The present invention relates to an image processing apparatus and method thereof. CROSS REFERENCES TO RELATED APPLICATIONS The present invention contains subject matter related to Japanese Patent Application JP 2006-073557 filed in the Japanese Patent Office on March 16, 2006, the entire contents of which are incorporated herein by reference. BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention generally relates to image processing apparatuses and methods, program recording media, and programs. More particularly, the invention relates to an image processing apparatus and method, a program recording medium, and a program that allow the quality of an image to be accurately enhanced by distinguishing artificial image components and natural image components included in an image from each other and by performing optimal processing on each of the artificial image components and natural image components. 2. Description of the Related Art The assignee of this application previously proposed classification adaptation processing in, for example, Japanese Unexamined Patent Application Publication No. 9- 167240. In the classification adaptation processing from an input first image a second image is determined. More specifically according to the pixel values of a plurality of pixels in a predetermined area of the input first image subject pixels of the second image are allocated into classes and then a linear expression of prediction coefficients which have been determined for the individual classes by learning processing and the pixel values of the plurality of pixels in the predetermined area of the input first image are calculated so that the second image can be determined from the input first image. For example if the first image is an image containing noise and the second image is an image with suppressed noise the classification adaptation processing serves as noise suppression processing. If.the first image is a standard definition (SD) image and the second image is a high definition (HD) image with a level of resolution higher than that of the SD image the classification adaptation processing serves as resolution conversion processing for converting a low-resolution image into a high-resolution image. In known learning processing to enable prediction of general moving pictures typified by broadcasting moving pictures instead of artificial images which are discussed in detail below natural images obtained by directly imaging subjects in nature are used as supervisor images and learner images. Accordingly if the first image is a natural image the second image which is a high-definition fine image can be predicted by performing classification adaptation processing using prediction coefficients obtained by learning processing. SUMMARY OF THE INVENTION Normally the first image is formed of a mixture of an area of artificial image components and an area of natural image components. Accordingly it is possible to predict the second image which is a high-definition fine image by performing classification adaptation processing on the area of the natural image components by using prediction coefficients determined by the above-described learning processing. If however classification adaptation processing is performed on the area of the artificial image components such as text or simple graphics of the first image by using the prediction coefficients determined by the learning processing using natural images the fineness of edged portions is excessively enhanced and flat noise is disadvantageously recognized as a correct waveform and the noise is further enhanced. As a result ringing and noise enhancement occur in part of the image. - 3 - Artificial images are images for example text or simple graphics exhibiting a small number of grayscale levels and distinct phase information concerning the positions of edges (outlines) i.e. including many flat portions. It is thus desirable to enhance the quality of a whole image by distinguishing an area of natural image components and an area of artificial image components contained in the image from each other and by performing optimal processing on each of the areas. According to an embodiment of the present invention there is provided an image processing apparatus including broad-range feature extraction means for extracting broadrange features including a plurality of types of broad-range features from pixels located in a predetermined area in relation to a subject pixel of a first image broad-range degree-of-artificiality calculation means for calculating in a multidimensional space represented by the plurality of types of broad-range features included in the broad-range features extracted by the broad-range feature extraction means from a positional relationship of the plurality of types of broad-range features according to a statistical distribution range of an artificial image which exhibits a small number of grayscale levels and distinct edges of the representing a degree by which the plurality of types of broad-range features belong to the statistical distribution range of the artificial image narrow-range feature extraction means for extracting narrow-range features including a plurality of types of narrow-range features from pixels located in the predetermined area in relation to the subject pixel of the first image narrow-range degree-ofartificiality calculation means for calculating in a multidimensional space represented by the plurality of types of narrow-range features included in the narrow-range features extracted by the narrow-range feature extraction means from a positional relationship of the plurality of types of narrow-range features according to a statistical distribution range of the artificial image of the first image a narrow-range degree of artificiality representing a degree by which the plurality of types of narrow-range features belong to the statistical distribution range of the artificial image and degree-of-artificiality calculation means for calculating a degree of artificiality of the subject pixel by combining the broad-range degree of artificiality and the narrow-range degree of artificiality. The image processing apparatus may further include first prediction means for predicting from the first image a second image which is obtained by increasing the quality