JP2016086262A - Image coding method, image decoding method, image coding program, and image decoding program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an image coding method and an image decoding method capable of obtaining a decoded image of higher quality with a smaller code amount, by improving the quality of a reference image.SOLUTION: Using a function identification technique, a predictive residual signal is reproduced with a function, and otherwise an input image is reproduced from its predictive signal with a function. The function information is coded. The function information is decoded and the predictive residual signal is generated from the function. Otherwise, an input image signal is reproduced from the function and the predictive signal to perform image decoding.SELECTED DRAWING: Figure 5

Description

  The present invention relates to an image encoding method, an image decoding method, an image encoding program, and an image decoding program.

  The irreversible video / image coding components can be classified into four elements: prediction, transformation, quantization, and entropy coding. The coding apparatus according to the prior art is configured to use both transform and inverse transform. Also, the decoding device according to the prior art is configured to use only inverse transformation without using transformation.

  The “transformation” in this component plays an important role in improving the encoding performance. In the still picture coding international standard JPEG (Joint Photographic Experts Group, see Non-Patent Document 1, for example), 8-point transform by DCT (Discrete Cosine Transform) is used. In addition, wavelet transform is used in the international standard JPEG2000 for still image coding (see, for example, Non-Patent Document 2). Furthermore, in the international video coding standard HEVC (High Efficiency Video Coding, see, for example, Non-Patent Document 3), DCT or DST (Discrete Sine Transform) is approximated by integers using 4-point, 8-point, 16-point, and 32-point transformations. It has been. In Patent Document 1, nonlinear conversion is optimally generated according to the video. By performing such conversion, the signal in which the original power is dispersed is changed to a signal in which the power is concentrated, and the coding efficiency is improved.

  In any of these encoding methods, “transformation” and “inverse transform” are always paired. That is, when DCT is used, inverse DCT is used as a pair in the encoding process and decoding process when inverse Wavelet transform is used. In the method of Patent Document 1, the inverse transformation corresponding to the nonlinear transformation is easily generated and used. However, in order to easily generate the inverse transformation, the transformation is limited to a structure called “lifting”.

  In addition, as an encoding method that does not use “transformation” and “inverse transform” as a pair, for example, there is a method using MP (Matching Pursuit) (for example, see Non-Patent Document 4). This is because a waveform group (generated by giving various parameters to the Gabor function in the example of the above method) is prepared in advance, and the encoding device combines the appropriate number of waveforms, “Combination information” that can reproduce a waveform close to the waveform of the input image is encoded and transmitted. Note that, here, a waveform in which values (pixel values) are distributed two-dimensionally, such as a still image or a video frame, is called a “waveform”.

JP 2014-082616 A

ISO / IEC 10918-1 "Information technology-Digital compression and coding of continuous-tone still images", 1993 ITU-T Rec. T.800 "Information technology-JPEG 2000 image coding system: Core coding system" Aug. 2002 ISO / IEC 23008-2 "Information technology-High efficiency coding and media delivery in heterogeneous environments-Part 2: High efficiency video coding", Apr. 2014 Matsuda, Ito: “Video coding by integrating MC and MP”, IEICE technical report. OFS, Office system no. 101 (299), pp. 7-14, Sep. 2001

  However, the restriction that “transform” and “inverse transform” are used in pairs is not preferable from the viewpoint of the degree of freedom of encoding. For example, in the case of linear transformation such as DCT, there is a restriction that the transformation is a linear operation. In many cases (at least HEVC, JPEG, MPEG-2, etc.), there is a restriction that the transformation is orthogonal transformation. In addition, in the case of Patent Document 1, it is possible to handle non-linear transformation beyond the limitation, but there is a limitation that only transformation (and inverse transformation) that can be expressed by a lifting structure can be handled. Another limitation is that it must be paired in the first place (an inverse transformation must exist for the transformation). For example, a transform that does not have an inverse transform (a transform that does not have a one-to-one correspondence between input and output, that is, a transform in which output values may match even if input values are different) can be used in conventional coding. There is a problem that you can not.

  The reason why the transform and inverse transform are paired in the conventional coding technique even though the decoder only performs inverse transform is that information necessary for the waveform representation of the decoder (ie, transform coefficients) is obtained. This is so that the encoding device can be obtained easily. Further, as in Non-Patent Document 4, there is a problem that a waveform group for transmission can be selected only from a predetermined shape (for example, a Gabor function). In order to pursue higher encoding performance, it is preferable that there are few such restrictions when trying various conversion possibilities.

