Abstract: An encoding method is provided for encoding a picture to generate a coded stream. The encoding method incldues: generating a first prediction image of a current block included in a current picture by referring to a first region included in a reference picture different from the current picture; operating a bi-directional optical flow process to generate a second prediction image based on the first prediction image by referring to a second region included in the first region, and not operating the bi-directional optical flow process by referring to a third region not included in the first region; and encoding the current block based on the second prediction image.

Abstract: When a transform-basis adaptive selection mode is enabled, an encoder that transforms residuals of a current block to encode an image: adaptively selects a first horizontal transform basis from among one or more transform basis candidates when a horizontal size of the current block is greater than a first horizontal threshold size; otherwise selects a fixed horizontal transform basis as a first horizontal transform basis; adaptively selects a first vertical transform basis from among the one or more transform basis candidates when a vertical size of the current block is greater than a first vertical threshold size; otherwise selects a fixed vertical transform basis as a first vertical transform basis; and generates first transform coefficients by performing a first horizontal transform and a first vertical transform on the residuals of the current block, using the first horizontal transform basis selected and the first vertical transform basis selected, respectively.

Abstract: An encoder that encodes a current block in a picture includes circuitry and memory. Using the memory, the circuitry: determines whether to use intra prediction for the current block; and when determining to use intra prediction, (i) performs a first transform on a residual signal of the current block using a first transform basis to generate first transform coefficients; and (ii-1) performs a second transform on the first transform coefficients using a second transform basis to generate second transform coefficients and quantizes the second transform coefficients, when an intra prediction mode of the current block is a predetermined mode or when the first transform basis is same as a predetermined transform basis; and (ii-2) quantizes the first transform coefficients without performing the second transform when the intra prediction mode is different from the predetermined mode and the first transform basis is different from the predetermined transform basis.

Abstract: When intra prediction is to be used, an encoder determines whether an adaptive basis selection mode is to be used and whether a size of the current block matches a determined size. When the adaptive basis selection mode is to be used and the size matches the determined size, the encoder fixes the first transform basis for the current block to a first determined transform basis in the adaptive basis selection mode, and generates first transform coefficients by performing first transform of residual signals of the current block using the first determined transform basis; quantizes the first transform coefficients when an intra prediction mode for the current block is a determined mode; and generates second transform coefficients by performing second transform of the first transform coefficients using a second transform basis, and quantizes the second transform coefficients, when the intra prediction mode is not the determined mode.

Abstract: An encoder that encodes a current block in a picture includes circuitry and memory. Using the memory, the circuitry: splits the current block into a first sub block, a second sub block, and a third sub block in a first direction, the second sub block being located between the first sub block and the third sub block; prohibits splitting the second sub block into two partitions in the first direction; and encodes the first sub block, the second sub block, and the third sub block.

Abstract: Various embodiments provide an encoder that performs an up-conversion and a down-conversion on a first quantization matrix to generate a second quantization matrix, and quantizes transform coefficients of a current block using the second quantization matrix. The first quantization matrix has a first number of rows and a first number of columns equal to the first number of rows, and the second quantization matrix has a second number of rows and a second number of columns different from the second number of rows. In the up-conversion, the circuitry generates the second quantization matrix such that one of the second number of rows or the second number of columns is larger than the first number of rows. In the down-conversion, the circuitry generates the second quantization matrix such that the other of the second number of rows or the second number of columns is smaller than the first number of rows.

Abstract: An encoder includes memory and circuitry. The circuitry, using the memory, (i) selects a mode from among a plurality of modes each for deriving a motion vector, and derives a motion vector for a current block via the selected mode, and (ii) performs inter prediction encoding on the current block, using the derived motion vector, via one of a skip mode and a non-skip mode different from the skip mode. The plurality of modes include a plurality of first modes each for predicting the motion vector for the current block based on an encoded block neighboring the current block without encoding information indicating a motion vector into a stream. When a second mode included in the plurality of first modes is selected, the current block is encoded via the non-skip mode regardless of presence or absence of a residual coefficient.

Abstract: Various embodiments provide a decoder configured to select a filter based on a block size of a first block and a block size of a second block in an image, and change values of pixels in the first block and the second block. The filter includes a first set of multipliers and a first set of offsets for the first block, and a second set of multipliers and a second set of offsets for the second block. The values of the pixels in the first block and the second block are changed by performing multiplication with each multiplier in the first set of multipliers, by performing multiplication with each multiplier in the second set of multipliers, and by using the first set of offsets and the second set of offsets.

Abstract: An encoder includes circuitry and memory. The circuitry, using the memory: derives a one-dimensional array of a plurality of reference samples for intra prediction; performs smoothing on the one-dimensional array of the plurality of reference samples which has been derived; and generates a prediction image using the plurality of reference samples. In deriving the one-dimensional array, the circuitry projects a value of at least one decoded pixel located on a first line onto a second line perpendicular to the first line, to derive at least one of the plurality of reference samples, and the smoothing is performed on the at least one decoded pixel projected onto the second line.

Abstract: An encoding method includes: changing values of luma pixels in a first block and a second block to filter a first boundary between the first block and the second block, using clipping such that change amounts of the respective values are within respective luma clip widths, the luma pixels in the first block and the second block being arranged along a first line across the first boundary; and changing values of chroma pixels in a third block and a fourth block to filter a second boundary between the third block and the fourth block, using clipping such that change amounts of the respective values are within respective chroma clip widths, the chroma pixels in the third block and the fourth block being arranged along a second line across the second boundary. The luma clip widths applied to the luma pixels are selected to be asymmetrical relative to the first boundary.

