Abstract: A system and method that computes correlation between a first signal and a second signal. The correlation is computed as a ratio of a numerator and a denominator. The numerator may be computed similar to computing the numerator of the Pearson correlation. The denominator may be computed by multiplying the variance of the second signal and the difference between the maximum and minimum value of the first signal. A threshold, which may be programmable, may be used to determine if the first and second signal match by comparing the numerator and the product of the threshold and the denominator. If the numerator is larger than the product then the first signal and the second signal match, otherwise, there is no match. The first signal may be a sliding window of a signal. The window may be slid over the signal until a match is found between the window and the second signal.

Abstract: A form image may be split into a plurality of image fragments. Each image fragment may correspond to a field of the form. Each form fragment may be deidentified to prevent unauthorized reconstruction of the form image from its respective image fragments. An index to associate each image fragment to its respective form and form field may be generated. Form fragments from a plurality of form images may be intermixed in an image fragment pool and selected for transmission to a third-party form processor. The third-party form processor may be an internal third-party form processor or an external, third-party form processor. The third-party form processor may assign a data value to each image fragments, associate each data value with a name corresponding to, or derived from the form image fragment name, and return the data values. The data values may be stored and associated with their respective forms and/or form fields using the index.

Abstract: The present invention relates to a system and method for indicating the presence of ancillary data in a header of a JPEG file. The system comprises a JPEG file having an EXIF header and associated image data, and at least one other file of digital data, and a computer. The computer is programmed to scan the JPEG image file for a special indicator in the application marker section of the EXIF header. If the marker is present, the value of marker indicates what type of ancillary digital data is present in the header. For instance, if the marker contains the string EKC-JPEG, then the ancillary data is known to be another JPEG file. Other types of data can be indicated as appropriate. The presence of the ancillary data is then used for the appropriate type of presentation to the user. A reveal icon is then used in presenting the data to indicate whether the ancillary data is another JPEG file, video, audio, sound, document, etc. The user would be presented with the data as appropriate.

Abstract: A method of producing an engraved image on a computer screen includes loading an image to be engraved and converting the image into a high contrast image using at least two colors. The first lighter color is used for the lighter portions of the high contrast image and a darker color is used for the darker portions of the high contrast image. Mixing of the colors is based on the luminance level of the image. A plurality of lines are drawn over the high contrast image with variations in the plurality of lines drawn being a function of the luminance of the underlying image.

Abstract: An image coding apparatus includes a rate control information extraction means for determining which up to a coding pass in which code block should be coded from the sum of the code amounts of the code blocks, the slope of an RD curve calculated from the distortion difference between a coding distortion at a time of coding each coding pass and a coding distortion at a time of coding a preceding coding pass, and the number of output bytes of the code amount of each coding pass, and the inverse of one of given rate control parameters which are listed in order of decreasing monotonously, and for outputting an end-of-coding pass, and a coded data extraction means for reading coded data including up to coded data corresponding to the end-of-coding pass, for adding the number of coding passes to the coded data, and for outputting them as a code stream.

Abstract: An electronic device includes: a PHLCT circuit (15), which includes an input signal DCT coefficient computation module configured to compute DCT coefficients of an input signal of a subject block region in a plurality of block regions and block regions adjacent to the subject block region, respectively, an offset function DCT coefficient computation module configured to compute DCT coefficients of a gradient offset function, which offsets the gradient of the input signal at a block boundary between each subject block region and its adjacent block regions from the DCT coefficients of the input signal, and a residual computation module configured to compute a residual of the DCT coefficients of the input signal and the DCT coefficients of the gradient offset function; a quantization circuit configured to quantize the residual to obtain compressed data; and an entropy coding circuit (17) configured to encode the compressed data.

Abstract: A time series data dimensional compression apparatus performing dimensional compression for improving the efficiency of searching for time series data without losing the features of data. The compression is made to a determined dimension so that a larger volume of information may be extracted therein. A time series subsequence generating section (112) generates time series subsequences of a specified segment width into which a plurality of pieces of time series data generated at a time series data generating section (110) are divided. A singular value decomposition processing section (113) performs singular value decomposition on all of the time series subsequences. A dimensional compression time series data generating section (114) generates dimensional compression time series data by using high-order elements of the singular value decomposition as a representative value of the time series subsequence.

