The rapid development of nanotechnology has promoted the processing and manufacturing of micro-nano structures, scientific research and industrial applications. The investigation on optical properties of micro-nano structures has recently been one of the hotspots in the field of optics, which has driven emerging disciplines such as nanophotonics, surface plasmonic optics, metasurface/metamaterial optics, topological photonics, and non-Hermitian optics. It provides the important technical fundamentals for full control of light with high precision. This article focused on the edge detection in all-optical image processing. The fundamentals, principles, technologies and applications of micro-/nano-scale structures and devices were discussed to realize optical mathematical computing (such as differential, convolution), followed by a detailed prospect about its future applications in ultrafast image processing, high-contrast microscopic imaging, convolutional neural networks and intelligent optics.