Coding of quantization matrices using parametric models
Quantization matrix can be used to adjust quantization of transform coefficients at different frequencies. In one embodiment, a single fixed parametric model, such as a polynomial is used to represent a quantization matrix. Modulation of bit cost and complexity is achieved by specifying only the n first polynomial coefficients, the remaining ones being implicitly set to zero or other default values. One form of the single fixed polynomial is a fully developed polynomial in (x, y), where x, y indicate the coordinates of a given coefficient in a quantization matrix, with terms ordered by increasing exponent. Since higher exponents are the last ones, reducing the number of polynomial coefficients reduces the degree of the polynomial, hence its complexity. The polynomial coefficients can be symmetrical in x and y, and thus reducing the number of polynomial coefficients that need to be signaled in the bitstream.
1. A method of video decoding, comprising:
decoding 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, {P i }, i=0, . . . , N−1;
forming a polynomial function, said polynomial function being a function of (x, y) and representing a sum of P i ·m i (x, y) i=0, . . . , N−1, M(x, y)=Σ i=0, . . . , N−1 P i ·m i (x, y), where x and y indicate matrix coordinates, P i is a polynomial coefficient at index i and m i (x, y) is a monomial at index i within polynomial representation of said matrix M(x, y), m i (x, y)=x px i y py i I, and px i and py i 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
decoding a block of an image based on said quantization matrix.
2. The method of claim 1 , wherein a matrix element of said quantization matrix is clipped such that all matrix elements of said quantization matrix is equal to or greater than a clipping value.
3. The method of claim 1 , wherein said N polynomial coefficients are symmetrical in x and y.
4. The method of claim 1 , wherein m i (x, y) is ordered by increasing degree of terms.
5. The method of claim 1 , wherein x and y are normalized respectively with respect to a horizontal and vertical size of said quantization matrix.
6. 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, {P i }, i=0, . . . , N−1;
form a polynomial function, said polynomial function being a function of (x, y) and representing a sum of P i ·m i (x, y), i=0, . . . , N−1, M(x, y)=Σ i=0, . . . , N−1 P i ·m i (x, y), where x and y indicate matrix coordinates, P i is a polynomial coefficient at index i and m i (x, y) is a monomial at index i within polynomial representation of said matrix M(x, y), m i (x, y)=x px i y py i , and px i and py i 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.
7. The apparatus of claim 6 , wherein a matrix element of said quantization matrix is clipped such that all matrix elements of said quantization matrix is equal to or greater than to a clipping value.
8. The apparatus of claim 6 , wherein said N polynomial coefficients are symmetrical in x and y.
9. The apparatus of claim 6 , wherein m i (x, y) is ordered by increasing degree of terms.
10. The apparatus of claim 6 , wherein x and y are normalized respectively with respect to a horizontal and vertical size of said quantization matrix.
11. 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, {P i }, i=0, . . . , N−1;
forming a polynomial function, said polynomial function being a function of (x, y) and representing a sum of P i ·m i (x, y), i=0, . . . , N−1, M(x, y)=Σ i=0, . . . , N−1 P i ·m i (x, y), where x and y indicate matrix coordinates, P i is a polynomial coefficient at index i and m i (x, y) is a monomial at index i within polynomial representation of said matrix M(x, y), m i (x, y)=x px i y py i , and px i and py i 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.
12. The method of claim 11 , wherein a matrix element of said quantization matrix is clipped such that all matrix elements of said quantization matrix is equal to or greater than a clipping value.
13. The method of claim 11 , wherein said N polynomial coefficients are symmetrical in x and y.
14. The method of claim 11 , wherein m i (x, y) is ordered by increasing degree of terms.
15. The method of claim 11 , wherein x and y are normalized respectively with respect to a horizontal and vertical size of said quantization matrix.
16. 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, {P i }, i=0, . . . , N−1;
form a polynomial function, said polynomial function being a function of (x, y) and representing a sum of P i ·m i (x, i=0, . . . , N−1, M(x, y)=Σ i=0, . . . , N−1 P i ·m i (x, y), where x and y indicate matrix coordinates, P i is a polynomial coefficient at index i and m i (x, y) is a monomial at index i within polynomial representation of said matrix M(x, y), m i (x, y)=x px i y py i , and px i and py i 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.
17. The apparatus of claim 16 , wherein a matrix element of said quantization matrix is clipped such that all matrix elements of said quantization matrix is equal to or greater than a clipping value.
18. The apparatus of claim 16 , wherein said N polynomial coefficients are symmetrical in x and y.
19. The apparatus of claim 16 , wherein m i (x, y) is ordered by increasing degree of terms.
20. The apparatus of claim 16 , wherein x and y are normalized respectively with respect to a horizontal and vertical size of said quantization matrix.