Abstract: A method is provided for processing minimum coded units (MCUs) in a Joint Photographic Expert Group (JPEG) bit stream representing an image. A data structure is generated for storing MCU block numbers, corresponding MCU block coordinates, and corresponding MCU block editing lists. When an editing operation to the image is received, the editing operation is saved to a group of the MCU block editing lists of a group of the MCUs affected by the editing operation. Later the MCUs are retrieved from the JPEG bit stream one at a time and then processed according to the editing operations in the corresponding MCU blocking editing lists.

Abstract: A substrate having a coding pattern disposed on a surface thereof. The coding pattern comprises a plurality of contiguous square tags of length l. Each tag comprises x-coordinate data and y-coordinate data. A y-axis is nominally defined as north-south and an x-axis is nominally defined as east-west. A plurality of data elements are contained in each tag, and x- and y-coordinate data are represented by respective sets of data elements. The x-coordinate data comprises a replicated part and a non-replicated part. The y-coordinate data comprises a replicated part and a non-replicated part. The non-replicated parts are represented in a central row and central column of the tag, each being of width q. Any square portion of the coding pattern having a length (l+q) is guaranteed to contain the x-coordinate data and the y-coordinate data for a tag irrespective of whether a whole tag is contained in the portion.

Abstract: To provide a matching technology for determining the similarity between two objects at high velocity with high precision. A matching method for comparing a set of feature points of two objects projected to an N-dimensional space and determining the similarity between the two objects, includes a mapping step (S3) of mapping the set to a one-dimensional space, a pairing step (S6) of creating a set of pairs of a feature point of first object that is the most approximate to a feature point of second object, a partial-set creating step (S7) of partly extracting the pairs in small order of the pair distance from the set of the pairs of the feature points and creating a partial set of the pairs of the feature points, an average-value calculating step (S8) of calculating a rating-scale of the pair belonging to the partial set of the pair of the feature points, and a determining step (S10) of determining the similarity between the first object and the second object on the basis of an average value of the distance.

Abstract: A non-dyadic spatial scalable wavelet transform may scale an original digital video frame or digital image at a non-dyadic ratio. The digital video frame or digital image is quantized to create a set of data representing the digital video frame or digital image. The set of data is then input to the non-dyadic spatial scalable wavelet transform. The non-dyadic spatial scalable wavelet transform may then transform the data associated with a first pixel to a high-pass coefficient and use the high-pass coefficient to transform the data associated with a second and third pixel to low-pass coefficients. The low-pass coefficients may then be converted to a digital image for viewing.

Abstract: Various systems, methods, and programs embodied in computer-readable mediums are provided for the global quantitative characterization of patterns. In one representative embodiment, a method is provided in which fractal analysis is performed on a pattern to generate a global quantitative characterization of the pattern in a computer system.

Abstract: A data encoding apparatus operable to encode a plurality of data blocks produces encoded data in accordance with at least one of a selectable target data quantity or a selectable target data quality.

Abstract: Provided are a method and an apparatus for encoding and decoding a color image. The method of encoding a color image includes generating a color transformation function for color format transformation for each block of the color image, performing color transformation on each block of the color image using the generated color transformation function, and performing encoding on each block of the color-transformed image.

Abstract: An interframe wavelet video coding (IWVC) method by which an average temporal distance (ATD) is minimized is provided. The IWVC method comprises receiving a group-of-frames and decomposing the group-of-frames into difference frames and first average frames between the frames in a first forward temporal direction and a backward temporal direction, wavelet-decomposing the first difference frames and the first average frames, and quantizing coefficients resulting from the wavelet-decomposition to generate a bitstream. The IWVC method provides improved video coding performance.

Abstract: An image processing apparatus generates a sub-self-similar set F, which is a subset of a self-similar set A with respect to contraction maps f1, . . . , fn and forms an image expressing the sub-self-similar set F. The apparatus includes a base-address-set designating section, a generation-rule acquiring section and a sub-self-similar set generating section. The base-address-set designating section selects m addresses each of which formed of infinite sequence of {1, . . . , n} and generates a base address set M including the selected addresses. The generation-rule acquiring section acquires a rule of generating a hypothetical sub-self-similar set G, which is a subset of a hypothetical self-similar set B with respect to n hypothetical contraction maps g1, . . . , gn, by using the generated base address set M. The sub-self-similar set generating section generates a sub-self-similar set F, which is a subset of the self-similar set A.

