How does this work? Each of the hundreds or perhaps thousands of built-in lenses is stretchable, so the lens can change its shape to adapt to the curvature of the sheet. This will avoid gaps between lenses that aren't flexible. As you bend the sheet in, its effective focal length increases. As you bend it outwards, it becomes a wide-angle lens.
The goal of this still-conceptual camera is to create a flexible imaging device that could be fitted on doors, self-driving cars, or as an almost flat camera with no protruding lenses or parts that could be used for snapshots and other photography, including black-and-white.
Here's an idea: Why not create a "sheet camera" using a similar concept that could be inserted into sheetfilm cameras for large-format digital photos?