We Claim:
1. An image encoding device comprising:
a filter that carries out a filtering process on a decoded image which is a result of addition of a difference image decoded from compressed data and a prediction image;
an encoder that encodes said compressed data and a filter parameter used when the filtering process is carried out, and generates a bitstream;
a slice partitioner that partitions an image into slices which are a plurality of part images;
a coding parameter determinator that determines the largest size of a coding block which is a unit to be processed when an encoding process is carried out and determines an upper limit on a number of hierarchies when a coding block having the largest size is partitioned hierarchically, and that assigns a coding mode to each of the coding blocks which are partitioned hierarchically;
a block partitioner that partitions a slice which is partitioned by said slice partitioner into coding blocks each having the largest size determined by said coding parameter determinator, and that can partition each of said coding blocks hierarchically into blocks until its number of hierarchies reaches the upper limit on the number of hierarchies which is determined by said coding parameter determinator;
a predictor that carries out a prediction process according to the coding mode assigned by said coding parameter determinator on each of the coding blocks which are partitioned by said block partitioner to generate a prediction image;
a difference image generator that generates a difference image between each of the coding blocks which are partitioned by said block partitioner and the prediction image generated by said predictor;

an image compressor that carries out a transformation process on the difference image generated by said difference image generator and quantizes transform coefficients of said difference image, and that outputs the transform coefficients quantized as compressed data; and
a decoded image generator that decodes the difference image from the compressed data outputted from said image compressor, and adds the difference image decoded and the prediction image generated by said predictor to generate a decoded image, wherein said filter
determines a classification method of a class on a coding block having a largest size,
carries out a classification on each pixel within said coding block having a largest size by using said classification method,
calculates an offset value for each class for said coding block having largest size, and
carries out a pixel adaptive offset process by which said offset value is added to a pixel value of a pixel belonging to a corresponding class; and said encoder
encodes an index indicating the classification method determined by said filter,
encodes a parameter about the offset value for each class on a basis of a binarization process using a truncated unary code, and
encodes header information of each slice including information about the partitioning into the slices by said slice partitioner, an index indicating an adaptation parameter set used by a corresponding slice, the compressed data outputted from said image compressor, the coding mode assigned by said coding parameter determinator, a quantization matrix parameter for generating a quantization matrix used when the transform coefficients are quantized by said image compressor, and the filter parameter used when the filtering process is carried out by said filter to generate a coded bitstream into which coded data

about said header information, the coded data about said compressed data, coded data about said coding mode, coded data about said quantization matrix parameter, and the coded data about said filter parameter are multiplexed;
the coding parameter determinator determines both a quantization parameter used when the difference image is compressed and a transformation block partitioning state for each of the coding blocks, and determines an intra prediction parameter or an inter prediction parameter used when the prediction process is carried out for each prediction block of said coding block;
the predictor carries out an intra-frame prediction process by using said intra prediction parameter when an intra coding mode is assigned by said coding parameter determinator and carries out a motion-compensated prediction process by using said inter prediction parameter when an inter coding mode is assigned by said coding parameter determinator; and
the image compressor carries out the transformation process on the difference image generated by the difference image generator for each transformation block determined by said coding parameter determinator, and quantizes the transform coefficients of said difference image by using the quantization parameter and the quantization matrix parameter which are determined by said coding parameter determinator and outputs the transform coefficients quantized as the compressed data about said difference image, and, when encoding said compressed data, the coding mode, said quantization matrix parameter, the filter parameter, and the header information of each slice, the encoder encodes the intra prediction parameter or the inter prediction parameter, which is determined by said coding parameter determinator, and transformation block partitioning information to generate the coded bitstream into which the coded data about said compressed data, the coded data about said coding mode, the coded data about said quantization matrix parameter, the coded data about said filter parameter, the coded data about said header information, coded data about said intra prediction parameter or said inter

prediction parameter, and coded data about said transformation block partitioning information are multiplexed.
2. An image decoding device comprising:
a decoder that decodes compressed data and a filter parameter from coded data multiplexed into a bitstream and decodes header information about each slice, a quantization matrix parameter, and a filter parameter from the coded data multiplexed into the coded bitstream, and that decodes compressed data and a coding mode associated with each of coding blocks which are hierarchically partitioned from said coded data;
a filter that carries out a filtering process on a decoded image decoded from the compressed data by using the filter parameter;
a predictor that carries out a prediction process according to the coding mode decoded by said decoder and associated with the coding block to generate a prediction image;
a difference image generator that inverse-quantizes transform coefficients which are compressed data decoded by said decoder and associated with the coding block by using a quantization parameter and said quantization matrix parameter which are decoded by said decoder, and that inverse-transforms the transform coefficients inverse-quantized to generate a difference image before compression; and
a decoded image generator that adds the difference image generated by said difference image generator and the prediction image generated by said predictor to generate a decoded image, wherein
said decoder
decodes, as a filter parameter, an index indicating a classification method of a class on a coding block having a largest size, and
decodes a parameter about an offset value for each class on which a binarization process using a truncated unary code is performed;
said filter

specifies the classification method of a class on the coding block having the largest size by using the index,
carries out a classification on each pixel by using the classification method, and
carries out a pixel adaptive offset process by which said offset value is added to a pixel value of a pixel belonging to a corresponding class;
when decoding the compressed data, the coding mode, and an adaptation parameter set from the coded data multiplexed into the coded bitstream, the decoder decodes an intra prediction parameter or an inter prediction parameter, and transformation block partitioning information,
when the coding mode decoded by said decoder and associated with the coding block is an intra coding mode, the predictor carries out the intra-frame prediction process by using said intra prediction parameter, and
when the coding mode decoded by said decoder and associated with the coding block is an inter coding mode, carries out the motion-compensated prediction process by using said inter prediction parameter, and the difference image generator inverse-transforms the transform coefficients inverse-quantized for each of transformation blocks acquired from the transformation block partitioning information decoded by said decoder to generate a difference image before compression.