Fruit trees in orchards are typically placed at equal distances in rows; therefore, their branches are intertwined. The precise segmentation of a target tree in this situation is very important for many agricultural tasks, such as yield estimation, phenotyping, spraying, and pruning. However, our survey on tree segmentation revealed that no study has explicitly addressed this intertwining situation. This paper presents a novel dataset in which a precise tree region is labeled carefully by a human annotator by delineating the branches and trunk of a target apple tree. Because traditional rule-based image segmentation methods neglect semantic considerations, we employed cutting-edge deep learning models. Five recently pre-trained deep learning models for segmentation were modified to suit tree segmentation and were fine-tuned using our dataset. The experimental results show that YOLOv8 produces the best average precision (AP), 93.7 box AP@0.5:0.95 and 84.2 mask AP@0.5:0.95. We believe that our model can be successfully applied to various agricultural tasks.