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Rate and quality-constrained rate control is very effective for video applications, since it can maintain constant quality while eliminating local rate spikes. An adaptive rate control method based on image activity measures (ARCIAM) is proposed for Motion JPEG2000. The algorithm can efficiently adjust the compressed bit rates to meet the rate and quality constraints for different types of colour sequences. It predicts the rate-distortion (RD) slope thresholds for frames based on image activity measure (IAM) before entropy coding. Thus, the encoding of unnecessary coding passes can be avoided. Experimental results show that the proposed method can meet the quality and rate constraints, and can achieve quality performance comparable to post-compression rate distortion optimisation at the same bit rate. Under 3 bpp and 40 dB constraints, ARCIAM can reduce the total encoding time and tier-1 encoding time for sequences by more than 20 and 30 , respectively. Moreover, the memory requirement for buffering bit-streams and RD-slope information is reduced by more than 30 on average. Besides, the method can be incorporated into the line-based JPEG2000 encoding system easily, and has been implemented on Kakadu.