Abstract: An encoder determines, based on a width and a height of a block, whether or not to disable a prediction mode in which the block is split along a partitioning line defined by a distance and an angle and then prediction is performed; and encodes the block with the prediction mode disabled or not disabled according to a result of the determination on whether or not to disable the prediction mode. Here, the distance is the shortest distance between the center of the block and the partitioning line, and the angle is an angle representing a direction from the center of the block toward the partitioning line in the shortest distance. The encoder determines to disable the prediction mode when (i) a width-to-height ratio is at least 8 or (ii) a height-to-width ratio is at least 8.

Abstract: An image decoder performs a first partitioning including using a first partition mode, without parsing first splitting information indicative of the first partition mode, 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 parsing second splitting information indicative of a second partition mode, 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 response to that the second block is located adjacent to the edge of the picture.

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: 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: 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: A video image decoding device receives, as the code string to be decoded, a first code string to be decoded including information 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 memory and circuitry which: (i) encodes an image block; (ii) when encoding the image block: binarizes coefficient information indicating coefficients of the image block; and controls whether to apply arithmetic encoding to a binary data string obtained by binarizing the coefficient information; and (iii) when binarizing the coefficient information: binarizes the coefficient information according to a first syntax structure when arithmetic encoding is applied to the data string and a predetermined condition is not satisfied; binarizes the coefficient information according to a second syntax structure when arithmetic encoding is applied to the data string and the predetermined condition is satisfied; binarizes the coefficient information according to the second syntax structure when no arithmetic encoding is applied to the data string; and subtracts 1 from a value of an initial non-zero coefficient when no arithmetic encoding is applied to the data string when encoding the image block.

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: A reproduction apparatus includes circuitry and memory coupled to the circuitry. In operation, the circuitry: obtains a first segment including first subpictures corresponding to points of time and a second segment including second subpictures corresponding to the points of time; combines the first subpictures and the second subpictures to generate access units corresponding to the points of time; and reproduces the access units generated.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in operation, determines whether a first block is available and whether a second block is available, the first block and the second block being defined relative to a current block to be processed; selects a context model based on whether the first block is available, whether the second block is available, which of inter prediction and intra prediction is to be applied to the first block, and which of inter prediction and intra prediction is to be applied to the second block; and encodes, using the context model selected, a parameter indicating which of intra prediction and inter prediction is to be applied to the current block.

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 connected to the circuitry. The circuitry, in operation: derives, as a first parameter, a total sum of absolute values of sums of horizontal gradient values respectively for pairs of relative pixel positions; derives, as a second parameter, a total sum of absolute values of sums of vertical gradient values respectively for the pairs of relative pixel positions; derives, as a third parameter, a total sum of horizontal-related pixel difference values respectively for the pairs of relative pixel positions; derives, as a fourth parameter, a total sum of vertical-related pixel difference values respectively for the pairs of relative pixel positions; derives, as a fifth parameter, a total sum of vertical-related sums of horizontal gradient values respectively for the pairs of relative pixel positions; and generates a prediction image to be used to encode the current block using the first, second, third, fourth, and fifth parameters.

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: A video decoding device, in the case where a video of the progressive format is inputted, processes a frame as a picture, in the case where a video of the interlace format is inputted, processes a field as a picture. A video decoding device performs display control corresponding to a format of the both video by analyzing display control information in display control information analyzer. The display control information includes sequence unit display control information which is commonly used in a display process of all pictures that belong to a sequence to be decoded and picture unit display control information which is individually used in a display process of a picture to be decoded. A second code string analyzer acquires each of the sequence unit display control information and the picture unit display control information from an extended information area in units of pictures.

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: 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.

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: 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 circuitry and memory. Using the memory, the circuitry: in an inter prediction mode in which an affine motion vector is calculated for each of sub-blocks constituting a current block of a picture in the video, based on motion vectors of neighboring blocks of the current block, changes a shape or size of the sub-block according to a variation in direction or variation in magnitude among the motion vectors of the neighboring blocks; calculates the affine motion vector for the sub-block having the shape or size changed; and performs the motion compensation for the sub-block having the shape or size changed.

Abstract: An encoder is an encoder that encodes a block in a picture using a prediction image of the block, and includes circuitry and memory. Using the memory, the circuitry: calculates a first average pixel value which is an average pixel value of first reference samples out of the first reference samples and second reference samples, The first reference samples are referable and located outside the block and adjacent to a first side of the block. The second reference samples are referable and located outside the block and adjacent to a second side of the block. When generating the prediction image, the circuitry applies the same prediction pixel value to inner samples among current samples to be processed that are included in the block. The inner samples constitute a quadrilateral region including at least two current samples in each of a horizontal direction and a vertical direction.