Fully invariant generalized Hough transform by out-of-focus multiview sensing with pupil array

Recognition of geometrical shapes in real-time and fully invariant (i.e., invariant under changes in position, scale, and orientation) is a demanding task in automated image analysis. In particular, the generalized Hough transform (GHT) is a well-known algorithm for the recognition of complex patterns out of edge binary images even with disconnected boundaries or corrupted by noise. In this work we present a space multiplexed optical implementation of the GHT which, by exploiting the redundancy derived from multiview sensing of a two-dimensional image and its out- of-focus capture with an adequate pupil array, allows us to obtain in a single shot the GHT of this image invariant to target shift, scale, and orientation. Experimental validation of the working principle is presented, along with an assessment of the robustness of the system against noise in the input.