In a background image encoding method using transformation/quantization, a rate control scheme adaptively switches a quantization scale based on an amount of encoded data that has previously been generated.  That scheme operates so that amount of encoded data to converge on an intended value to control bit rate, and accordingly does not guarantee not exceeding the intended value. 
In a one-pass encoding scheme, an amount of encoded data may exceed a target amount.  If an encoder is implemented on hardware, a size of a bit stream has to be previously determined.  In that case the bit stream is broken up when the size of the bit stream exceeds the target amount of encoded data. 
In that regard, an encoding scheme has been proposed that avoids a stream buffer overflowing and failing.  In that scheme, the minimum and the maximum amount of encoded data of each macro block is preliminarily determined.  When an amount of encoded data of a target block exceeds the maximum amount, all the remaining macro blocks are encoded with the minimum amount of encoded data. 
In that scheme, an encoding condition is selected according to whether the buffer will overflow or not.  Generally, it is preferable that encoding in the minimum amount is not selected, because the image encoded by the minimum amount of encoded data is greatly deteriorated in image quality.  In a background method, the minimum amount of encoded data is not sufficiently small, so there may be a problem that encoding in the minimum amount is easily selected.