Video signals are encoded and decoded using a set of quantization tables that is generated from a base matrix and a scale matrix, which are both explicitly encoded into the encoded video bitstream. The sets of quantization tables may be changed as often as needed as long as the new base and scale matrices are explicitly encoding into the bitstream.

A video signal is converted into compressed frame signals, each comprising a coefficient signal of block coefficient signals for each frame in a video image. Each of the block coefficient signals represents the pixels in a pixel map block (420) with the coefficients in a hybrid polynomial. The hybrid polynomial contains discrete cosine terms, a constant term separated from the discrete cosine terms, and polynomial terms extracted from the discrete cosine terms. Each block coefficient signal contains a background component representing a coefficient of the constant term, a linear component representing the coefficients of the polynomial terms, and a nonlinear component representing the coefficients of the discrete cosine terms.

An image coding apparatus which improves the picture quality of an image. A quantization index arithmetic operation section calculates, based on motion vector residuals of macro block and the sum total of the motion vector residual outputted from a motion vector residual buffer section, a weighted average of the motion vector residual. The quantization index arithmetic operation section calculates, based on the value of activity of the macro block and the sum total of the activity outputted from an activity buffer section, a weighted average of the activity. The quantization index arithmetic operation section calculates a quantization index based on the weighted average of the vector residual or the weighted average of the activity.

A system and method for determining quantization level versus bit-rate characteristics of raw video signals in video frames during a pre-encoding phase for video technologies such as MPEG and MPEG-2. During a pre-encoding phase, various quantization levels are assigned to various parts of a frame, and the frame is then pre-encoded to determine a bit-rate for each quantization level used in the pre-encoding phase. Depending on the embodiment, quantization levels are assigned in one of many ways: checkerboard style, block style or any other distribution that avoids statistical anomalies. The method and system repeat the pre-encoding for plural frames, recording all quantization level versus bit-rate statistics on a frame by frame basis. These statistics are then used during encoding or re-encoding of a digital video to control the number of bits allocated to one segment of the digital video as compared to another segment, based on a target quality and target storage size for each segment. The resulting encoded digital video is stored on a digital storage medium, such as a compact disc.

An encoder and a decoder for still and moving pictures are provided. The encoder has a memory for storing a default quantization matrix including a plurality of quantization elements having predetermined values. A generator is also provided for producing a particular quantization matrix after a number of frames. The particular quantization matrix is read in a predetermined zigzag pattern, and the reading is terminated at a selected position which is in the middle of the zigzag pattern. An end code is added after the read quantization elements of a former portion of the particular quantization matrix. The quantization elements in the default quantization matrix are read in the same zigzag pattern from a position immediately after the selected position, and produce a latter portion of the default quantization matrix. The former portion of the particular quantization matrix and the latter portion of the default quantization matrix are synthesized to form a synthesis quantization matrix.