  The present invention has been made in view of such circumstances, and an image encoding method capable of increasing the degree of freedom of waveform reproduction in image encoding and obtaining a higher quality decoded video with a smaller code amount. An object of the present invention is to provide an image decoding method, an image encoding program, and an image decoding program.

  The present invention is an image encoding method performed by an image encoding device that encodes an input video signal, and a function identification step for generating a function that approximates a prediction residual signal of inter-screen prediction or intra-screen prediction; The method includes a coding step for coding function information representing the function to be approximated, and a signal reproduction step for reproducing the prediction residual signal using the function information.

  The present invention is an image encoding method performed by an image encoding apparatus that encodes an input video signal, and generates a conversion coefficient by converting a prediction residual signal of inter-screen prediction or intra-screen prediction by a predetermined conversion method. A transform step that performs quantization, a quantization step that quantizes the transform coefficient to generate an initial coefficient, a transform base used in the transform method and the initial coefficient that are included in the population of evolutionary calculations, and prediction of inter-screen prediction or intra-screen prediction A function identification step for generating a function approximating the residual signal, an encoding step for encoding function information expressing the function to be approximated, and a signal reproduction step for reproducing the predicted residual signal using the function information It is characterized by having.

  The present invention is an image encoding method performed by an image encoding device that encodes an input video signal, and a function identification step for generating a function that approximates a prediction residual signal of inter-screen prediction or intra-screen prediction; A coding step for coding function information representing the function to be approximated, and a decoded image reproduction step for reproducing a decoded image using the function information and an intra-screen prediction signal or an inter-screen prediction signal. To do.

  The present invention is an image encoding method performed by an image encoding device that encodes an input video signal, the input video signal and an intra-screen prediction signal or an inter-screen prediction signal being input, and the input video signal A function identification step for generating a function that approximates the function, a coding step for encoding function information that expresses the function to be approximated, a decoded image using the function information and the intra prediction signal or inter prediction signal. And a decoded image reproduction step to reproduce.

  The present invention is an image decoding method performed by an image decoding apparatus for decoding a video signal encoded by the image encoding method, wherein the decoding step decodes function information from the encoded video signal; And a signal reproduction step of reproducing the video signal using the function information.

  The present invention is an image decoding method performed by an image decoding apparatus for decoding a video signal encoded by the image encoding method, wherein the decoding step decodes function information from the encoded video signal; And a decoded image reproduction step for reproducing the decoded image using the function information.

  The present invention is an image encoding program for causing a computer to execute the image encoding method.

  The present invention is an image decoding program for causing a computer to execute the image decoding method.

  According to the present invention, since the degree of freedom of waveform reproduction can be increased in image coding, an effect that a decoded video with higher quality can be obtained with a smaller code amount can be obtained.

It is a block diagram which shows the structure of a general image coding apparatus. It is a flowchart which shows the processing operation of the image coding apparatus shown in FIG. It is a block diagram which shows the structure of a general image decoding apparatus. It is a flowchart which shows the processing operation of the image decoding apparatus shown in FIG. It is a block diagram which shows the structure of the image coding apparatus in 1st Embodiment of this invention. 6 is a flowchart showing a processing operation of the image encoding device shown in FIG. 5. It is a block diagram which shows the structure of the image coding apparatus in 2nd Embodiment of this invention. It is a flowchart which shows the processing operation of the image coding apparatus shown in FIG. It is a block diagram which shows the structure of the image coding apparatus in 3rd Embodiment of this invention. Fig. 10 is a flowchart showing a processing operation of the image encoding device shown in Fig. 9. It is a block diagram which shows the structure of the image coding apparatus in 4th Embodiment of this invention. It is a flowchart which shows the processing operation of the image coding apparatus shown in FIG. It is a flowchart which shows the processing operation of the function identification part. It is a block diagram which shows the structure of the image decoding apparatus in 5th Embodiment of this invention. It is a flowchart which shows the processing operation of the image decoding apparatus shown in FIG. It is a block diagram which shows the structure of the image decoding apparatus in 6th Embodiment of this invention. FIG. 17 is a flowchart showing a processing operation of the image decoding device shown in FIG. 16. FIG.

