Fourier analysis of LiDAR scanned 3D point cloud data for surface reconstruction and fruit size estimation

Describing and monitoring fruit size along the supply chain plays a key role in assessment of fruit quality by non-destructive technologies contributing to resilience against climate change. Light detection and ranging (LiDAR) laser scanner can provide 3D point cloud of physical objects. This work developed a method to estimate the surface shape of partially scanned spheres (60 mm, 80 mm) previously scanned and manually segmented. The method was tested on a 3D point cloud of a scanned apple described by a Fourier series expansion. An ideal sphere point cloud was obtained by geometry generator software, and subsequently the 2D signature in spherical coordinates of the 3D point cloud was described by 1-D and 2-D Fourier series expansion, which served as the reference 2D signature for each scanned point cloud. Data preprocessing captured outlier removal by means of interquartile range (IQR) algorithm. Subsequently, the eigenvectors of each point cloud were estimated using singular value decomposition algorithm, where an estimated sphere centroid was approximated iteratively based on a root mean squared error (RMSE) minimization of each point cloud respect to an ideal sphere. The $\boldsymbol{\text { RMSE }_{\text {min }}}$ reached 4,94 mm and 4,34 mm for the spheres of 60 and 80 mm diameter, respectively. Moreover, the diameter estimation of an apple was approximated by using a Fourier series expansion, showing an approximated error of 0.99%.