IMAGE CODING DEVICE, IMAGE DECODING DEVICE, IMAGE CODING METHOD, AND IMAGE DECODING METHOD Technical Field [0001] The present invention relates to an image signal coding device, an image signal decoding device, an image signal coding method, and an image signal decoding method which are used for a technology of image compression coding, a technology of transmitting compressed image data, and the like. Background Art [0002] International standard video coding methods such as MPEG and ITU-T H.26x mainly use a standardized input signal format referred to as a 4:2:0 format for a signal to be subjected to the compression processing. The 4:2:0 format is a format obtained by transforming a color motion image signal such as an RGB signal into a luminance component (Y) and two color difference components (Cb, Cr), and reducing the number of samples of the color difference components to a half of the number of samples of the luminance component both in the horizontal and vertical directions. The color difference components are low in visibility compared to the luminance component, and hence the international standard video coding methods such as MPEG-4 AVC/H.264 (hereinbelow, referred to as AVC) (see Non-patent Document 1) are based on the premise that, by applying down-sampling to the color difference components before the coding, original information content to be coded is reduced. On the other hand, for contents such as digital cinema, in order to precisely reproduce, upon viewing, the color representation defined upon the production of the contents, a direct coding method in a 4:4:4 format which, for coding the color difference components, employs the same number of samples as that of the luminance component without the down-sampling is recommended. As a method suitable for this purpose, there are standard methods described in Non-patent Document 2 and Non-patent Document 3. FIG. 31 illustrates a difference between the 4:2:0 format and the 4:4:4 format. In this figure, the 4:2:0 format includes the luminance (Y) signal and the color difference (Cb, Cr) signals, and one sample of the color difference signal corresponds to 2x2 samples of the luminance signal while the 4:4:4 format does not specifically limit the color space for expressing the colors to Y, Cb, and Cr, and the sample ratio of the respective color component signals is 1:1. [0003] Non-patent Document 1: MPEG-4 AVC(ISO/IEC 14496-10)/ITU-T H.264 standard Non-patent Document 2: JPEG2000(ISO/IEC 15444) standard Non-patent Document 3: MPEG-4 AVC(ISO/IEC 14496-10)/ITU-T H.264 Amendment2 Disclosure of the Invention Problem to be solved by the Invention [0004] For example, the coding in the 4:4:4 format described in Non-patent Document 3, as illustrated in FIG. 32, first, input video signals 1001 (in the 4:4:4 format) to be coded are, in advance, transformed into signals in an appropriate color space (such as YCbCr space) directly or through a color space transformation unit 1002, and are input, as video signals to be coded 1003, to a prediction unit 1004 while a macroblock (rectangular block of 16 pixels by 16 lines) is set as a unit. The prediction unit 1004 predicts image signals of the respective color components in the macroblock within a frame and between frames, thereby obtaining prediction error signals 1005. The compression unit 1006 applies transform processing such as the discrete cosine transform (DCT) to the prediction error signals 1005 to remove signal correlations, and quantizes resulting signals into compressed data 1007. The compressed data 1007 is coded through the entropy coding by a variable-length coding unit 1008, is output as a bit stream 1009, and is also sent to a local decoding unit 1010, and decoded prediction error signals 1011 are obtained. These signals are respectively added to predicted signals 1012 used for generating the prediction error signals 1005, thereby obtaining decoded signals 1013. The decoded signals 1013 are stored in a memory 1014 in order to generate the predicted signals 1012 for the subsequent video signals to be coded 1003. It should be noted that parameters for predicted signal generation 1015 determined by the prediction unit 1004 in order to obtain the predicted signals 1012 are sent to the variable-length coding unit 1008, and are output as the bit stream 1009. On this occasion, the parameters for predicted signal generation 1015 contain, for example, an intra prediction mode indicating how the spatial prediction is carried out in a frame, and motion vectors indicating the quantity of motion between frames. [0005] A video signal in the 4:4:4 format contains the same number of samples for the respective color components, and thus contains redundant information contents compared with a video signal in the conventional 4:2:0 format. In order to increase the compression efficiency of the video signal in the 4:4:4 format, it is necessary to further reduce the redundaricy between color components compared to the fixed color space definition (Y, Cb, Cr) in the conventional 4:2:0 format. In Non-patent Document 3, the video signals to be coded 1003 are obtained by uniformly transforming the entire image through a specific color space transform processing independently of local characteristics of the signals, and signal processing that considers the removal of the correlation between the color components is not carried out in any of the prediction unit 1004, the compression unit 1006, and the variable-length coding unit 1008. For this reason, it is not considered that the signal correlation is maximally removed between the color components in the same pixel position. [0006] It is therefore an object of the present invention to provide a method of efficiently compress information by removing signal correlations according to local characteristics of a video signal in a 4:4:4 format which is to be coded, and, as described as the conventional technology, for coding a motion video signal, such as a signal in a 4:4:4 format, which does not have a difference in sample ratio among color components, to provide an image coding device, an image decoding device, an image coding method, and an image decoding method, which are enhanced in optimality. Means for solving the Problem [0007] According to the present invention, there is provided an image coding device