Coding of quantization matrices using parametric models

An apparatus for video decoding, comprising:

• one or more processors, wherein said one or more processors are configured to:
• decode at least a syntax element representing a value, N, indicating a number of polynomial coefficients, N being determined from among a plurality of values;
• obtain N polynomial coefficients, {Pi}, i=0, . . . , N−1;
• form a polynomial function, said polynomial function being a function of (x, y) and representing a sum of Pi·mi(x, y), i=0, . . . , N−1, M(x, y)=Σi=0, . . . , N−1 Pi·mi (x, y), where x and y indicate matrix coordinates, Pi is a polynomial coefficient at index i and mi(x, y) is a monomial at index i within polynomial representation of said matrix M(x, y), mi(x, y)=xpxiypyi, and pxi and pyi are exponents of x and y;
• obtain a quantization matrix based on said polynomial function, wherein an element of said quantization matrix at matrix coordinates (x, y) is obtained based on M(x, y);
• and
• decode a block of an image based on said quantization matrix.

A method of video encoding, comprising:

• encoding at least a syntax element representing a value, N, indicating a number of polynomial coefficients, N being determined from among a plurality of values;
• obtaining N polynomial coefficients, {Pi}, i=0, . . . , N−1;
• forming a polynomial function, said polynomial function being a function of (x, y) and representing a sum of Pi·mi(x, y), i=0, . . . , N−1, M(x, y)=Σi=0, . . . , N−1 Pi·mi(x, y), where x and y indicate matrix coordinates, Pi is a polynomial coefficient at index i and mi(x, y) is a monomial at index i within polynomial representation of said matrix M(x, y), mi(x, y)=xpxiypyi, and pxi and pyi are exponents of x and y;
• obtaining a quantization matrix based on said polynomial function, wherein an element of said quantization matrix at matrix coordinates (x, y) is obtained based on M(x, y);
• and
• encoding a block of an image based on said quantization matrix.

An apparatus for video encoding, comprising:

• one or more processors, wherein said one or more processors are configured to:
• encode at least a syntax element representing a value, N, indicating a number of polynomial coefficients, N being determined from among a plurality of values;
• obtain N polynomial coefficients, {Pi}, i=0, . . . , N−1;
• form a polynomial function, said polynomial function being a function of (x, y) and representing a sum of Pi·mi(x, i=0, . . . , N−1, M(x, y)=Σi=0, . . . , N−1 Pi·mi(x, y), where x and y indicate matrix coordinates, Pi is a polynomial coefficient at index i and mi(x, y) is a monomial at index i within polynomial representation of said matrix M(x, y), mi(x, y)=xpxiypyi, and pxi and pyi are exponents of x and y;
• obtain a quantization matrix based on said polynomial function, wherein an element of said quantization matrix at matrix coordinates (x, y) is obtained based on M(x, y);
• and
• encode a block of an image based on said quantization matrix.