Abstract: An image encoder performs a first partitioning including using a first partition mode, without writing first splitting information indicative of the first partition mode into a bitstream, to split a first block into a plurality of second blocks in response to that the first block is located adjacent to an edge of a picture and that the dimensions of the first block satisfy a first condition; and performs a second partitioning on the second block by writing second splitting information indicative of a second partition mode into the bitstream, wherein the second partition mode allows at least one of a quad tree splitting and a binary splitting, and using the second partition mode to split the second block into a plurality of coding units (CUs), wherein the second partition mode prohibits the quad tree splitting of the second block in certain conditions.

Abstract: An encoding method includes: determining a merge mode to be applied to a current block, the merge mode including a sub-block merge mode and a first merge mode, wherein in the merge mode, inter-prediction parameters are inferred from a neighboring block neighboring the current block, and wherein in the sub-block merge mode, the current block includes a plurality of sub-blocks, and inter-prediction parameters are provided for each of the plurality of sub-blocks; in response to the merge mode being determined to be the first merge mode, generating a prediction image for the current block by performing a bi-directional optical flow prediction process, wherein the bi-directional optical flow prediction process uses a spatial gradient for the current block; and in response to the merge mode being determined to be the sub-block merge mode, generating a prediction image for the current block by not performing the bi-directional optical flow prediction process.

Abstract: An image decoder includes circuitry and a memory, wherein the circuitry, in operation, determines whether inter prediction is to be applied to a current block; in response to determining that the inter prediction is to be applied to the current block, performs a partition prediction process; and, in response to determining that the inter prediction is not to be applied, decodes the current block without using the partition prediction process. The partition prediction process includes predicting first values of a set of pixels between a first partition and a second partition in the current block, using a first motion vector for the first partition; predicting second values of the set of pixels, using a second motion vector for the second partition; weighting the first values and the second values; and generating a prediction image for the current block using the weighted first values and the weighted second values.

Abstract: An encoder includes circuitry and memory. The circuitry, using the memory: prohibits a first splitting method when arrangement and shapes of blocks obtained by splitting a first block multiple times by the first splitting method are identical to arrangement and shapes of blocks obtained by splitting the first block multiple times by a second splitting method different from the first splitting method, and when scan order of the blocks obtained by the first splitting method is identical to scan order of the blocks obtained by the second splitting method; and encodes the first block.

Abstract: An encoder includes circuitry and memory. Using the memory, the circuitry, in inter prediction processing: derives a first motion vector of a current block to be processed, using a motion vector of a previous block which has been previously processed; derives a second motion vector of the current block by performing motion estimation in the vicinity of the first motion vector; and generates a prediction image of the current block by performing motion compensation using the second motion vector.

Abstract: An encoder encodes a video, and includes: circuitry; and memory coupled to the circuitry. Using the memory, the circuitry: obtains at least two items of prediction information for a first partition included in the video; derives at least one template from neighboring samples which neighbor the first partition; calculates at least two costs, using the at least one template and the at least two items of prediction information; using the at least two costs, (i) determines at least one splitting direction for the first partition or (ii) assigns one of the at least two items of prediction information to a second partition split from the first partition according to the splitting direction, and another thereof to a third partition split from the first partition according to the splitting direction; and encodes the first partition according to the splitting direction and the at least two items of prediction information.

Abstract: An encoder is an encoder that encodes a block in a picture using a prediction image of the block, and includes circuitry and memory. Using the memory, the circuitry: calculates a first average pixel value which is an average pixel value of first reference samples out of the first reference samples and second reference samples, The first reference samples are referable and located outside the block and adjacent to a first side of the block. The second reference samples are referable and located outside the block and adjacent to a second side of the block. When generating the prediction image, the circuitry applies the same prediction pixel value to inner samples among current samples to be processed that are included in the block. The inner samples constitute a quadrilateral region including at least two current samples in each of a horizontal direction and a vertical direction.

Abstract: An encoder is an encoder that encodes a block in a picture using a prediction image of the block, and includes circuitry and memory. Using the memory, the circuitry: calculates a first average pixel value which is an average pixel value of first reference samples out of the first reference samples and second reference samples, The first reference samples are referable and located outside the block and adjacent to a first side of the block. The second reference samples are referable and located outside the block and adjacent to a second side of the block. When generating the prediction image, the circuitry applies the same prediction pixel value to inner samples among current samples to be processed that are included in the block. The inner samples constitute a quadrilateral region including at least two current samples in each of a horizontal direction and a vertical direction.

Abstract: An encoder which includes circuitry and memory. Using the memory, the circuitry generates a list which includes candidates for a first motion vector for a first partition. The list has a maximum list size and an order of the candidates, and at least one of the maximum list size or the order of the candidates is dependent on at least one of a partition size or a partition shape of the first partition. The circuitry selects the first motion vector from the candidates included in the list; encodes an index indicating the first motion vector among the candidates in the list into the bitstream based on the maximum list size; and generates the predicted image for the first partition using the first motion vector.

Abstract: An encoder includes memory, and circuitry accessible to the memory. The circuitry accessible to the memory: determines whether OBMC is applicable to generation of a prediction image of a current block, according to whether BIO is to be applied to the generation of the prediction image of the current block; when BIO is to be applied to the generation of the prediction image of the current block, determines that OBMC is not applicable to the generation of the prediction image of the current block, and applies BIO to the generation of the prediction image of the current block without applying OBMC.