for receiving, as an input, a color image formed of a plurality of color components, performing compression coding in a unit of a first region obtained by dividing the color image, and generating a bit stream. The image coding device includes a signal analysis unit for obtaining, for a signal of each of the plurality of color components belonging to the first region, an average in a unit of a second region obtained by dividing the first region, and obtaining an average separated signal corresponding to the second region; an average signal coding unit for applying, independently for the each of the plurality of color components, prediction coding to an average signal formed of the average obtained in the unit of the second region obtained by dividing the first region; and an average separated signal coding unit for transforming the average separated signals of the plurality of color components, which are obtained in the unit of the second region obtained by dividing the first region, by switching among a plurality of inter-color-component transform methods provided, and coding the transformed average separated signals independently of the average signal coding unit, in which the average separated signal coding unit outputs information indicating selected inter-color-component transform methods to the bit stream as a part of coded data. Effects of the Invention [0008] According to the image coding device, the image decoding device, the image coding method, and the image decoding method of the present invention, for coding which uses various color spaces without limitation to a fixed color space such as the YCbCr color space, there can be provided a configuration in which local signal correlations present between respective color components are adaptively removed, and even when there are various definitions of the color space, optimal coding processing can be carried out. [0009] Brief Description of the Drawings [FIG. 1] An explanatory diagram illustrating a configuration of an image ; coding device according to a first embodiment. [FIG 2] An explanatory diagram illustrating an internal configuration of a signal analysis unit 103. [FIG. 3] An explanatory diagram illustrating an example of processing when N=4. [FIG 4] An explanatory diagram illustrating an internal configuration of a first signal coding unit 106. ; [FIG 5] An explanatory diagram illustrating an internal configuration of j I a second signal coding unit 107. j I s [FIGS. 6] Explanatory diagrams illustrating a structure of a bit stream J j 111 according to the first embodiment. | [FIG 7] An explanatory diagram illustrating a configuration of an image I decoding device according to the first embodiment. ! [FIG. 8] An explanatory diagram illustrating an internal configuration of { i a signal composition unit 205. [FIG 9] An explanatory diagram illustrating an example of processing when N=4. [FIG 10] An explanatory diagram illustrating an internal configuration of a first signal decoding unit 201. [FIG. 11] An explanatory diagram illustrating an internal configuration of a second signal decoding unit 202. [FIG. 12] An explanatory diagram illustrating a configuration of another image coding device according to the first embodiment. [FIG. 13] An explanatory diagram illustrating a configuration of an image coding device according to a second embodiment. [FIG. 14] An explanatory diagram illustrating an internal configuration of a CO component coding unit 300. [FIG. 15] An explanatory diagram illustrating an internal configuration of an AC signal generation unit 308. [FIG. 16] An explanatory diagram illustrating an internal configuration of a CI component coding unit 310. [FIG. 17] An explanatory diagram illustrating an internal configuration of a DC prediction unit 311. [FIG. 18] An explanatory diagram illustrating a configuration of an image decoding device according to the second embodiment. [FIGS. 19] Explanatory diagrams illustrating a structure of a bit stream 111 according to the second embodiment. [FIG. 20] An explanatory diagram illustrating an internal configuration of a CO component decoding unit 401. [FIG. 21] An explanatory diagram illustrating an internal configuration of a CI component decoding unit 402. [FIG. 22] An explanatory diagram illustrating a configuration of an image coding device according to a third embodiment. [FIG. 23] An explanatory diagram illustrating an internal configuration of a prediction unit 500. [FIG. 24] An explanatory diagram illustrating an internal configuration of a prediction mode determination unit 522. [FIGS. 25] Explanatory diagrams illustrating a structure of a bit stream 111 according to the third embodiment. [FIG. 26] An explanatory diagram illustrating a configuration of an image decoding device according to the third embodiment. [FIG. 27] An explanatory diagram illustrating an internal configuration of a prediction unit 601. [FIG 28] An explanatory diagram illustrating sampling density patterns. [FIG. 29] An explanatory diagram illustrating sampling density patterns. [FIG. 30] An explanatory diagram illustrating sampling density patterns. [FIG. 31] An explanatory diagram illustrating a difference between a 4:2:0 format and a 4:4:4 format. [FIG. 32] An explanatory diagram illustrating conventional coding for the 4:4:4 format. Best Modes for carrying out the Invention [0010] First Embodiment In a first embodiment, a description is given of a coding device for coding a video frame input in a 4:4:4 format in a unit of a rectangular region of MxM pixels for respective color components by using intra-frame and inter-frame adaptive predictions, and a corresponding decoding device, [0011] 1. Overview of Operation of Coding Device FIG. 1 illustrates a configuration of an image coding device according to a first embodiment. Input signals 100 in the 4:4:4 format are each formed of signals of three color components CO, CI, and C2, are divided by a region dividing unit 101 into coding unit blocks 102 each formed of a rectangular block of a MxM pixel size for the CO, CI, and C2 components, and are sequentially input to a signal analysis unit 103. FIG. 2 illustrates an internal configuration of the signal analysis unit 103. In the signal analysis unit 103, first, a sub-block dividing unit 112 divides the coding unit block 102 into NxN pixel blocks (N