Abstract: According to one aspect of the present disclosure, a decoder includes memory and a processor coupled to the memory. The processor is configured to split a current picture into tiles, generate a slice having a rectangular shape and located at a lower-right corner of the current picture, the slice including at least a part of a tile among the tiles, generate first information on a region of the slice with header information, the header information not including information identical to the first information, and decode the slice with the first 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: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in response to a first reconstructed image sample being located outside a virtual boundary, duplicates a reconstructed sample located inside and adjacent to the virtual boundary to generate the first reconstructed image sample. The circuitry generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to the first reconstructed image sample of a luma component. The circuitry generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry generates a third coefficient value by adding the first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value.

Abstract: An encoder includes circuitry and memory connected to the circuitry. In operation, the circuitry corrects a base motion vector using a correction value in a fixed direction; and encodes a current partition by using the corrected base motion vector corrected. The correction value is specified by an index indicating one of correction values included in a table. The table is selected from among a plurality of tables, wherein the correction values in one of the plurality of tables have different increments from the correction values in another one of the plurality of tables.

Abstract: Provided is an encoder including circuitry and memory coupled to the circuitry. A prediction mode for a current block is an affine mode, and in operation, the circuitry: derives a base motion vector which is a motion vector to be used in a prediction process for the current block, and is a motion vector at an affine-mode control point in the current block; derives a first motion vector different from the base motion vector; derives a motion vector difference based on a difference between the base motion vector and the first motion vector; determines whether the motion vector difference is greater than a threshold; if so, modifies a second motion vector different from the base motion vector and the first motion vector, and if not, does not modify the second motion vector; and encodes the current block using the second motion vector modified or the second motion vector not modified.

Abstract: When a transform-basis adaptive selection mode is enabled, an encoder that transforms residuals of a current block to encode an image: adaptively selects a first horizontal transform basis from among one or more transform basis candidates when a horizontal size of the current block is greater than a first horizontal threshold size; otherwise selects a fixed horizontal transform basis as a first horizontal transform basis; adaptively selects a first vertical transform basis from among the one or more transform basis candidates when a vertical size of the current block is greater than a first vertical threshold size; otherwise selects a fixed vertical transform basis as a first vertical transform basis; and generates first transform coefficients by performing a first horizontal transform and a first vertical transform on the residuals of the current block, using the first horizontal transform basis selected and the first vertical transform basis selected, respectively.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. In operation, the circuitry: encodes information for deriving a parameter into a header of a bitstream; filters reconstructed samples in a first image using a filtering process, to generate a second image; determines whether the parameter has a predefined value; encodes a third image using the second image when the parameter has the predefined value; and encodes the third image using the first image when the parameter does not have the predefined value.

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: 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 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.

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: circuitry; and memory coupled to the circuitry. In operation, the circuitry: derives a base motion vector to be used in predicting a current block to be encoded; derives a first motion vector different from the base motion vector; derives a motion vector difference based on a difference between the base motion vector and the first motion vector; determines whether the motion vector difference is greater than a threshold; modifies the first motion vector when the motion vector difference is determined to be greater than the threshold, and does not modify the first motion vector when the motion vector difference is determined not to be greater than the threshold; and encodes the current block using the first motion vector modified or the first motion vector not modified.

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 image decoder has circuitry coupled to a memory. The circuitry splits a current image block into a plurality of partitions. The circuitry predicts a first motion vector from a set of uni-prediction motion vector candidates for a first partition of the plurality of partitions, and decodes the first partition using the first motion vector.

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 circuitry and memory connected to the circuitry. In operation, the circuitry: derives an average value of motion vector values of two prediction candidates in a prediction candidate list for a merge mode, and registers the average value derived as new motion vector information of a new prediction candidate into the prediction candidate list; and derives new correction processing information regarding correction processing of a prediction image, and registers the new correction processing information derived into the prediction candidate list in association with the new motion vector information.

Abstract: An encoder includes circuitry and memory connected to the circuitry. The circuitry: derives an absolute value of a sum of gradient values in first and second ranges; derives, as a first parameter, a total sum of absolute values of sums of gradient values derived respectively for pairs of relative pixel positions; derives a pixel difference value between pixel values in the first and second ranges; inverts or maintains a plus or minus sign of the pixel difference value, according to a plus or minus sign of the sum of the gradient values indicating the sum of the gradient values in the first and second ranges; derives, as a second parameter, a total sum of pixel difference values each having the plus or minus sign inverted or maintained, the pixel difference values derived respectively for the relative pixel positions; and generates a prediction image using the first and second parameters.

Abstract: An image encoder performs a first partitioning including using a first partition mode, without writing first splitting information indicative of the first partition mode into a bitstream, to split a first block into a plurality of second blocks in response to that the first block is located adjacent to an edge of a picture and that the dimensions of the first block satisfy a first condition; and performs a second partitioning on the second block by writing second splitting information indicative of a second partition mode into the bitstream, wherein the second partition mode allows at least one of a quad tree splitting and a binary splitting, and using the second partition mode to split the second block into a plurality of coding units (CUs), wherein the second partition mode prohibits the quad tree splitting of the second block in certain conditions.

Abstract: A video image decoding device receives, as the code string to be decoded, a first code string to be decoded including in formation based on an encoded residual coefficient and header information or a second code string to be decoded including a residual image obtained in encoding the code string to be decoded and header information. The video image decoding device, when the code string to be decoded that is received by the receiver is the first code string to be decoded, adds the residual decoded image and the predictive image to each other to generate and output a reconstructed image and, when the code string to be decoded received by the receiver is the second code string to be decoded, adds a residual image included in the second code string to be decoded and the predictive image to each other to generate and output a reconstructed image.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. In operation, the circuitry: performs quantization on a plurality of transform coefficients of a current block to be encoded, using a quantization matrix when orthogonal transform is performed on the current block and secondary transform is not performed on the current block; and performs quantization on the plurality of transform coefficients of the current block without using the quantization matrix when orthogonal transform is not performed on the current block and when both orthogonal transform and secondary transform are performed on the current block.