| CPC H04N 19/126 (2014.11) [H04N 19/176 (2014.11); H04N 19/18 (2014.11); H04N 19/82 (2014.11)] | 6 Claims |

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1. An image encoding apparatus for encoding an image, comprising:
a generation unit configured to generate, from a first quantization matrix having a size of 8×8, a second quantization matrix having a size of 4×16 (the size of 4×16 indicates a size of 4 in a horizontal direction and a size of 16 in a vertical direction), wherein the first quantization matrix has a r-th row and a r-th column (r is an integer which satisfies 0≤r≤7), and the second quantization matrix has a p-th row and a q-th column (p is an integer which satisfies 0≤p≤15, and q is an integer which satisfies 0≤q≤3);
a transformation unit configured to transform prediction errors to derive transformation coefficients; and
a quantization unit configured to quantize the transformation coefficients in a block having a size corresponding to the size of 4×16 using the second quantization matrix,
wherein the generation unit generates the second quantization matrix at least (a) by decreasing elements of the first quantization matrix having the size of 8×8 in a horizontal direction without increasing elements of the first quantization matrix having the size of 8×8 in the horizontal direction when generating the second quantization matrix from the first quantization matrix so that all elements at a 1-th column, a 3-th column, a 5-th column, and a 7-th column of the first quantization matrix are removed, and (b) by increasing elements of the first quantization matrix having the size of 8×8 in a vertical direction so that an element at an m-th row and a 2n-th column in the first quantization matrix is arranged as an element at a 2m-th row and an n-th column in the second quantization matrix and an element at a (2m+1)-th row and the n-th column in the second quantization matrix, wherein m and n are integers of 0 or more, and
wherein the generation unit is capable of generating a third quantization matrix having a size of 16×4 (the size of 16×4 indicates a size of 16 in a horizontal direction and a size of 4 in a vertical direction) from the first quantization matrix.
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