Super-resolution microscopy using normal flow decoding and geometric constraints

Prior knowledge about the observed scene provides the key to restoration of frequencies beyond the bandpass of an imaging system (super-resolution). In conjunction with microscopy two super-resolution mechanisms have been mainly reported: analytic continuation of the frequency spectrum, and constrained image deconvolution. This paper describes an alternative approach to super-resolution. Prior knowledge is imposed through geometric and dynamic models of the scene. We illustrate our concept based on the stereo reconstruction of a micropipette moving in close proximity to a stationary target object. Information about the shape and the movement of the pipette is incorporated into the reconstruction algorithm. The algorithm was tested in a microrobot environment, where the pipette tip was tracked at sub-Rayleigh distances to the target. Based on the tracking results, a machine vision module controlled the manipulation of microscopic objects, e.g. latex beads or diamond mono-crystals. In the theoretical part of this paper we prove that knowledge of the form 'the pipette has moved between two consecutive frames of the movie' must result in a twofold increase in resolution. We used the normal flow of an image sequence to decode positional measures from motion evidence. In practice, super-resolution factors between 3 and 5 were obtained. The additional gain originates from the geometric constraints that were imposed upon the stereo reconstruction of the pipette axis.