Efficient Autocorrelation Computation and Its Fourier Optical Implementation for Off-Center Image Perception

With the development of Artificial Intelligence (AI), deep neural networks have shown promising capabilities for image signal processing tasks. However, in practical applications of image processing and visual perception, the object of interest may deviate from the image center, therefore, more complex networks are required to overcome the influence of object position. Besides these data-driven approaches, some physics-inspired signal processing methods can efficiently extract intrinsic features from the object. In this paper, we propose an Autocorrelation computation and its Fourier Optical implementation (AFO) scheme to obtain the position-independent spatial features of the object, enabling robust perception tasks such as classification for off-center objects. To enhance computational efficiency, we use Fast Fourier Transform (FFT) and phase elimination in the frequency domain to equate the autocorrelation. Based on the algorithmic foundation, we construct an optical Fourier system to physically implement the proposed feature extraction. The algorithm-hardware co-designed prototype is verified through simulation and real-world experiments on 3 handcrafted image classification datasets and achieves an average improvement of 36$\%$ in accuracy and 44$\%$ in computational efficiency. The AFO prototype demonstrates the potential for conducting efficient computing in the optical chain, paving the way for ultra-efficient, low-latency visual perception applications.