. This study captures images of grape clusters from three 120˚ perspectives, employs image processing segmentation to obtain regional parameters of the clusters, and uses the projection area method and cross-sectional accumulation method to approximate the convex hull volume of the grape clusters. The results showed that the convex hull volume obtained using the projection area method had a deviation of 1% to 7%, while the deviation of the convex hull volume obtained using the cross-sectional accumulation method was smaller, ranging from 0.76% to 5.86%, with an average deviation of only 2.48%. Therefore, the cross-sectional accumulation method provides a viable reference approach for subsequent calculations of the convex hull volume related to the compactness of grape clusters.