Observability of shape from focus

We consider a closed-loop system consisting of a commercial video camera with auto-focus. We view the position of the lens as the controlled input, the brightness array on the CCD sensor as the measured output, and the auto-focus' task to maintain a region of the image "in focus". As we see, the (non-linear and distributed) input/output map that describes the imaging process depends upon the shape of the scene being viewed. The aim of the paper is to study the observability of three-dimensional shape from two-dimensional images of a static scene obtained by controlling the focus of the camera.