A geometric modelling approach to estimate apple fruit size by means of LiDAR 3D point clouds

Remote sensing in agriculture aims to search new methods to monitor fruit at the tree, thus improving the estimation of yield-related variables. Light detection and range (LiDAR) scanning was introduced to obtain geometric and radiometric information from fruit surfaces by means of 3D point clouds. A geometric model to estimate apple size by means of segmented 3D point cloud of fruit is proposed in the present study. The model consists in the approximation of 3D point clouds to a reference shape given by 2D Fourier series expansion. Each point cloud was approximated to its reference shape using an iterative error minimization routine. The geometric model was applied to laboratory and field data of spheres and apples during fruit growth, ranging from 60 to 151 days after full bloom (DAFB). An overall RMSE between measured and predicted fruit radius of 20.1, 76.8, and 119.1% was found for the geometric model, mean, and maximum Euclidean distance approaches, respectively, including all studied growth periods in field conditions. Moreover, the linear regression on measured and predicted values showed considerably improved coefficient of determination (R2) of the geometric model in comparison to Euclidean distance calculations with R2 values of 0.76 and 0.49 for laboratory and field scanned apples, respectively. The data processing method enables fruit monitoring and their application of terrestrial LiDAR sensing in precise orchard management.