Most, if not all, action cameras have a wide FOV between 140˚ to 180˚. The only way to produce that wide field of view is by using a fisheye lens. Without it, the view becomes much narrower, but the fisheye lens does cause the distortion.
There are two major advantages to recording fisheye distortion.
First, it is optically easier to do, which means one can make lenses that are better in other metrics (such as chromatic aberration, resolution, vignetting, etc) while remaining small enough and light enough to fit into the body of an action camera.
Second, the relative size of an object doesn't change radically as it moves from center to edge when the camera is not under tight control.
For that reason, it is possible to define a crop area that follows the subject as it bounces around the full frame and then uses motion tracking to create a relatively stable view of the object, which can then be de-fished. If it were rectilinear, the stabilization process might have to do some major zoom and tilt corrections as well, which would be very distracting.
So it's normal that if you take pictures using the action camera with a wide FOV.
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