Abstract: An encoder includes circuitry and memory connected to the circuitry. The circuitry: derives an absolute value of a sum of horizontal gradient values; derives, as a first parameter, the total sum of the absolute values of horizontal gradient values; derives, as a second parameter, the total sum of the absolute values of vertical gradient values; derives a horizontal-related pixel difference value; derives, as a third parameter, the total sum of the absolute values of horizontal-related pixel difference values; derives a vertical-related pixel difference value; derives, as a fourth parameter, the total sum of the absolute values of vertical-related pixel difference values; and generates a prediction image using the first to fourth parameters.

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 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: Provided is an encoder which includes circuitry and memory. The circuitry encodes an image block using the memory. In encoding the image block, the circuitry: obtains one or more size parameters related to a size of the image block; determines whether the one or more size parameters and one or more thresholds satisfy a determined relationship; encodes a split parameter when the one or more size parameters and the one or more thresholds are determined to satisfy the determined relationship, the split parameter indicating whether the image block is to be split into a plurality of partitions including a non-rectangular partition; and encodes the image block after splitting the image block into the plurality of partitions when the split parameter indicates that the image block is to be split into the plurality of partitions.

Abstract: An encoder includes circuitry and memory. Using the memory, the circuitry performs prediction on an image. A motion vector predictor list used in the prediction includes a spatially neighboring motion vector predictor obtained from a block spatially neighboring a current block, and a spatially broad motion vector predictor obtained from a block positioned at any of a plurality of predetermined positions in a second range that is broader than a first range that spatially neighbors the current block. The plurality of predetermined positions are defined by a regular interval using the top-left of a current picture as a reference point.

Abstract: An image encoder/decoder includes circuitry and a memory coupled to the circuitry. When a geometry of a block of a picture satisfies a first condition, the circuitry splits the block of the picture into sub blocks having a first set of geometries. When the geometry of the block does not satisfy the first condition, the circuitry splits the block of the picture into sub blocks having a second set of geometries, the second set of geometries being different from the first set of geometries. The circuitry encodes/decodes the sub blocks of the block.

Abstract: Provided is an encoder which includes circuitry and memory. The circuitry encodes an image block using the memory. In encoding the image block, the circuitry: obtains one or more size parameters related to a size of the image block; determines whether the one or more size parameters and one or more thresholds satisfy a determined relationship; encodes a split parameter when the one or more size parameters and the one or more thresholds are determined to satisfy the determined relationship, the split parameter indicating whether the image block is to be split into a plurality of partitions including a non-rectangular partition; and encodes the image block after splitting the image block into the plurality of partitions when the split parameter indicates that the image block is to be split into the plurality of partitions.

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 encoding method is provided for encoding a picture to generate a coded stream. The encoding method includes: 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 encoding the current block based on the second prediction image.

Abstract: An encoder according to one aspect of the present disclosure encodes a block of an image, and includes a processor and memory connected to the processor. Using the memory, the processor partitions a block into a plurality of sub blocks and encodes a sub block included in the plurality of sub blocks in an encoding process including at least a transform process or a prediction process. The block is partitioned using a multiple partition including at least three odd-numbered child nodes and each of a width and a height of each of the plurality of sub blocks is a power of two.

Abstract: A decoding method includes: decoding, from a bitstream, cropping information indicating an amount of cropping corresponding to an amount of padding of a first subpicture that is a subpicture (i) which is among a plurality of subpictures constituting a picture, (ii) in which at least one end of the subpicture is included in at least one end of the picture, (iii) to which at least one subpicture is adjacent on a side opposite to the at least one end of the subpicture, and (iv) which is padded so that a size of the subpicture reaches an integer multiple of a preconfigured coding unit size in at least one direction; decoding the first subpicture from the bitstream; and cropping the first subpicture according to the amount of cropping.

Abstract: An encoder which encodes a current block of a picture includes a processor and memory. Using the memory, the processor: determines whether intra prediction is to be used for the current block; and when it is determined that intra prediction is to be used for the current block, generates first transform coefficients by performing first transform of residual signals of the current block using a first transform basis; quantizes the first transform coefficients when an intra prediction mode for the current block is a determined mode and the first transform basis is different from a determined transform basis; 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 for the current block is not the determined mode or when the first transform basis matches the determined transform basis.

Abstract: An encoder according to one aspect of the present disclosure encodes a block of an image, and includes a processor and memory connected to the processor. Using the memory, the processor partitions a block into a plurality of sub blocks and encodes a sub block included in the plurality of sub blocks in an encoding process including at least a transform process or a prediction process. The block is partitioned using a multiple partition including at least three odd-numbered child nodes and each of a width and a height of each of the plurality of sub blocks is a power of two.

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; splits the block into a plurality of sub blocks in a second direction parallel to the second shorter side of the block when the ternary split process is not allowed; and encodes the plurality of sub blocks.

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 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 image decoder parses an encoded bitstream to obtain a first parameter and a second parameter, and derives a partition mode based on the first and second parameters. Responsive to the derived partition mode being a first partition mode, the image decoder executes the first partition mode including; splitting a block of a picture into a plurality of first blocks including a N×2N block sized N pixels by 2N pixels; splitting the N×2N block, wherein a ternary split is allowed to split the N×2N block in a vertical direction, which is a direction along the 2N pixels, into a plurality of sub blocks including at least one sub block sized N/4×2N, while a binary split is not allowed to split the N×2N block in the vertical direction into two sub blocks that are equally sized N/2×2N; and decoding the plurality of sub blocks.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in operation: determines whether a size of a current block, which is a unit for which a vector candidate list including vector candidates is generated, is less than or equal to a threshold; when the size of the current block is less than or equal to the threshold, generates the vector candidate list by registering a history-based motion vector predictor (HMVP) vector candidate in the vector candidate list from an HMVP table without performing a first pruning process; when the size of the current block is greater than the threshold, generates the vector candidate list by performing the first pruning process and registering the HMVP vector candidate in the vector candidate list from the HMVP table; and encodes the current block using the vector candidate list.

Abstract: Provided is an encoder which includes circuitry and memory. The circuitry encodes an image block using the memory. In encoding the image block, the circuitry: obtains one or more size parameters related to a size of the image block; determines whether the one or more size parameters and one or more thresholds satisfy a determined relationship; encodes a split parameter when the one or more size parameters and the one or more thresholds are determined to satisfy the determined relationship, the split parameter indicating whether the image block is to be split into a plurality of partitions including a non-rectangular partition; and encodes the image block after splitting the image block into the plurality of partitions when the split parameter indicates that the image block is to be split into the plurality of partitions.

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.