Abstract: A method of authenticating a user through a validated mutual authentication system is provided. In an exemplary embodiment, the method includes establishing a validating fractal image during an enrollment or other process. A plurality of fractal images are provided to a client during an authentication attempt by the user, and the plurality of fractal images includes the validating fractal image. Fractal image selection data is received from the client, and the system uses the received fractal image selection data to determine a fractal image selected by the user from the plurality of fractal images. The user is authenticated only if the fractal image selected by the user is the validating fractal image.

Abstract: A method for segmenting an image is disclosed wherein a fractal map of the image is generated by estimating the fractal dimension of each pixel in the image. The image is segmented by thresholding the fractal map of the image.

Abstract: A method for identification of anomalous structures, such as defects, includes the steps of providing a digital image and applying fractal encoding to identify a location of at least one anomalous portion of the image. The method does not require a reference image to identify the location of the anomalous portion. The method can further include the step of initializing an active contour based on the location information obtained from the fractal encoding step and deforming an active contour to enhance the boundary delineation of the anomalous portion.

Abstract: A compressed-code generating method that is used for compressing information on characters including numerical data, sound and images, and a compressed-code expanding method that is used for restoring and expanding the compressed code generated by using the compressed-code generating method to the original information. Bit strings {y}1 and {y}2 are obtained respectively from a bit string {y} of information to be compressed. A reversible loop that exists in chaos is operated to these obtained bit strings, thereby to execute a reversible compression/expansion of the information using the chaos.

Abstract: The invention provides techniques for thinning halftone dots in a halftone dot bit map. A bit map filter may be used to thin the dots. For example, a target glyph may passed over the bit map. If any subsets of bits within the bit map match the target glyph, the subsets of bits can be replaced with bits defined by a thinned glyph. In this manner, the ink of a halftone print can be reduced in a manner that enhances the visual appearance of the print.

Abstract: LL subbands of first and second intermediate images obtained by an inverse quantizer are stored in an intermediate image memory. A scene change judging unit compares data stored in the intermediate image memory and thereby determines whether there is a scene change or not.

Abstract: A method of compressing a color image is provided. The color image comprises color data for a plurality of pixels. The method includes the step of obtaining red, green and blue pixel values of an object of interest in the image. A calculation is made of the complement of the red, green and blue values of the object of interest. Transformation coefficients are calculated which transform the complements of red, green and blue values of the object of interest into representations in a transformation color space. The transformation coefficients are applied to all the pixels in the image to thereby obtain a transformed data set representing the image having components along three mutually orthogonal axes (A, B and C herein) in a three-dimensional transformed color space. The transformed data set is scaled in accordance with the color quantization used in the system; e.g., the A, B and C values are between 0 and 255 for an 8 bit quantization. A compression algorithm, e.g.

Abstract: An apparatus for image coding using tree-structured vector quantization based on a wavelet transform and a method therefor are provided. The apparatus for image coding using a tree-structured vector quantization based on wavelet transform has a wavelet transform unit, a vector construct unit, an error vector unit, a scan unit, a first quantization unit and a second quantization unit. The wavelet transform unit wavelet transforms an input image signal. The vector construct unit constructs vectors, each having a tree structure in a different direction, using the wavelet transformed result. The error vector generation unit generates a plurality of error vectors by setting one of the vectors as a basic vector and performing a calculation on each of the vectors remaining with respect to the basic vector. The scan unit scans the coefficients of each of the basic vector and error vectors in a different direction.

Abstract: A method of image transforming is proposed.

Abstract: A method of manipulating spectral content of a block of pixels for compression includes the step of classifying each pixel within a selected block of pixels as relevant or irrelevant. A forward transform is applied to the selected block to generate a coefficient block. The coefficient values are modified to generate a modified coefficient block subject to a set of pre-determined constraints including a constraint that the relevant pixels have a same value in an inverse transformation of the modified coefficient block as in the selected block. Proceeding in a reverse zig zag coefficient order the method is repeated for other coefficients having non-zero quantized values.

