Improving the efficiency of current neural networks and modeling them in biological neural systems have become popular research directions in recent years. Pulse-coupled neural network (PCNN) is a well applicated model for imitating the computation characteristics of the human brain in computer vision and neural network fields. However, differences between the PCNN and biological neural systems remain: limited neural connection, high computational cost, and lack of stochastic property. In this study, random-coupled neural network (RCNN) is proposed. It overcomes these difficulties in PCNN's neuromorphic computing via a random inactivation process. This process randomly closes some neural connections in the RCNN model, realized by the random inactivation weight matrix of link input. This releases the computational burden of PCNN, making it affordable to achieve vast neural connections. Furthermore, the image and video processing mechanisms of RCNN are researched. It encodes constant stimuli as periodic spike trains and periodic stimuli as chaotic spike trains, the same as biological neural information encoding characteristics. Finally, the RCNN is applicated to image segmentation, fusion, and pulse shape discrimination subtasks. It is demonstrated to be robust, efficient, and highly anti-noised, with outstanding performance in all applications mentioned above.