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Fisheye cameras are widely employed in automatic parking, and the video stream object detection (VSOD) of the fisheye camera is a fundamental perception function to ensure the safe operation of vehicles. In past research work, the difference between the output of the deep learning model and the actual situation at the current moment due to the existence of delay of the perception system is generally ignored. But the environment will inevitably change within the delay time which may cause a potential safety hazard. In this paper, we propose a real-time detection framework equipped with a dual-flow perception module (dynamic and static flows) that can predict the future and alleviate the time-lag problem. Meanwhile, we use a new scheme to evaluate latency and accuracy. The standard bounding box is unsuitable for the object in fisheye camera images due to the strong radial distortion of the fisheye camera and the primary detection objects of parking perception are vehicles and pedestrians, so we adopt the rotate bounding box and propose a new periodic angle loss function to regress the angle of the box, which is the simple and accurate representation method of objects. The instance segmentation ground truth is used to supervise the training. Experiments demonstrate the effectiveness of our approach. Code is released at: https://gitee.com/hiyanyx/fisheye-streaming-perception.