Hereinafter, an image encoding method and an image decoding method according to an embodiment of the present invention will be described with reference to the drawings. First, H. H.265 / HEVC and H.264 The configuration of H.264 / AVC and other general image encoding devices will be described. FIG. 1 is a block diagram illustrating a configuration of a general image encoding device. The encoding apparatus shown in FIG. 1 receives a video signal 100 to be encoded, divides it into blocks, encodes each block, and outputs it as encoded data. FIG. 2 is a flowchart showing the processing operation of the image encoding device shown in FIG.
First, in the video block, the prediction signal 101 generated separately is subtracted by the subtraction unit 102 to obtain a prediction residual signal 119 (step S1). The prediction residual signal 119 is converted by the conversion unit 103, quantized by the quantization unit 104 (step S2), entropy-encoded by the entropy encoding unit 105, and output as encoded data 106 (step S3).

  On the other hand, the quantized value is inversely quantized by the inverse quantization unit 107, inversely transformed by the inverse transform unit 108 (step S4), and added to the predicted signal 101 by the adder 109 to reproduce the decoded image (step S4). S5). Subsequently, the signal is subjected to distortion removal in the distortion removal filter unit 110 (step S6) and stored in the frame memory 111 (step S7). The stored signal is the same signal as the decoded video signal required by the image decoding apparatus corresponding to this apparatus. Using this, the intra prediction unit 112 or the inter prediction unit 113 generates the prediction signal 101 of the unit to be encoded next (step S8).

  Next, the configuration of a general image decoding device will be described. FIG. 3 is a block diagram illustrating a configuration of a general image decoding apparatus. The image decoding device shown in FIG. 3 outputs the video signal of the decoded image by inputting and decoding the encoded data encoded by the image encoding device shown in FIG. FIG. 4 is a flowchart showing the processing operation of the image decoding apparatus shown in FIG. In order to perform decoding, the entropy decoding unit 201 receives the encoded data 200, decodes it, and outputs a quantized coefficient (step S21). The inverse quantization unit 202 inversely quantizes the quantization coefficient and outputs it. The inverse transform unit 203 inversely transforms this and outputs a decoded prediction residual signal (step S22).

  The adder 204 adds the separately generated prediction signal 210 and the decoded prediction residual signal, and outputs a signal that is a source of the decoded image (step S23). This signal is subjected to filtering processing to reduce the coding distortion in the distortion removal filter unit 205, and becomes a decoded signal of the decoding target block (step S24). This signal is stored in the frame memory 206 (step S25) and at the same time is output as a decoded video 207. This decoded signal is referred to by the intra-screen prediction unit 208 and the inter-screen prediction unit 209, and is output as the prediction signal 210 (step S26).

<First Embodiment>
Next, the configuration of the image encoding device according to the first embodiment of the present invention will be described with reference to FIG. FIG. 5 is a block diagram illustrating a configuration of the image encoding device according to the embodiment. In this figure, the same parts as those in the general apparatus shown in FIG. The apparatus shown in this figure is different from the general apparatus shown in FIG. 1 in that a function identification unit 114, a signal reproduction unit is used instead of the transformation unit 103, the quantization unit 104, the inverse quantization unit 107, and the inverse transformation unit 108. 116 is provided.

  The function identification unit 114 performs function identification for reproducing a waveform close to a given waveform by a function while allowing an arbitrary degree of freedom. “Function identification” is realized by a technique generally called “genetic programming”. Since genetic programming is a known technique (see, for example, Patent Document 1), detailed description thereof is omitted here. In addition, a procedure for obtaining the code amount of a function is also known in order to automatically construct an optimum function in terms of code amount and distortion without increasing the degree of freedom without limitation (see, for example, Patent Document 1). Then, detailed description is abbreviate | omitted.

  FIG. 6 is a flowchart showing the processing operation of the image encoding device shown in FIG. 6, the same processing operations as those in FIG. 2 are denoted by the same reference numerals, and the description thereof is omitted. The function identification unit 114 receives the prediction residual signal 119 and generates a function that well reproduces this signal (waveform) by a technique such as genetic programming (step S9). The function information 115 output from the function identification unit 114 is encoded by the entropy encoding unit 105 (step S3). On the other hand, the signal reproduction unit 116 reproduces the prediction residual signal 119 using the function information 115 once obtained (step S10).

Second Embodiment
Next, the configuration of the image encoding device according to the second embodiment of the present invention will be described with reference to FIG. FIG. 7 is a block diagram showing a configuration of an image encoding device according to the second embodiment of the present invention. In this figure, the same parts as those in the apparatus shown in FIG. The apparatus shown in this figure is different from the apparatus shown in FIG. 5 in that a conversion unit 103 and a quantization unit 104 are provided.

