In recent decades, precision agriculture and geospatial technologies have made it possible to ensure sustainability in an olive-growing sector. The main goal of this study is the extraction of olive tree canopies by comparing two approaches, the first of which is related to geographic object-based analysis (GEOBIA), while the second one is based on the use of vegetation indices (VIs). The research area is a micro-location within the Lun olives garden, on the island of Pag. The unmanned aerial vehicle (UAV) with a multispectral (MS) sensor was used for generating a very high-resolution (VHR) UAVMS model, while another mission was performed to create a VHR digital orthophoto (DOP). When implementing the GEOBIA approach in the extraction of the olive canopy, user-defined parameters and classification algorithms support vector machine (SVM), maximum likelihood classifier (MLC), and random trees classifier (RTC) were evaluated. The RTC algorithm achieved the highest overall accuracy (OA) of 0.7565 and kappa coefficient (KC) of 0.4615. The second approach included five different VIs models (NDVI, NDRE, GNDVI, MCARI2, and RDVI2) which are optimized using the proposed VITO (VI Threshold Optimizer) tool. The NDRE index model was selected as the most accurate one, according to the ROC accuracy measure with a result of 0.888 for the area under curve (AUC).