Abstract: The invention relates to a method for the optical detection of objects or object streams, wherein the surfaces of the objects or object streams are capable of reflecting or of scattering light, and wherein the objects or object streams can exhibit or form or generate self-affine or self-similar or fractal patterns or structures on the surfaces or in themselves, by employing an illuminating device for illuminating the objects or object streams and an optical imaging and receiving device with a following electronic evaluation for receiving and evaluating the imaging light reflected or scattered by the surfaces. The imaging ray bundle is scanned as a sequence of light patterns, wherein a similitude-transformation algorithm forms the basis of the scanning such that the connection of the individual light patterns relative to each other spatially and/or timely is a scaling or rotation or translation of self-affine or self-similar or fractal, and wherein at least two variables are set up.

Abstract: An apparatus for transmitting multimedia, wherein the apparatus includes an image compression unit for compressing an image portion of a multimedia data frame, an audio compression unit for compressing an audio portion of the multimedia frame, and a bit rate manager in communication with the image compression unit and the audio compression unit for controlling frame flow. A merger unit in communication with each of the image compression unit and the audio compression unit is provided for merging a compressed image portion and a compressed audio portion into a single compressed multimedia frame, wherein the image compression unit utilizes multidimensional hierarchical categorization trees to compress the image portion.

Abstract: An image display apparatus having a lower data transmission speed and less degradation of the image quality for displaying the image having a lower data-rate according to the state of a communications network and a method for enabling the same are provided. The apparatus, which transmits and receives data by way of the communications network, includes a screen size determiner which determines the screen size of image signals input according to control signals; an encoder which encodes the image signals according to the determined screen size; a controller which outputs control signals which determine the screen size by evaluating the state of the communications network and for transmitting the encoded image signals through the communications network; a decoder which decodes the image signals transmitted through the communications network; and a display which displays the decoded image signals.

Abstract: Disclosed is an input image data compressor which comprises an image recording controller for generating image information on respective input objects from the input image data, generating image information on a moving object using the image information, comparing the previously input image data with the presently input image data, generating new image information on the moving object and compressing the new image information; a storage unit for storing signals or data generated during compression operation of the image recording controller in a corresponding established address; and a compressed image storage unit for storing the compressed image data compressed by the control operation of the image recording controller.

Abstract: A method for fractal image compression using reinforced learning is disclosed. The reinforced learning algorithm improves the performance of fractal image compression algorithms by improving image partitioning and transform family selection while considering the impact of domain to range matching. The present invention differs from other fractal image compression algorithms in that it makes decisions about transform family and image partitioning by generalizing from experience compressing small portions of an image to compressing an image as a whole.

Abstract: A method of compressing digital representations of images stores the images in multiple subsampling quality scales in a progressive manner such that a higher quality scale contains only data incremental to the data in an adjacent lower quality scale. The data in each quality scale is transformed, quantized, and entropy encoded. A discrete wavelet cosine transformation combining frequency transformation features of a discrete cosine transformation and spatial transformation features of a wavelet transformation is provided. Sequences of subsampling quality scales are provided for multi-scale representations of images. A novel context selection method is used which treats color components and coefficients of different positions differently. An image compressed in a given quality scale can be transmitted or decompressed progressively allowing progressive downloading or transmission over the Internet.

Abstract: The methods of the invention can be used with image data divided into domain blocks. A predetermined search pattern of range blocks centered on a domain block is defined for use in the methods. The first method includes a step of generating at least one error descriptor data based on domain block data and range block data. The error descriptor data can be derived by scaling the range blocks to the pixel size of a domain block, and subtracting the means of the range blocks and domain block from each pixel thereof. The mean-adjusted, scaled pixel intensity levels of the scaled range blocks are subtracted from mean-adjusted pixel intensity levels of the domain block to produce difference data. The absolute value of the difference data is taken and the positive difference data are summed to produce summed error data for each range block. The summed error data is used to derive at least one error descriptor data for the image.

Abstract: A method for identification of anomalous structures, such as defects, includes the steps of providing a digital image and applying fractal encoding to identify a location of at least one anomalous portion of the image. The method does not require a reference image to identify the location of the anomalous portion. The method can further include the step of initializing an active contour based on the location information obtained from the fractal encoding step and deforming an active contour to enhance the boundary delineation of the anomalous portion.

