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This work presents a new perceptually motivated bit allocation strategy for region of interest (ROI) coding in video sequences. It is not possible to assure any minimum target foreground quality in the approaches reported so far in the literature. In our proposed strategy reported herein, the bit-allocation is based on a target quality for the foreground and allowing perceptually tolerable graceful quality degradation for the background within the specified bit-rate constraint. In cases where it is difficult to satisfy the target foreground quality within the bit rate constraints, the closest possible quality is assured. Our algorithm is implemented on the H.264/AVC standards. Results on some standard video sequences are presented and these are very encouraging.