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, 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 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.

Abstract: An encoder, includes: circuitry; and memory. Using the memory, the circuitry: in inter prediction for a current block, determines a base motion vector, and writes, in an encoded signal, a delta motion vector representing (i) one direction among a plurality of directions including a diagonal direction and (ii) a distance from the base motion vector; and encodes the current block using the delta motion vector and the base motion vector as a motion vector of the current block.

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, when sub-block encoding is to be performed, determines a plurality of sub-blocks in a first image block, the plurality of sub-blocks including a first sub-block, determines a first motion vector for the first sub-block by referring to a first candidate list, performs first inter prediction processing on the first sub-block using the first motion vector, and encodes the first image block using a result of the first inter prediction processing. When partition encoding is to be performed, the encoder, in operation, determines a plurality of partitions in a second image block, the plurality of partitions including a first partition, determines a second motion vector for the first partition by referring to a second candidate list, performs second inter prediction processing on the first partition using the second motion vector, and encodes the second image block using a result of the second inter prediction processing.

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 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. The circuitry derives a first motion vector in a unit of a prediction block using a first inter frame prediction mode that uses a degree of matching between two reconstructed images of two regions in two difference pictures, the prediction block being obtained by splitting an image included in a video; and performs, in the unit of the prediction block, a first motion compensation process that generates a prediction image by referring to a spatial gradient of luminance in an image generated by performing motion compensation using the first motion vector derived.

Abstract: An encoder partitions into blocks using a set of block partition modes. The set of block partition modes includes a first partition mode for partitioning a first block, and a second block partition mode for partitioning a second block which is one of blocks obtained after the first block is partitioned. When the number of partitions of the first block partition mode is three, the second block is a center block among the blocks obtained after partitioning the first block, and the partition direction of the second block partition mode is same as the partition direction of the first block partition mode, the second block partition mode indicates that the number of partitions is only three. A parameter for identifying the second block partition mode includes a first flag indicating a horizontal or vertical partition direction, and does not include a second flag indicating the number of partitions.

Abstract: Provided is an encoder which includes circuitry and memory. Using the memory, the circuitry splits an image block into a plurality of partitions, obtains a prediction image for a partition, and encodes the image block using the prediction image. When the partition is not a non-rectangular partition, the circuitry obtains (i) a first prediction image for the partition, (ii) a gradient image for the first prediction image, and (iii) a second prediction image as the prediction image using the first prediction image and the gradient image. When the partition is a non-rectangular partition, the circuitry obtains the first prediction image as the prediction image without using the gradient image.

Abstract: An encoder that encodes a current block in a picture includes circuitry and memory. Using the memory, the circuitry: performs a first transform on a residual signal of the current block using a first transform basis to generate first transform coefficients; and 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 the first transform basis is the same as a predetermined transform basis; and quantizes the first transform coefficients without performing the second transform, when the first transform basis is different from the predetermined transform basis.

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: A decoder that decodes a current block using a motion vector includes: a processor; and memory. Using the memory, the processor: derives a first candidate vector from one or more candidate vectors of one or more neighboring blocks that neighbor the current block; determines, in a first reference picture for the current block, a first adjacent region that includes a position indicated by the first candidate vector; calculates evaluation values of a plurality of candidate regions included in the first adjacent region; and determines a first motion vector of the current block, based on a first candidate region having a smallest evaluation value among the evaluation values. The first adjacent region is included in a first motion estimation region determined based on the position indicated by the first candidate vector.

Abstract: An encoder includes circuitry and memory. Using the memory, the circuitry, in operation, selects an encoding mode from among candidates including a decoder-side motion vector refinement (DMVR) encoding mode and a partition encoding mode. When the DMVR encoding mode is selected, the circuitry: obtains a first motion vector for a first image block; derives a second motion vector from the first motion vector using motion search; and generates a prediction image for the first image block using the second motion vector. When the partition encoding mode is selected, the circuitry: determines a plurality of partitions in a second image block; obtains a third motion vector for each partition; and generates a prediction image for the second image block using the third motion vector, without deriving a fourth motion vector from the third motion vector using motion search.

Abstract: An encoder, when sub-block encoding is to be performed, determines a plurality of sub-blocks in a first image block, the plurality of sub-blocks including a first sub-block, determines a first motion vector for the first sub-block by referring to a first candidate list, performs first inter prediction processing on the first sub-block using the first motion vector, and encodes the first image block using a result of the first inter prediction processing. When partition encoding is to be performed, the encoder, in operation, determines a plurality of partitions in a second image block, the plurality of partitions including a first partition, determines a second motion vector for the first partition by referring to a second candidate list, performs second inter prediction processing on the first partition using the second motion vector, and encodes the second image block using a result of the second inter prediction processing.

Abstract: An encoder includes circuitry and a memory coupled to the circuitry. The circuitry, in operation, determines whether or not a ternary split process of splitting a block into three sub blocks in a first direction parallel to a first longer side of the block is allowed by comparing a size of a second shorter side of the block to a minimum threshold value. The circuitry, responsive to the ternary split process being allowed, writes, into a bitstream, a split direction parameter indicative of a splitting direction. The circuitry, in operation, splits the block into a plurality of sub blocks in a direction indicated by the split direction parameter; and encodes the plurality of sub blocks. The minimum threshold value corresponds to a minimum size supported in a transform process.

Abstract: An encoder that encodes a video includes a processor and memory. Using the memory, the processor: derives a prediction error of an image included in the video, by subtracting a prediction image of the image from the image; determines a secondary transform basis based on a primary transform basis, the primary transform basis being a transform basis for a primary transform to be performed on the prediction error, the secondary transform basis being a transform basis for a secondary transform to be performed on a result of the primary transform; performs the primary transform on the prediction error using the primary transform basis; performs the secondary transform on a result of the primary transform using the secondary transform basis; performs quantization on a result of the secondary transform; and encodes a result of the quantization as data of the image.

Abstract: An image decoder includes circuitry and a memory, wherein the circuitry, in operation, calculates first values of a first partition in a current block, using a first motion vector for the first partition; calculates second values of a second partition in the current block, using a second motion vector for the second partition; calculates third values of a set of pixels between the first partition and the second partition, using the first motion vector; calculates fourth values of the set of pixels, using the second motion vector; and weights the third values and the fourth values. A number of pixels in a row in the set of pixels is two or more, and two or more weights applied to the third values increase along the row.

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: A decoder comprises circuitry and memory. The circuitry, using the memory, in operation, determines a number of first pixels and a number of second pixels used in a deblocking filter process, wherein the first pixels are located at an upper side of a block boundary and the second pixels are located at a lower side of the block boundary, and performs the deblocking filter process on the block boundary. The number of the first pixels and the number of the second pixels are selected from among candidates, wherein the candidates include at least 4 and M larger than 4. Response to a location of the block boundary being a predetermined location, the number of the first pixels used in the deblocking filter process is limited to be 4.