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Crop discrimination at the plant or patch level is vital for modern technology-enabled agriculture. Multispectral and hyperspectral remote sensing data have been widely used for crop classification. Even though spectral data are successful in classifying row-crops and orchards, they are limited in discriminating vegetable and cereal crops at plant or patch level. Terrestrial laser scanning is a potential remote sensing approach that offers distinct structural features useful for classification of crops at plant or patch level. The objective of this research is the improvement and application of an advanced deep learning framework for object-based classification of three vegetable crops: cabbage, tomato, and eggplant using high-resolution LiDAR point cloud. Point clouds from a terrestrial laser scanner (TLS) were acquired over experimental plots of the University of Agricultural Sciences, Bengaluru, India. As part of the methodology, a deep convolution neural network (CNN) model named CropPointNet is devised for the semantic segmentation of crops from a 3D perspective. The CropPointNet is an adaptation of the PointNet deep CNN model developed for the segmentation of indoor objects in a typical computer vision scenario. Apart from adapting to 3D point cloud segmentation of crops, the significant methodological improvements made in the CropPointNet are a random sampling scheme for training point cloud, and optimization of the network architecture to enable structural attribute-based segmentation of point clouds of unstructured objects such as TLS point clouds crops. The performance of the 3D crop classification has been validated and compared against two popular deep learning architectures: PointNet, and the Dynamic Graph-based Convolutional Neural Network (DGCNN). Results indicate consistent plant level object-based classification of crop point cloud with overall accuracies of 81% or better for all the three crops. The CropPointNet architecture proposed in this research can be generalized for segmentation and classification of other row crops and natural vegetation types.