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: 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 that; obtains two prediction images by performing motion compensation using two motion vectors; obtains a gradient value of each of pixels included in the two prediction images; derives a local motion estimation value for each of sub-blocks based on the pixel value and the gradient value of each of the pixels, the sub-blocks being obtained by partitioning the current block; and generates a final prediction image for the current block using the pixel value and the gradient value of each of the pixels, and the local motion estimation value derived for each of the sub-blocks. Each of the pixels in the two prediction images is interpolated with sub-pixel accuracy, and a reference range for the interpolation is included in a normal reference range that is referred to for motion compensation for the current block in normal inter prediction performed without using the local motion estimation value.

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: 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 that encodes a video includes a processor and memory. Using the memory, the processor: derives a prediction error of an image included in the video, by subtracting a prediction image of the image from the image; determines a secondary transform basis based on a primary transform basis, the primary transform basis being a transform basis for a primary transform to be performed on the prediction error, the secondary transform basis being a transform basis for a secondary transform to be performed on a result of the primary transform; performs the primary transform on the prediction error using the primary transform basis; performs the secondary transform on a result of the primary transform using the secondary transform basis; performs quantization on a result of the secondary transform; and encodes a result of the quantization as data of the image.

Abstract: An encoding method includes: changing values of luma pixels in a first block and a second block to filter a first boundary between the first block and the second block, using clipping such that change amounts of the respective values are within respective luma clip widths, the luma pixels in the first block and the second block being arranged along a first line across the first boundary; and changing values of chroma pixels in a third block and a fourth block to filter a second boundary between the third block and the fourth block, using clipping such that change amounts of the respective values are within respective chroma clip widths, the chroma pixels in the third block and the fourth block being arranged along a second line across the second boundary. The luma clip widths applied to the luma pixels are selected to be asymmetrical relative to the first boundary.

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: 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: 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: 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: 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: 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: 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 (100) that encodes an image on a per block basis includes circuitry and memory. Using the memory, the circuitry: performs first partitioning of dividing the image using a square block having a fixed block size, to generate the image into a plurality of blocks including the square block which has the fixed block size and a first non-square block which has a size smaller than the fixed block size; performs second partitioning on the plurality of blocks; adds information on the second partitioning into a bitstream; and prohibits a quad tree splitting of the first non-square block in the second partitioning.

Abstract: An encoder which encodes a current block to be encoded in an image includes: a transformer which performs a primary transform from residuals of the current block to primary coefficients, determines whether to apply a secondary transform to the current block, and performs the secondary transform from the primary coefficients to secondary coefficients when the secondary transform is applied; a quantizer which calculates quantized primary coefficients by performing a first quantization on the primary coefficients when a secondary transform is not applied, and calculates quantized secondary coefficients by performing a second quantization different from the first quantization on the secondary coefficients when the secondary transform is applied; and an entropy encoder which generates an encoded bitstream by encoding either quantized primary coefficients or quantized secondary coefficients.

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, using clipping such that change amounts of the respective values do not exceed respective thresholds, the pixels in the first block and the second block being arranged along a line across the boundary. The pixels include type one pixels and type two pixels different from the type one pixels. The respective thresholds for the type one pixels in the first block and the second block are selected to be symmetrical or asymmetrical with respect to the boundary based on block sizes of the first block and the second block.

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 includes circuitry and memory. The circuitry, using the memory: derives a one-dimensional array of a plurality of reference samples for intra prediction; performs smoothing on the one-dimensional array of the plurality of reference samples which has been derived; and generates a prediction image using the plurality of reference samples. In deriving the one-dimensional array, the circuitry projects a value of at least one decoded pixel located on a first line onto a second line perpendicular to the first line, to derive at least one of the plurality of reference samples, and the smoothing is performed on the at least one decoded pixel projected onto the second line.

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.