of the artificial image second prediction means for - 5 - predicting from the first image a third image which is obtained by increasing the quality of a natural image exhibiting a large number of grayscale levels and indistinct edges and synthesizing means for combining the second image and the third image on the basis of the degree of artificiality. The first prediction means may include first classification means for classifying pixels of the second image into first classes first storage means for storing a first prediction coefficient for each of the first classes the first prediction coefficient being obtained by conducting learning by using a plurality of artificial images and first computation means for determining from the first image the second image having a higher quality than the first image by performing computation using the first image and the first prediction coefficients for the first classes into which the pixels of the second image are classified. The second prediction means may include second classification means for classifying pixels of the third image into second classes second storage means for storing a second prediction coefficient for each of the second classes the second prediction coefficient being obtained by conducting learning by using a plurality of natural images and second computation means for determining the third image from the first image by performing computation using the first image and the second prediction coefficients for the second classes into which the pixels of the third image are classified. The broad-range degree-of-artificiality calculation means may include broad-range artificial-image distribution range storage means for storing the statistical distribution range of the artificial image of the first image in the multidimensional space represented by the plurality of types of broad-range features and the broad-range degree-ofartificiality calculation means may calculate the broadrange degree of artificiality from the positional relationship of the plurality of types of broad-range features extracted by the broad-range feature extraction means according to the statistical distribution range of the artificial image in the multidimensional space stored in the broad-range artificial-image distribution range storage means. . The narrow-range degree-of-artificiality calculation means may include narrow-range artificial-image distribution range storage means for storing the statistical distribution range of the artificial image of the first image in the multidimensional space represented by the plurality of types of narrow-range features and the narrow-range degree-ofartificiality calculation means may calculate the narrowrange degree of artificiality from the positional relationship of the plurality of types of narrow-range features extracted by the narrow-range feature extraction means according to the statistical distribution range of the artificial image in the multidimensional space stored in the narrow-range artificial-image distribution range storage means. The broad-range feature extraction means may include edge feature extraction means for extracting a feature representing the presence of an edge from the pixels located in the predetermined area and flat feature extraction means for extracting a feature representing the presence of a flat portion from the pixels located in the predetermined area. The edge feature extraction means may extract as the feature representing the presence of an edge a difference dynamic range of the pixels located in the predetermined area by using a difference of pixel values between the subject pixel and each of the pixels located in the predetermined area. The edge feature extraction means may extract as the feature representing the presence of an edge a difference dynamic range of the pixels located in the predetermined area by using a difference of the pixel values between the subject pixel and each of the pixels located in the predetermined area after applying a weight to the difference of the pixel values in accordance with a distance - 8 - therebetween. The edge feature extraction means may extract as the feature representing the presence of an edge a predetermined order of higher levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area. The edge feature extraction means may extract as the feature representing the presence of an edge the average of higher first through second levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area or the sum of the higher first through second levels of the difference absolute values after applying a weight to each of the difference absolute values. The flat feature extraction means may extract as the feature representing the presence of a flat portion the number of difference absolute values between adjacent pixels of the pixels located in the predetermined area which are smaller than a predetermined threshold. The predetermined threshold may be set based on the feature representing the presence of an edge. The flat feature extraction means may extract as the feature representing the presence of a flat portion the sum of difference absolute values between adjacent pixels of the pixels located in the predetermined area after transforming the difference absolute values by a predetermined function. The flat feature extraction means may extract as the feature representing the presence of a flat portion the sum of difference absolute values between the adjacent pixels of the pixels located in the predetermined area after transforming the difference absolute values by a predetermined function and after applying a weight to each of the transformed difference absolute values in accordance with a distance from the subject pixel to each of the pixels located in the predetermined area. The predetermined function may be a function associated with the feature representing the presence of an edge. The flat feature extraction means may extract as the feature representing the presence of a flat portion a predetermined order of lower levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area. . The flat feature extraction means may extract as the feature representing the presence of a flat portion the average of lower first through second levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area or the sum of