  FIG. 8 is a flowchart showing the processing operation of the image encoding device shown in FIG. 8, the same processing operations as those in FIGS. 2 and 6 are denoted by the same reference numerals, and the description thereof is omitted. The conversion unit 103 receives the prediction residual signal 119 and performs conversion (DCT, DST, MP). The quantization unit 104 quantizes the output of the conversion unit 103 and outputs the result as an initial coefficient 117 (step S2). The initial coefficient 117 is used as an initial coefficient when the function identification unit 114 performs function identification. For example, the initial coefficient 117 is updated by a multidimensional search to obtain a coefficient that can further improve the coding efficiency. In this embodiment, a basis function (cos function in the case of DCT, sin function in the case of DST, mainly Gabor function in the case of MP) corresponding to the conversion used in the conversion unit 103 can be applied as an initial value of the identification function, This is updated by a technique such as dynamic programming to obtain an identification function that can further improve the coding efficiency.

<Third Embodiment>
Next, the configuration of an image encoding device according to the third embodiment of the present invention will be described with reference to FIG. FIG. 9 is a block diagram showing a configuration of an image encoding device according to the third embodiment of the present invention. In this figure, the same parts as those in the apparatus shown in FIG. The apparatus shown in this figure is different from the apparatus shown in FIG. 5 in that the prediction signal 101 (here, B) is output to the function identification unit 114, and the addition unit 109 and the signal reproduction unit 116 are integrated. Thus, a decoded image reproduction unit 118 is provided. This configuration makes it possible to increase the degree of freedom.

  FIG. 10 is a flowchart showing the processing operation of the image encoding device shown in FIG. 10, the same processing operations as those in FIG. 8 are denoted by the same reference numerals, and the description thereof is omitted. In the apparatus configuration shown in FIG. 9, as function information 115 (here, X), a signal (here, F (X)) reproduced by a function (here, F) obtained by the function identification unit 114. And the prediction signal 101 (here, B) is simply added and F (X) + B is output instead of outputting F (X) + B (step S9). In other words, the function F includes the configurations shown in FIGS. 5 and 7, and the prediction signal 101 (B) has a higher degree of freedom by inputting the prediction signal 101 (B), and a value closer to the input video signal 100 is output. Will be able to.

<Fourth embodiment>
Next, with reference to FIG. 11, the structure of the image coding apparatus in 4th Embodiment of this invention is demonstrated. FIG. 11 is a block diagram showing a configuration of an image encoding device according to the fourth embodiment of the present invention. In this figure, the same parts as those in the apparatus shown in FIG. The apparatus shown in this figure is different from the apparatus shown in FIG. 9 in that the subtraction unit 102 is integrated into the function identification unit 114.

  FIG. 12 is a flowchart showing the processing operation of the image encoding device shown in FIG. 12, the same processing operations as those in FIG. 10 are denoted by the same reference numerals, and the description thereof is omitted. The function identifying unit 114 does not function-identify the difference (V−B) between the input video signal 100 (here, V) and the prediction signal 101 (here, B), but the video signal 100 ( V) The function itself is identified and output as function information 115 (step S9). This configuration has a higher degree of freedom than the configurations shown in FIGS. 5, 7, and 9, and can output a value closer to the input video signal 100.

  Next, the processing operation of the function identification unit 114 shown in FIGS. 5, 7, 9, and 11 will be described with reference to FIG. FIG. 13 is a flowchart showing the processing operation of the function identification unit 114. The function identification unit 114 generates a group of functions (for example, a function equivalent to a transformation such as an existing DCT, a function that randomly combines exponentiation, addition / subtraction / division, etc.) as a source of evolution by population generation processing ( Step S31). Next, the function identification unit 114 performs parent selection and child individual generation in the replication selection / child generation process (step S32). “Child generation” is performed by processing such as crossover, mutation, and inversion.

  Next, the function identification unit 114 uses the individual (representing the function) generated in step S2, generates a function based on this function in the encoding process, adds the prediction signal 101 to the function, and outputs the image signal. Generate (step S33). Next, the function identification unit 114 calculates the error sum D and code amount R of the image block in the square error sum D / code amount R calculation process (step S34), and also calculates the information amount Ro of the individual (step S35). ).

