Suppose an object detection algorithm is good at detecting objects and people when an object and person is close to a camera and upright. If the person walks farther away from the camera and is "upside-down" from the perspective of the camera (e.g. a fisheye camera), should the algorithm still be good at detecting people and objects in this position?
Not necessarily. Supposing your data is from the distribution of possible images containing an upright person close to the camera. Something like a neural network would perform poorly on the new data since it comes from a distribution other than on what it was trained.
You could try augmenting the dataset to try to get some synthetic "far away upside down people" but there are no guarantees here.
I'll look for the source but A. Ng cite's an experiment where a team trained a neural network on a large dataset of vehicle images. They did not realize that the cars were all facing the same direction and their model performed very poorly on images that were very similar with the primary difference being a horizontal flip.