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 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 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 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 prediction mode used for the first block, the first filter including a first set of filter coefficients; select a second filter for a 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, by multiplying the values of pixels in the first block by the first set of filter coefficients, respectively, and multiplying the values of pixels in the second block by the second set of filter coefficients, respectively, the pixels in the first block and the second block being arranged along a line across the boundary.

Abstract: Various embodiments provide a decoder configured to select a filter based on a block size of a first block and a block size of a second block in an image, and change values of pixels in the first block and the second block. The filter includes a first set of multipliers and a first set of offsets for the first block, and a second set of multipliers and a second set of offsets for the second block. The values of the pixels in the first block and the second block are changed by performing multiplication with each multiplier in the first set of multipliers, by performing multiplication with each multiplier in the second set of multipliers, and by using the first set of offsets and the second set of offsets.

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: Various embodiments provide an encoder that generates a plurality of quantization matrix elements for a current block; generates a quantization matrix using the plurality of quantization matrix elements; and quantizes, using the quantization matrix, transform coefficients of the current block. The quantization matrix includes only a subset of quantization matrix elements of the plurality of quantization matrix elements. Each of the subset of quantization matrix elements has an x-coordinate value less than a threshold x-coordinate value, a y-coordinate value less than a threshold y-coordinate value, or an x-coordinate value less than the threshold x-coordinate value and a y-coordinate value less than the threshold y-coordinate value.

Abstract: An image decoder includes circuitry and a memory, wherein the circuitry, in operation, performs a boundary smoothing operation along a boundary between a first partition having a triangular shape and a second partition having a triangular shape that are split from an image block. The boundary smoothing operation includes: first-deriving a first motion vector for the first partition from a first set of motion vector candidates; second-deriving a second motion vector for the second partition from a second set of motion vector candidates; first-predicting first values of a set of pixels of the first partition along the boundary, using the first motion vector; second-predicting second values of the set of pixels of the first partition along the boundary, using the second motion vector; weighting the first values and the second values; and decoding the first partition using the weighted first values and the weighted second values.

Abstract: A decoder that includes: circuitry; and a memory coupled to the circuitry. The circuitry, in operation: determines whether or not a first splitting of splitting a block into three sub blocks in a first direction parallel to a first side of the block is available by determining a magnitude relation between a size of a second side of the block and a first value, the second side being different from the first side, the first side being a longer side of the block; when the first splitting is available, parses, from a bitstream, a split direction parameter indicative of a splitting direction; splits the block into a plurality of sub blocks in a direction indicated by the split direction parameter; and decodes the plurality of sub blocks.

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: The present disclosure provides systems and methods for video coding. The systems include, for example, an image encoder comprising: circuitry; and a memory coupled to the circuitry, wherein the circuitry, in operation, performs the following: predicting a first block of prediction samples for a current block of a picture, wherein predicting the first block of prediction samples includes at least a prediction process with a motion vector from a different picture; padding the first block of prediction samples to form a second block of prediction samples, wherein the second block is larger than the first block; calculating at least a gradient using the second block of prediction samples; and encoding the current block using at least the calculated gradient.

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 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 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 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 memory and circuitry. The circuitry (i) encodes first control information indicating one mode, (ii) encodes second control information indicating whether it is possible to perform the motion compensation in a unit of a sub-block, (iii) derives the motion vector of the block in the one mode, (iv) determines whether to perform the motion compensation in the unit of the sub-block or the motion compensation in a unit of the block, (v) derives a motion vector of the sub-block and performs the motion compensation in the unit of the sub-block using the motion vector of the sub-block when determining to perform the motion compensation in the unit of the sub-block, and (vi) performs the motion compensation in the unit of the block using the motion vector of the block when determining to perform the motion compensation in the unit of the 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 includes circuitry and memory. The circuitry performs: obtaining first motion vector information of a first partition; obtaining second motion vector information of a second partition; deriving a set of prediction samples for the first partition; and encoding the first partition using the set. When the difference between the motion vector information is not greater than a value, the circuitry reflects a second set of samples to a first set of samples. The first set has been predicted for the first partition using the first motion vector information, and the second set has been predicted for a first range using the second motion vector information. When the difference is greater than the value, the circuitry reflects, to the first set of samples, a third set of samples predicted for a second range larger than the first range using the second motion vector information.

Abstract: An encoding method is provided for encoding a picture to generate a coded stream. The encoding method incldues: 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 not operating the bi-directional optical flow process by referring to a third region not included in the first region; and encoding the current block based on the second prediction image.

Abstract: The encoder includes processing circuitry, and memory. Using the memory, the processing circuitry: generates a predicted image of an input image that is a current image to be encoded, based on generated data output from a generator network in response to a reference image being input to the generator network, the generator network being a neural network; calculates a prediction error by subtracting the predicted image from the input image; and generates an encoded image by at least transforming the prediction error.