Abstract: Provided is an encoder including: circuitry; and memory coupled to the circuitry. In operation, the circuitry: performs a mapping process of Luma Mapping with Chroma Scaling (LMCS) for transforming a first pixel value space applied to a luma display image signal into a second pixel value space applied to a luma encoding process signal, using line segments forming a transform curve, each of which corresponds to a different one of sections obtained by partitioning the first pixel value space; and encodes an image, and in the performing of the LMCS, the circuitry determines the transform curve so that among boundary values in the second pixel value space, a first value obtained by dividing a boundary value by a base width defined according to a bit depth of the image is not equal to a second value obtained by dividing another boundary value by the base width.

Abstract: An encoder that encodes a current block to be encoded in an image is provided. The encoder includes: processor; and memory coupled to the processor, in which, in operation, the processor: generates a first prediction image based on a motion vector, the first prediction image being an image with full-pel precision; generates a second prediction image using an interpolation filter by interpolating a value at a fractional-pel position between full-pel positions included in the first prediction image; and encodes the current block based on the second prediction image, and in the using of the interpolation filter, the interpolation filter is switched between a first interpolation filter and a second interpolation filter differing in a total number of taps from the first interpolation filter.

Abstract: An encoder includes circuitry and memory connected to the circuitry. In operation, the circuitry: stores MV information and correction processing information into a FIFO buffer for an HMVP mode in association, the MV information being derived for a processed block and correction processing information being related to correction processing of a prediction image of the processed block; registers, in a prediction candidate list for a merge mode, one or more prediction candidates each being a combination of MV information and correction processing information, the prediction candidates including a prediction candidate which is a combination of the motion vector information and the correction processing information stored in the FIFO buffer; and selects a prediction candidate from the prediction candidate list when a current block is to be processed in the merge mode, and performs correction processing of a prediction image of the current block, based on the correction processing information.

Abstract: An image encoder is provided including circuitry and a memory coupled to the circuitry. The circuitry, in operation, responds to a size of a block satisfying a size condition by generating a prediction image using a prediction mode selected from a plurality of prediction modes. The plurality of prediction modes include a first prediction mode in which a prediction process uses a motion vector and a reference block in a same picture as the block. The circuitry encodes the block using the prediction image.

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 includes circuitry and memory connected to the circuitry. In operation, the circuitry: stores MV information and correction processing information into a FIFO buffer for an HMVP mode in association, the MV information being derived for a processed block and correction processing information being related to correction processing of a prediction image of the processed block; registers, in a prediction candidate list for a merge mode, one or more prediction candidates each being a combination of MV information and correction processing information, the prediction candidates including a prediction candidate which is a combination of the motion vector information and the correction processing information stored in the FIFO buffer; and selects a prediction candidate from the prediction candidate list when a current block is to be processed in the merge mode, and performs correction processing of a prediction image of the current block, based on the correction processing information.

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 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 coupled to the circuitry. In operation, the circuitry: writes, into a sequence parameter set which is header information of a sequence, video usability information syntax which is information for realizing an additional function in display of an image, and syntax different from the video usability information syntax. The syntax includes at least one parameter related to display timing of the image.

Abstract: An encoder includes circuitry and memory connected to the circuitry. The circuitry, in operation: derives, as a first parameter, a total sum of absolute values of sums of horizontal gradient values respectively for pairs of relative pixel positions; derives, as a second parameter, a total sum of absolute values of sums of vertical gradient values respectively for the pairs of relative pixel positions; derives, as a third parameter, a total sum of horizontal-related pixel difference values respectively for the pairs of relative pixel positions; derives, as a fourth parameter, a total sum of vertical-related pixel difference values respectively for the pairs of relative pixel positions; derives, as a fifth parameter, a total sum of vertical-related sums of horizontal gradient values respectively for the pairs of relative pixel positions; and generates a prediction image to be used to encode the current block using the first, second, third, fourth, and fifth parameters.

Abstract: An encoder determines, based on a width and a height of a block, whether or not to disable a prediction mode in which the block is split along a partitioning line defined by a distance and an angle and then prediction is performed; and encodes the block with the prediction mode disabled or not disabled according to a result of the determination on whether or not to disable the prediction mode. Here, the distance is the shortest distance between the center of the block and the partitioning line, and the angle is an angle representing a direction from the center of the block toward the partitioning line in the shortest distance. The encoder determines to disable the prediction mode when (i) a width-to-height ratio is at least 8 or (ii) a height-to-width ratio is at least 8.

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 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: Provided is an encoder including circuitry and memory coupled to the circuitry. A prediction mode for a current block is an affine mode, and in operation, the circuitry: derives a base motion vector which is a motion vector to be used in a prediction process for the current block, and is a motion vector at an affine-mode control point in the current block; derives a first motion vector different from the base motion vector; derives a motion vector difference based on a difference between the base motion vector and the first motion vector; determines whether the motion vector difference is greater than a threshold; if so, modifies a second motion vector different from the base motion vector and the first motion vector, and if not, does not modify the second motion vector; and encodes the current block using the second motion vector modified or the second motion vector not modified.

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 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 an inter prediction mode in which an affine motion vector is calculated for each of sub-blocks constituting a current block of a picture in the video, based on motion vectors of neighboring blocks of the current block, changes a shape or size of the sub-block according to a variation in direction or variation in magnitude among the motion vectors of the neighboring blocks; calculates the affine motion vector for the sub-block having the shape or size changed; and performs the motion compensation for the sub-block having the shape or size changed.

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: 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.