This paper considers a video coding system for surveillance applications. It consists of one "base encoder" that encodes a down-sampled, full-view version of the input video sequence and one "region of interest" (ROI) encoder that encodes an ROI of the video sequence at the original image resolution. An important requirement of the video coding system is that the ROI bit stream and the base bit stream should be independently decodable. We explore the inter-relationship between the full-view video sequence and the ROI video sequence and apply it to improve the computational efficiency of the ROI encoder. The proposed algorithm achieves an average of 170% speedup