the lower first through second levels of the difference absolute values after applying a weight to each of the difference absolute values. The narrow-range feature extraction means may extract - 10 - from the pixels located in the predetermined area the narrow-range features including two types of features selected from features representing thin lines edges points flat portions in the vicinity of edges and gradation. : The narrow-range feature extraction means may include first narrow-range feature extraction means for extracting as a first feature of the narrow-range features a pixelvalue dynamic range obtained by subtracting a minimum pixel value from a maximum pixel value of pixels located in a first area included in the predetermined area and second narrow-range feature extraction means for extracting as a second feature of the narrow-range features a pixel-value dynamic range obtained by subtracting a minimum pixel value from a maximum pixel value of pixels located in a second area including the subject pixel and included in the first area. The second narrow-range feature extraction means may extract as the second feature a minimum pixel-value dynamic range of pixel-value dynamic ranges obtained from a plurality of the second areas. The first narrow-range feature extraction means may extract as the first feature of the narrow-range features a pixel-value dynamic range of the pixel values of the pixels located in the predetermined area. The second narrow-range feature extractic n means may extract as the second feature of the narrow-: ange features the sum of difference absolute values between the subject pixel and the pixels located in the predetermined area after transforming the difference absolute values by a predetermined function and after applying a weight to each of the transformed difference absolute values. The second narrow-range feature extraction means may include weight calculation means for calculating the weight in accordance with the sum of the difference absolute values between adjacent pixels of all the pixels located on a path from the subject pixel to the pixels located in the first area. The predetermined function may be a function associated with the first feature. According to another embodiment of the present invention there is provided an image processing method including the steps of extracting broad-range features including a plurality of types of broad-range features from pixels located in a predetermined area in relation to a subject pixel of a first image calculating in a multidimensional space represented by the plurality of types of broad-range features included in the extracted broadrange features from a positional relationship of the plurality of types of broad-range features according to a - 12 - statistical distribution range of an artificial image which exhibits a small number of grayscale levels and distinct edges of the first image a broad-range degree of artificiality representing a degree by which the plurality of types of broad-range features belong to the statistical distribution range of the artificial image extracting narrow-range features including a plurality of types of narrow-range features from pixels located in the predetermined area in relation to the subject pixel of the first image calculating in a multidimensional space represented by the plurality of types of narrow-range features included in the extracted narrow-range features from a positional relationship of the plurality of types of narrow-range features according to a statistical distribution range of the artificial image of the first image a narrow-range degree of artificiality representing a degree by which the plurality of types of narrow-range features belong to the statistical distribution range of the artificial image and calculating a degree of artificiality of the subject pixel by combining the broad-range degree of artificiality and the narrow-range degree of artificiality. According to another embodiment of the present invention there is provided a program recording medium recorded thereon a computer-readable program. The computerreadable program includes the steps of extracting broad- - 13 - range features including a plurality of types of broad-range features from pixels located in a predetermined area in relation to a subject pixel of a first image calculating in a multidimensional space represented by the plurality of types of broad-range features included in the extracted broad-range features from a positional relationship of the plurality of types of broad-range features according to a statistical distribution range of an artificial image which exhibits a small number of grayscale levels and distinct edges of the first image a broad-range degree of artificiality representing a degree by which the plurality of types of broad-range features belong to the statistical distribution range of the artificial image extracting narrow-range features including a plurality of types of narrow-range features from pixels located in the predetermined area in relation to the subject pixel of the first image calculating in a multidimensional space represented by the plurality of types of narrow-range features included in the extracted narrow-range features from a positional relationship of the plurality of types of narrow-range features according to a statistical distribution range of the artificial image of the first image a narrow-range degree of artificiality representing a degree by which the plurality of types of narrow-range features belong to the statistical distribution range of the artificial image and calculating a degree of artificiality of the subject pixel by combining the broad-range degree of artificiality and the narrow-range degree of artificiality. According to another embodiment of the present invention there is provided a program allowing a computer to execute processing including the steps of extracting broad-range features including a plurality of types of broad-range features from pixels located in a predetermined area in relation to a subject pixel of a first image calculating in a multidimensional space represented by the plurality of types of broad-range features included in the extracted broad-range features from a positional relationship of the plurality of types of broad-range features