Despite the great possibilities of modern neural network architectures concerning the problems of object detection and recognition, the output of such models is the local (pixel) coordinates of objects bounding boxes in the image and their predicted classes. However, in several practical tasks, it is necessary to obtain more complete information about the object from the image. In particular, for robotic apple picking, it is necessary to clearly understand where and how much to move the grabber. To determine the real position of the apple relative to the source of image registration, it is proposed to use the Intel Real Sense depth camera and aggregate information from its depth and brightness channels. The apples detection is carried out using the YOLOv3 architecture; then, based on the distance to the object and its localization in the image, the relative distances are calculated for all coordinates. In this case, to determine the coordinates of apples, a transition to a symmetric coordinate system takes place by means of simple linear transformations. Estimating the position in a symmetric coordinate system allows estimating not only the magnitude of the shift but also the location of the object relative to the camera. The proposed approach makes it possible to obtain position estimates with high accuracy. The approximate root mean square error is 7–12 mm, depending on the range and axis. As for precision and recall metrics, the first is 100% and the second is 90%.