Abstract: A transformation of a data object called a personal logo contains personal data for transmitting from a client computer to a server computer. The personal data is embedded into transformation coefficients derived using one of several encoding techniques. The personal data is extracted from the transformation coefficients by the server computer to complete the transaction. The personal logo is created by or selected by a user and is made unique using a randomization algorithm to ensure differentiation from every other personal logo. Personal data is embedded into the unique personal logo in a way that hides it and makes it difficult for an unauthorized party to extract. The personal data includes data use limitations that limit what an authorized receiver may do with the personal data after receipt. Network transactions are automated through the creation of a drag-and-drop interface representing the act of data transmission.

Abstract: Efforts are made to construct a digital index that represents properties or the appearance of portions of an image so as to automatically rediscover in it a sample of the image during a subsequent search, after having set up a sample index in the same way and having compared the indices while searching for similarities. In this invention, the mesh dividing up the image or the sample into portions is founded on points of interest and is not uniform, and the index is made up of information coming, for each portion, from this same portion or from a specified assembly of neighboring portions. Furthermore, a redundant mesh is proposed (FIG. 9A) in order to describe the image several times and to attenuate the consequences of any omissions from the points of interest (E) on the other modeling (FIG. 9B).

Abstract: A method for producing an image. The method includes the steps of forming a procedural representation of the image. Then there is the step of taking samples of the image. Next there is the step of rendering larger shapes in the samples as progressively smaller shapes which cover the larger shapes until the larger shapes become represented by smaller shapes each occupying exactly one pixel, wherein the time it takes to render each smaller shape is essentially the same. An apparatus for producing an image. The apparatus includes a computer. The apparatus includes a memory connected to the computer. The apparatus includes a computer display connected to the computer. The apparatus includes a pointer device connected to the computer. The apparatus includes a mechanism for taking samples of the image and rendering larger shapes in the samples of the image as progressively smaller shapes which cover the larger shapes until the larger shapes become represented by smaller shapes each occupying exactly one pixel.

Abstract: An image processing apparatus includes a sort unit for sorting original image data into edge image data and planar image data, a first coding unit for coding the sorted planar image data according to the fractal block coding method, and a second coding unit for coding the sorted edge image data according to a coding method differing from the fractal block coding method. Thus, an image processing apparatus is provided that can have picture quality of a reproduced image improved even for a block that has maximum density difference such as an edge portion.

Abstract: A system for the compression and decompression of image files is provided. A library of basic waveforms is produced by applying selected digital initialization codes to a chaotic system. Each basic waveform is in one-to-one correspondence with an initialization code. A weighted sum of selected basic waveforms is used to approximate each slice of an image. The basic waveforms are then discarded and only the weighting factors and the corresponding initialization codes are stored in a compressed image file. When the compressed image file is decompressed for playback, the stored initialization codes are stripped out and applied to a similar chaotic system to regenerate the basic waveforms, which are recombined according to the stored weighting factors to produce an approximation of the original image slice.

Abstract: A wavelet transform system and an inverse wavelet transform system are disclosed that respectively implement a wavelet transform and an inverse wavelet transform. Semi-orthogonal standard wavelets are used as the basic wavelets in the wavelet transform and the inverse wavelet transform. As a result, two finite sequences of decomposition coefficients are used for decomposition in the wavelet transform. Furthermore, two finite sequences of reconstruction coefficients that are derived from the two finite sequences of decomposition coefficients are used for reconstruction in the inverse wavelet transform. The finite sequences of decomposition and reconstruction coefficients are not infinite sequences of coefficients that have been truncated. Furthermore, in one embodiment, downsampling is not used in the wavelet transform and upsampling is not used in the inverse wavelet transform.

Abstract: A video image searching method and apparatus that partially restores a picture according to a determined image restoring ratio, in order to reduce the searching time required compared to complete restoration of the picture as in conventional video image search. In the image searching method and apparatus, a dominant image element is extracted using a fractal image compression method, so that the image is partially restored, to thereby effectively search for the video image.

Abstract: Picture data which has been caused to undergo repetitive transform encoding (e.g., fractal encoding) is caused to undergo repetitive transform decoding while implementing scaling at a repetitive transform decoding unit 20 to temporarily preserve the decoded picture thus obtained at a buffer section 9. At the shape information calculating section 12, an approach is employed to calculate shape of object while implementing scaling thereto to send the object shape thus obtained (e.g., polygon) to a picture mapping section 10 to implement mapping to decoded picture from the buffer section 9. Thus, there is realized a texture mapping apparatus such that picture quality of texture is difficult to be deteriorated even when deformation takes place, such as, for example, at the time of zooming, etc.

