Abstract: An encoder determines a filter to be used for deblocking filtering from among a plurality of filters including a first filter and a second filter. The first filter uses M pixels located at an upper side of the block boundary and M pixels located at a lower side of the block boundary, and the second filter uses first pixels located at the upper side of the block boundary and second pixels located at the lower side of the block boundary, where M is an integer of at least 2. The number of the first pixels is any one of a plurality of first candidate values, and the number of the second pixels is any one of a plurality of second candidate values. The plurality of first pixel candidate values and the plurality of second pixel candidate values are each a value greater than or equal to M.

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: A decoder includes a memory and processing circuitry. The processing circuitry, in operation, changes values of pixels in a first block and a second block to filter a boundary therebetween, using clipping such that change amounts of the respective values are within respective clip widths. The clip widths for the pixels in the first block and the second block are selected based on block sizes of the first block and the second block. The pixels in the first block include a first pixel located at a first position, and the pixels in the second block include a second pixel located at a second position corresponding to the first position with respect to the boundary. The clip widths include a first clip width and a second clip width corresponding to the first pixel and the second pixel, respectively, and the first clip width is different from the second width.

Abstract: An encoder includes circuitry and memory. The circuitry, using the memory: stores, in a storage region, a probability parameter for entropy encoding of a first current slice included in a first picture, the probability parameter becoming available when encoding of a final coding unit (CU) of the first current slice is completed; and initializes, with reference to the probability parameter stored in the storage region, a probability parameter for entropy encoding of a second current slice included in a second picture when encoding of a leading CU of the second current slice starts. The first picture is a reference picture referred to when the second current slice is encoded, and the first current slice includes a CU located at the same position as a position of the leading CU of the second current slice.

Abstract: An encoder includes: circuitry; and memory. Using the memory, the circuitry: performs, when a size of a current block to be subjected to transform processing is not a power of 2, complementary processing of adding a complementary region to the current block to cause the size to be a power of 2; performs transform processing on the current block which has been subjected to the complementary processing; performs inverse transform processing on the current block which has been subjected to the transform processing; and eliminates the complementary region included in the current block which has been subjected to the inverse transform processing.

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, in which using the memory, the circuitry, in affine motion compensation prediction in inter prediction for a current block, places a limit on a range within which motion estimation or motion compensation is performed, and performs the motion compensation for the current block.

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 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: An encoder that encodes a current block in a picture includes circuitry and a memory coupled to the circuitry. The circuitry, in operation: selects at least one transform basis from among candidates for a transform basis which include a basis of a type-II discrete cosine transform (DCT-II) and at least one of a basis of a type-IV discrete cosine transform (DCT-IV) or a basis of a type-IV discrete sine transform (DST-IV); and transforms prediction error values of the current block, using the at least one transform basis selected. When the size of the current block is greater than a threshold size, the circuitry selects at least one transform basis after excluding at least one of the basis of the DCT-IV or the basis of the DST-IV from the candidates. The threshold size is at most half a maximum size to which the DCT-II is applicable.

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 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 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 the boundary between the first block and the second block such that change amounts of the respective values are smaller than respective thresholds, the pixels being arranged along a line across the boundary; and encode a third block. The pixels in the first block include a first pixel located at a first position, and the pixels in the second block include a second pixel located at a second position corresponding to the first position with respect to the boundary. The thresholds include a first threshold and a second threshold corresponding to the first pixel and the second pixel, respectively. The first threshold is different from the second threshold.

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 is an encoder which encodes a video, and includes: circuitry; and memory. The circuitry, using the memory, derives a motion vector of a current block included in a current picture, by referring to a reference picture different from the current picture; when a reference region indicated by the motion vector includes a region outside a boundary of the reference picture, performs padding for generating a plurality of pixels outside the boundary in the reference region, using one of a plurality of pixels inside the boundary of the reference picture, to generate the plurality of pixels outside the boundary; performs smoothing on the plurality of pixels outside the boundary; and generates a prediction image, using the plurality of pixels outside the boundary on which the smoothing has been performed.

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 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. 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 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: 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.