according to a statistical distribution range of an artificial image which exhibits a small number of grayscale levels and distinct edges of the first image a broad-range degree of artificiality representing a degree by which the plurality of types of broad-range features belong to the statistical distribution range of the artificial image extracting narrow-range features including a plurality of types of narrow-range features from pixels located in the predetermined area in relation to the subject pixel of the first image calculating in a multidimensional space represented by the plurality of types of narrow-range features included in the extracted narrow-range features from a positional relationship of the plurality of types of narrow-range features according to a'Statistical distribution range of the artificial image of the first image a narrow-range degree of artificiality representing a degree by which the plurality of types of narrow-range features belong to the statistical distribution range of the artificial image and calculating a degree of artificiality of the subject pixel by combining the broad-range degree of artificiality and the narrow-range degree of artificiality. In the image processing apparatus and method and the program according to an embodiment of the present invention broad-range features including a plurality of types of broad-range features are extracted from pixels located in a predetermined area in relation to a subject pixel of a first image. In a multidimensional space represented by the plurality of types of broad-range features included in the extracted broad-range features from a positional relationship of the plurality of types of broad-range features according to a statistical distribution range of an artificial image which exhibits a small number of grayscale levels and distinct edges of the first image a broad-range degree of artificiality representing a degree by which the plurality of types of broad-range features belong to the statistical distribution range of the artificial image is calculated. Narrow-range features including a plurality of types of narrow-range features are extracted from pixels located in the predetermined area in relation to the subject pixel of the first image. In a multidimensional space represented by the plurality of types of narrow-range features included in the extracted narrow-range features from a positional relationship of the plurality of types of narrow-range features according to a statistical distribution range of the artificial image of the first image a narrow-range degree of artificiality representing a degree by which the plurality of types of narrow-range features belong to the statistical distribution range of the artificial image is calculated. The degree of artificiality of the subject pixel is calculated by combining the broadrange degree of artificiality and the narrow-range degree of artificiality. The image processing apparatus according to an embodiment of the present invention may be an independent apparatus or a block performing image processing. According to an embodiment of the present invention the quality of a whole image can be enhanced. According to an embodiment of the present invention it is possible to perform optimal processing on an area of natural image components and an area of artificial image components contained in an image by distinguishing the two areas from each other. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a block diagram illustrating an example of the configuration of an image conversion device according to an embodiment of the present invention; Fig. 2 is a flowchart illustrating image conversion processing performed by the image conversion device shown in Fig. 1; Fig. 3 is a block diagram illustrating the detailed configuration of a natural-image prediction unit; Fig. 4 illustrates an example of the tap structure of class taps; Fig. 5 illustrates an example of the tap structure of prediction taps; ; Fig. 6 is a flowchart illustrating details of naturalimage prediction processing; Fig. 7 is a block diagram illustrating the configuration of a learning device; Fig. 8 illustrates the positional relationship between pixels of a supervisor image and pixels of a learner image; Fig. 9 is a flowchart illustrating an example of learning processing; Fig. 10 is a block diagram illustrating the configuration of an artificial-image prediction unit; Fig. 11 is a block diagram illustrating the detailed configuration of a classification portion; Fig. 12 illustrates another example of the tap structure of class taps; • Fig. 13 is a block diagram illustrating the detailed configuration of a prediction portion; Fig. 14 illustrates another example of the tap structure of prediction taps; Fig. 15 is a flowchart illustrating artificial-image prediction processing; Fig. 16 is a flowchart illustrating classification processing; Fig. 17 is a block diagram illustrating the configuration of another learning device; Fig. 18 is a block diagram illustrating the detailed configuration of a generator; Fig. 19 is a flowchart illustrating another example of learning processing; Fig. 20 is a block diagram illustrating the configuration of a natural-image/artificial-image determining unit; Fig. 21 is a block diagram illustrating an example of the configuration of a broad edge parameter (BEP) extracting portion; ; Fig. 22 is a block diagram illustrating an example of the configuration of a broad flat parameter (BFP) extracting portion; Fig. 23 is a block diagram illustrating an example of the configuration of a (primary narrow discrimination parameter (PNDP) extracting portion; Fig. 24 is a block diagram illustrating an example of the configuration of a secondary narrow discrimination parameter (SNDP) extracting portion; Fig. 25 is a flowchart illustrating naturalimage/ artificial-image determination processing performed by the natural-image/artificial-image determining unit shown in Fig. 20; Fig. 26 is a flowchart illustrating BEP extraction processing performed by the BEP extracting portion shown in Fig. 21; Fig. 27 illustrates reference pixels; Fig. 28 is a flowchart illustrating BFP extraction processing performed by the BFP extracting portion shown in Fig. 22; Fig. 29 illustrates the relationship among reference pixels to determine the