Bit allocation or quantizer assignment problem is a basic and essential issue in lossy picture coding. The optimal solution for the bit allocation problem can be found by the Lagrangian method. However, it requires much computational time and memory. To reduce complexity overhead, we propose a fast scheme using a picture activity measure. Comparison among the existing activity measurement methods is presented to select the most reliable activity measure and the mapping relation between the activity value, and a quantization parameter is proposed.