Abstract: An encoder which encodes a video including a plurality of pictures includes circuitry and memory. Using the memory, the circuitry performs: encoding a first picture among the plurality of pictures; and performing (i) a first operation for encoding a parameter set for a second picture which follows the first picture in coding order among the plurality of pictures after encoding the first picture, and encoding the second picture after encoding the parameter set, or (ii) a second operation for encoding the second picture without encoding the parameter set after encoding the first picture. The circuitry performs the first operation when the second picture is a determined picture, in the performing of the first operation or the second operation.

Abstract: An encoder which codes a moving picture includes: a processor; and a memory, wherein the processor, using the memory: subtracts a prediction image of an image included in the moving picture from the image so as to derive a prediction error; sequentially selects a plurality of transform basis candidates; derives an evaluation value of a transform basis candidate selected; compares the evaluation value with a threshold value; based on a result of the comparison, skips selection of one or more transform basis candidates that have not been selected; determines the transform basis from one or more transform basis candidates selected; performs the transform of the prediction error, using the transform basis; quantizes a result of the transform; and codes a result of the quantization as data of the image.

Abstract: An encoder includes memory and circuitry configured to determine a merge mode to be applied to a current block, wherein the merge mode includes a sub-block merge mode and a first merge mode. In the merge mode, inter-prediction parameters are inferred from a neighboring block neighboring the current block. 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. When the merge mode is determined to be the first merge mode, the circuitry generates 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. When the merge mode is determined to be the sub-block merge mode, the circuitry generates a prediction image for the current block by not performing the bi-directional optical flow prediction process.

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 performs: deriving a plurality of reference samples positioned on a first line, for intra prediction; and generating a prediction image using the plurality of reference samples. The deriving includes interpolating a value on a second line perpendicular to the first line using values of encoded pixels on the second line to generate an interpolated value, and deriving one of the plurality of reference samples by projecting the interpolated value onto the first line.

Abstract: An encoder includes processing circuitry and a memory coupled to the processing circuitry. The processing circuitry is configured to: select a first filter for a first block based at least on a block size of the first block, the first filter including a first set of filter coefficients; select a second filter for a second block based at least on a block size of the second block, the second filter including a second set of filter coefficients; and change values of pixels in the first block and the second block to filter a boundary between the first block and the second block. The first set of filter coefficients applied in the first block and the second set of filter coefficients applied in the second block are selected to be asymmetrical with respect to the boundary based on the block size of the first block and the second block.

Abstract: An encoder is disclosed which includes circuitry and memory. Using the memory, the circuitry, in a first operating mode, derives first motion vectors for a first block obtained by splitting a picture, and generates a prediction image corresponding to the first block, with a bi-directional optical flow flag settable to true, and by referring to spatial gradients of luminance generated based on the first motion vectors. Using the memory, the circuitry, in a second operating mode, derives second motion vectors for a sub-block obtained by splitting a second block, the second block being obtained by splitting the picture, and generates a prediction image corresponding to the sub-block, with the bi-directional optical flow flag set to false.

Abstract: Various embodiments provide an encoder that generates a first quantization matrix including a plurality of matrix elements; generates, using the first quantization matrix, a subset of the first quantization matrix including only a subset of matrix elements of the plurality of matrix elements; and quantizes, using the subset of matrix elements included in the subset of the first quantization matrix, transform coefficients of a current block. Each of the subset of matrix elements and each of the transform coefficients has an x-coordinate value that is less than a threshold x-coordinate value, a y-coordinate value that is less than a threshold y-coordinate value, or an x-coordinate value that is less than the threshold x-coordinate value and a y-coordinate value that is less than the threshold y-coordinate value.

Abstract: An encoder includes circuitry and memory. Using the memory, the circuitry: encodes an original image and decodes the original image encoded, to generate a first bitstream and a local decoded image; encodes supplemental information and decodes the encoded supplemental information, to generate a second bitstream and local decoded supplemental information; inputs data based on the local decoded image and the local decoded supplemental information to a post processing network which is a neural network, to cause a reconstructed image to be output from the post processing network, the reconstructed image corresponding to the original image and being to be used to encode a following original image which follows the original image; and concatenates the first bitstream and the second bitstream to generate a concatenated bitstream.

Abstract: An encoder includes processing circuitry and memory. Using the memory, the processing circuitry: encodes and reconstructs an image to generate a reconstructed image; determines, according to a characteristic of a block in the reconstructed image, an interpolation method for interpolating pixels located outside a referable region including the block; interpolates the pixels located outside the referable region, using the interpolation method determined; and applies a filter to the block using the pixels interpolated.

Abstract: An encoder includes processing circuitry and a memory coupled to the processing circuitry. Using the memory, the processing circuitry is configured to: change values of pixels in a first block and a second block to filter a boundary between the first block and the second block. The pixels include type one pixels and type two pixels different from the type one pixels. The first set of filter coefficients applied to the type one pixels in the first block and the second set of filter coefficients applied to the type one pixels in the second block are selected to be asymmetrical with respect to the boundary based on block sizes of the first block and the second block.

Abstract: Provided is an encoder that achieves further improvement. The encoder includes processing circuitry and memory. Using the memory, the processing circuitry: obtains two prediction images from two reference pictures; derives a luminance gradient value of each pixel position in each of the two prediction images; derives a luminance local motion estimation value of each pixel position in a current block; generates a luminance final prediction image using a luminance value and the luminance gradient value in each of the two prediction images, and the luminance local motion estimation value of the current block; and generates a chrominance final prediction image using at least one of the luminance gradient value of each of the two prediction images or the luminance local motion estimation value of the current block, and chrominance of each of the two prediction images.

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 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: Provided is an encoder which includes circuitry and memory. Using the memory, the circuitry: splits an image block into a plurality of partitions; generates a motion vector candidate list; obtains a motion vector from the motion vector candidate list; performs inter prediction processing using the motion vector; and encodes the image block using a result of the inter prediction processing. When a partition is a non-rectangular partition, the circuitry generates the motion vector candidate list using at least one motion vector among a plurality of motion vectors for a plurality of spatially neighboring partitions or a plurality of motion vectors for a plurality of temporally neighboring partitions, without using a plurality of motion vectors for a plurality of sub-partitions.

Abstract: An encoder includes circuitry and memory. Using the memory, the circuitry performs a primary transform on a derived prediction error, performs a secondary transform on a result of the primary transform, quantizes a result of the secondary transform, and encodes a result of the quantization as data of an image. When a current block to be processed has a predetermined shape, the encoder performs the secondary transform using, among secondary transform basis candidates that are secondary bases usable in the secondary transform, only a secondary transform basis candidate having a size that is not largest size containable in the current block.

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: An encoder that encodes a picture to generate a coded stream includes: circuitry and a memory coupled to the circuitry. The circuitry performs, using the memory: generating a 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 correct the prediction image by referring to a second region included in the first region, and not operating the bi-directional optical flow process in response to the second region not being included in the first region; and encoding the current block based on the prediction image.

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 includes: circuitry; and memory, in which the circuitry: determines which mode is used to perform a prediction process, among modes including a first mode in which the prediction process is performed based on a motion vector of each block in a video and a second mode in which the prediction process is performed based on a motion vector of each sub-block obtained by splitting the block; when the prediction process is performed in the first mode, determines whether to perform a correction process on a prediction image using a spatial gradient of pixel values in the prediction image obtained by performing the prediction process, and performs the correction process when it is determined to perform the correction process; and when the prediction process is performed in the second mode, does not perform the correction process.