  Next, the function identification unit 114 determines whether or not to survive in the survival selection process using the value of the Lagrangian cost C = D + λ (R + Ro) as an evaluation value (step S36). The Lagrange undetermined multiplier λ may be the same value as that used in the RD optimization in the encoding process, or a different one may be designated separately. The smaller the Lagrangian cost C, the better the individual is. Then, the function identification unit 114 determines whether the evolution has converged (step S37). For example, as a convergence condition, the reduction rate of the Lagrangian cost C is less than a certain value (for example, 0.1%), the number of evaluations is more than a certain value (for example, 10,000), and the like can be applied.

  Next, if it is determined that the function has not yet converged, the function identification unit 114 returns to step S32 and repeats the process. If it is determined that the function has converged, the function identifying unit 114 ends the process. By this processing operation, a function for improving the coding efficiency is automatically generated.

<Fifth Embodiment>
Next, with reference to FIG. 14, the structure of the image decoding apparatus in 5th Embodiment of this invention is demonstrated. FIG. 14 is a block diagram showing a configuration of an image decoding device according to the fifth embodiment of the present invention. In this figure, the same parts as those in the general apparatus shown in FIG. The apparatus shown in this figure is different from the apparatus shown in FIG. 3 in that a signal reproduction unit 212 is provided instead of the inverse quantization unit 202 and the inverse transform unit 203. This image decoding apparatus outputs a video signal of a decoded image by inputting and decoding the encoded data encoded by the image encoding apparatus shown in FIGS.

  FIG. 15 is a flowchart showing the processing operation of the image decoding apparatus shown in FIG. 15, the same processing operations as those in FIG. 4 are denoted by the same reference numerals, and the description thereof is omitted. In order to perform decoding, the entropy decoding unit 201 receives the encoded data 200 and performs entropy decoding on the function information 211 of the decoding target block (step S21). The signal reproduction unit 212 inputs this function information and outputs a decoded prediction residual signal based on the function information to perform signal reproduction (step S27). The adder 204 adds the separately generated prediction signal 210 and the decoded prediction residual signal, and outputs a signal that is a source of the decoded image (step S23). This signal is subjected to filtering processing to reduce coding distortion in the distortion removal filter unit 205 (step S24), and becomes a decoded signal of the decoding target block. This signal is stored in the frame memory 206 (step S25) and at the same time is output as a decoded video 207. This decoded signal is referred to by the intra-screen prediction unit 208 and the inter-screen prediction unit 209, and is output as the prediction signal 210 (step S26).

<Sixth Embodiment>
Next, with reference to FIG. 16, the structure of the image decoding apparatus in 6th Embodiment of this invention is demonstrated. FIG. 16 is a block diagram showing a configuration of an image decoding device according to the sixth embodiment of the present invention. In this figure, the same parts as those of the apparatus shown in FIG. The apparatus shown in this figure is different from the apparatus shown in FIG. 14 in that a decoded image reproduction unit 213 in which a signal reproduction unit 212 and an addition unit 204 are integrated is provided. This image decoding apparatus outputs a video signal of a decoded image by inputting and decoding the encoded data encoded by the image encoding apparatus shown in FIGS.

  FIG. 17 is a flowchart showing the processing operation of the image decoding apparatus shown in FIG. 17, the same processing operations as those in FIG. 15 are denoted by the same reference numerals, and the description thereof is omitted. The decoded image reproduction unit 213 receives the function information 211 and the prediction signal 210 output from the intra-screen prediction unit 208 or the inter-screen prediction unit 209, combines the inputs based on the function information 211, and reproduces the decoded image (step S23). . This configuration is a more general configuration with a high degree of freedom, including the configuration shown in FIG.

  As described above, the decoded signal is brought close to the original image by using function identification by an evolutionary method in image coding. According to this configuration, the degree of freedom of waveform reproduction can be dramatically increased. Therefore, in image encoding, encoding can be performed with the best function in the relationship between code amount and distortion, and a decoded image with higher quality can be obtained with a smaller code amount.

  In addition, although the load on the encoding device is greater than in the past, the information necessary for the waveform representation of the decoding device (inverse conversion procedure and conversion coefficient) is generated by the encoding device through repeated optimization, thereby performing the inverse conversion. Therefore, a higher quality decoded video can be obtained with a smaller amount of code without using the “conversion” that is a pair of the above.