Abstract: A game machine for high-speed execution of iterated transformation decoding based on a drawing command or data loaded from a recording medium. The drawing command, fractal transformation parameters or data loaded from a recording medium 24 are stored in a main memory 21. A drawing texture, expanded on a VRAM 23 in a graphics processing unit 22, is iteratively transformation decoded in accordance with the drawing command or the fractal transformation parameters transferred under control of the CPU 20. The generated texture is displayed as a picture on a CRT 32 of the graphics processing unit. This realizes high-speed iterated transformation decoding of the texture and a restored picture of high picture quality while realizing iterated transformation decoding with a significantly reduced calculation volume.

Abstract: A method for wavelet encoding image-representative signals, including the following steps: identifying shape information of a shape in the image; within rows of pixels of a shape, performing wavelet decompositions for segments of consecutive pixels in the shape; for segments of pixels having out of the shape pixels in a wavelet decomposition, forming a zero tree that includes don't-care nodes and having uncoded don't-care descendents of don't-care nodes.

Abstract: A video image searching method and apparatus that partially restores a picture according to a determined image restoring ratio, in order to reduce the searching time required compared to complete restoration of the picture as in conventional video image search. In the image searching method and apparatus, a dominant image element is extracted using a fractal image compression method, so that the image is partially restored, to thereby effectively search for the video image.

Abstract: A method and device that operates in accordance with the method are provided for primary processing a set of data (IM, f) representing physical quantities. The method comprises a step of constructing a global contractive mapping of a first type for the set of data, the fixed point of which constitutes an approximation of all or part of this set. At least one mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings is employed to construct the global contractive mapping. A next step includes determining parameters (ai, b) of the global contractive mapping so as to allow the use of a method of successive approximations converging towards the fixed point of the global contractive mapping. The determined set of parameters (ai, b) constitutes a primary representation of the set of data.

Abstract: An iterated image transformation and decoding apparatus and method, and a recording medium are provided. The iterated image transformation and decoding apparatus includes a transformation map analysis device for unscrambling a coded bit stream and analyzing a transformation map between two polygons; a polygon information generation device for generating information for generating one of the polygons; an image transformation and generation device for performing map transformation by using a representative map extracted by the transformation map analysis device; an image memory for storing the transformed polygonal image at the transformed position; and a control device for performing control so that the transformation and generation of the polygon is iteratively processed. Therefore, it is possible to generate a decoded image having a special reproduction effect.

Abstract: A method of compressing data utilizes the prime number series to generate unique compression parameters that may be used to recover an original data stream. The original data is converted from a binary form to a decimal form. Various compression parameters are selected to initialize the system. The compression parameters include the number of prime numbers which will be used in the compression process and an exponential value corresponding to each prime number. A header is constructed which includes the compression parameters. The data is compressed by a compression algorithm which performs successive division operations by the series of prime numbers selected. The compression algorithm generates a plurality of exponential values corresponding to each of the prime numbers. The header is then assembled with the exponential values and transmitted to a receiving station.

Abstract: A technique for encoding an image by splitting an input image into a plurality of first and second block portions and transform processing each second block portion. The transformed block portion most similar to a preselected first block portion and located in the same predefined area of the input image as the preselected first block is determined and the second block portion corresponding to this transformed block portion is selected. Block position information indicating the position of the selected second block portion and a transformation parameter representing the transform processing of the selected second block portion are output as the code. This code is decoded by recursively performing a transformation processing on the block indicated by the block position information and based on the transformation parameter until a predetermined condition is met for each block to be decoded within the predetermined area of the image.

Abstract: Encoding/decoding apparatus includes an encoding device having a picture memory for storing input picture data and having a search range determining unit for determining a range of a picture to be iteratively coded. A coded bit stream is generated from the picture data that is iterative coded within the determined range. A decoding device has a picture memory for storing picture data obtained from the coded bit stream received from the encoding device. The decoding device also has maximum allowable memory capacity determining unit for calculating maximum decodable capacity of the picture memory to carry out iterated function decoding on the coded bit stream and to output the decoded data as decoded picture data. The encoding/decoding apparatus provides high coding efficiency by using small memory capacity and a picture of high quality.