We develop a novel Fourier-domain optical convolutional neural networks (FOCNNs) with multi-stage framework to hierarchical learn the image features at the speed of light. The FOCNN consists of two optical convolutional layers integrated with multiple parallel kernels and one optical fully-connected layer to form an all-optical CNN-like physical network structure. The FOCNN convolute the whole Fourier spectrum of the objects rather than the local receptive field of the objects, so it could extract the global and non-local features of the objects. In addition, the vortex phase is introduced to the optical convolutional kernels to extract the edge features. We incorporate this Fourier optics-based, parallel, one-step FOCNN in the tasks of semantic segmentation for pixel-level classification, and the capability of video-rate segmentation for objects is also demonstrated based on the programmable spatial light modulators, which demonstrated the computational power of FOCNN located in the range of Peta operations per second (POPS). Therefore, the FOCNN is useful for the real-time dynamic inference tasks, such as robotic vision, autonomous driving, and so on.
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