  You may make it implement | achieve the image coding apparatus and image decoding apparatus in embodiment mentioned above with a computer. In that case, a program for realizing this function may be recorded on a computer-readable recording medium, and the program recorded on this recording medium may be read into a computer system and executed. Here, the “computer system” includes an OS and hardware such as peripheral devices. The “computer-readable recording medium” refers to a storage device such as a flexible medium, a magneto-optical disk, a portable medium such as a ROM and a CD-ROM, and a hard disk incorporated in a computer system. Furthermore, the “computer-readable recording medium” dynamically holds a program for a short time like a communication line when transmitting a program via a network such as the Internet or a communication line such as a telephone line. In this case, a volatile memory inside a computer system serving as a server or a client in that case may be included and a program held for a certain period of time. Further, the program may be for realizing a part of the functions described above, and may be a program capable of realizing the functions described above in combination with a program already recorded in the computer system. It may be realized using hardware such as PLD (Programmable Logic Device) or FPGA (Field Programmable Gate Array).

  As mentioned above, although embodiment of this invention has been described with reference to drawings, the said embodiment is only the illustration of this invention, and it is clear that this invention is not limited to the said embodiment. is there. Therefore, additions, omissions, substitutions, and other modifications of the components may be made without departing from the technical idea and scope of the present invention.

  In lossy encoding of images / videos, the present invention can be applied to applications where it is essential to encode / decode images for the purpose of improving video quality and reducing the encoding bit rate.

  DESCRIPTION OF SYMBOLS 100 ... Video signal 101 ... Prediction signal 102 ... Subtraction part 103 ... Conversion part 104 ... Quantization part 105 ... Entropy encoding part 106 ... Encoded data 107 ... Inverse quantization part 108 ... Inverse conversion 109: Adder, 110 ... Distortion removal filter unit, 111 ... Frame memory, 112 ... In-screen prediction unit, 113 ... Inter-screen prediction unit, 114 ... Function identification unit, 115 ... Function information, 116 ... Signal reproduction unit, 117 ... Initial coefficient 118 ... Decoded image reproduction unit 119 ... Prediction residual signal 200 ... Encoded data 201 ... Entropy decoding unit 202 ... Inverse quantization unit 203 ... Inverse transform unit 204 ... Adder unit 205 DESCRIPTION OF SYMBOLS ... Distortion removal filter part, 206 ... Frame memory, 207 ... Decoded video, 208 ... In-screen prediction part, 209 ... Inter-screen prediction part, 210 ... Prediction signal, 211 ... Function information, 212 Signal reproducing unit, 213 ... decoding image reproducing unit

Claims (8)

An image encoding method performed by an image encoding device that encodes an input video signal,
A function identification step that generates a function approximating a prediction residual signal of inter-screen prediction or intra-screen prediction;
An encoding step for encoding function information representing the approximating function;
And a signal reproduction step of reproducing the prediction residual signal using the function information. An image encoding method performed by an image encoding device that encodes an input video signal,
A conversion step of converting a prediction residual signal of inter-screen prediction or intra-screen prediction by a predetermined conversion method to generate a conversion coefficient;
A quantization step of quantizing the transform coefficient to generate an initial coefficient;
A function identification step of generating a function that approximates a prediction residual signal of inter-screen prediction or intra-screen prediction by including the conversion base used in the conversion method and the initial coefficient in a population of evolutionary calculation;
An encoding step for encoding function information representing the approximating function;
And a signal reproduction step of reproducing the prediction residual signal using the function information. An image encoding method performed by an image encoding device that encodes an input video signal,
A function identification step that generates a function approximating a prediction residual signal of inter-screen prediction or intra-screen prediction;
An encoding step for encoding function information representing the approximating function;
A decoded image reproduction step of reproducing a decoded image using the function information and an intra-screen prediction signal or an inter-screen prediction signal. An image encoding method performed by an image encoding device that encodes an input video signal,
A function identification step of inputting the input video signal and the intra prediction signal or the inter prediction signal, and generating a function approximating the input video signal;
An encoding step for encoding function information representing the approximating function;
A decoded image reproduction step of reproducing a decoded image using the function information and the intra prediction signal or inter prediction signal. An image decoding method performed by an image decoding apparatus for decoding a video signal encoded by the image encoding method according to claim 1,
A decoding step of decoding function information from the encoded video signal;
And a signal reproduction step of reproducing the video signal using the function information. An image decoding method performed by an image decoding device that decodes a video signal encoded by the image encoding method according to claim 3 or 4,
A decoding step of decoding function information from the encoded video signal;
A decoded image reproduction step for reproducing a decoded image using the function information.   An image encoding program for causing a computer to execute the image encoding method according to claim 1.   An image decoding program for causing a computer to execute the image decoding method according to claim 5 or 6.

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