adjacent-pixel difference absolute values therebetween; Fig. 30 illustrates transform function f; Fig. 31 is a flowchart illustrating broad-range degreeof- artificiality calculation processing; Fig. 32 illustrates broad-range boundaries; - 20 - Fig. 33 is a flowchart illustrating PNDP extraction processing performed by the PNDP extracting portion shown in Fig. 23; Fig. 34 illustrates a long tap; Fig. 35 is a flowchart illustrating SNDP extraction processing performed by the SNDP extracting portion shown in Fig. 24; Fig. 36 illustrates short taps; Fig. 37 is a flowchart illustrating narrow-range degree-of artificiality calculation processing; Fig. 38 illustrates narrow-range boundaries; Fig. 39 is a block diagram illustrating another example of the configuration of a BEP extracting portion; Fig. 40 is a flowchart illustrating BEP extraction processing performed by the.BEP extracting portion shown in Fig. 39; : Fig. 41 illustrates BEP extraction processing performed by the BEP extracting portion shown in Fig. 39; Fig. 42 is a block diagram illustrating another example of the configuration of the BFP extracting portion; Fig. 43 is a flowchart illustrating BFP extraction processing performed by the BFP extracting portion shown in Fig. 42; Fig. 44 illustrates BFP extraction processing performed by the BFP extracting portion shown in Fig. 42; Fig. 45 is a block diagram illustrating another example of the configuration of the PNDP extracting portion; Fig. 46 is a flowchart illustrating PNDP extracting portion performed by the PNDP extracting portion shown in Fig. 45; Fig. 47 is a block diagram illustrating another example of the configuration of an SNDP extracting portion; Fig. 48 is a flowchart illustrating SNDP extraction processing performed by the SNDP extracting portion shown in Fig. 47; Fig. 49 illustrates transform function F; Fig. 50 illustrates pixels to be interpolated; Fig. 51 illustrates another example of the configuration of an image conversion device; Fig. 52 is a flowchart illustrating image conversion processing performed by the image conversion device shown in Fig. 51; Figs. 53A 53B and 53C illustrate broad-range artificial image boundaries and broad-range natural image boundaries; Figs. 54A 54B and 54C illustrate narrow-range artificial image boundaries and narrow-range natural image boundaries; and Fig. 55 is a block diagram illustrating the configuration of a personal computer implementing the image conversion device. DESCRIPTION OF THE PREFERRED EMBODIMENTS Before describing an embodiment of the present invention the correspondence between the features of the claims and the embodiment disclosed in the present invention is discussed below. This description is intended to assure that the embodiment supporting the claimed invention is described in this specification. Thus even if an element in the following embodiment is not described as relating to a certain feature of the present invention that does not necessarily mean that the element does not relate to that feature of the claims. Conversely even if an element is described herein as relating to a certain feature of the claims that does not necessarily mean that the element does not relate to other features of the claims. Furthermore this description should not be construed as restricting that all the aspects of the invention disclosed in the embodiment are described in the claims. That is the description does not deny the existence of aspects of the present invention that are described in the embodiment but not claimed in the invention of this application i.e. the existence of aspects of the present invention that in future may be claimed by a divisional application or that may be additionally claimed through amendments. An image processing apparatus according to an embodiment of the present invention includes broad-range feature extraction means (e.g. a broad-range feature extracting portion 911 shown in Fig. 20) for extracting broad-range features including a plurality of types of broad-range features from pixels located in a predetermined area in relation to a subject pixel of a first image broadrange degree-of-artificiality calculation means (e.g. a broad-range degree-of-artificiality calculator 912 shown in Fig. 20) for calculating in a multidimensional space represented by the plurality of types of broad-range features included in the broad-range features extracted by the broad-range feature extraction means from a positional relationship of the plurality of types of broad-range features according to a statistical distribution range of an artificial image which exhibits a small number of grayscale levels and distinct edges of the first image a broad-range degree of artificiality representing a degree by which the plurality of types of broad-range features belong to the statistical distribution range of the artificial image narrow-range feature extraction means (e.g. a narrow-range feature extracting portion 914 shown in Fig. 20) for extracting narrow-range features including a plurality of types of narrow-range features from pixels located in the predetermined area in relation to the subject pixel of the first image narrow-range degree-of-artificiality calculation means (e.g. a narrow-range degree-ofartificiality calculator 915 shown in Fig. 20) for calculating in a multidimensional space represented by the plurality of types of narrow-range features included in the narrow-range features extracted by the narrow-range feature extraction means from a positional relationship of the plurality of types of narrow-range features according to a statistical distribution range of the artificial image of the first image a narrow-range degree of artificiality representing a degree by which the plurality of types of narrow-range features belong to the statistical distribution range of the artificial image and degree-of-artificiality calculation means (e.g. a degree-of-artificiality calculator 913 shown in Fig: 20) for calculating a degree of artificiality of the subject pixel by combining the broadrange degree of artificiality and the narrow-range degree of artificiality. The image processing apparatus may further include first prediction means (e.g. an artificial-image prediction unit 132 shown in Fig. 1) for predicting from the first image a second image which is obtained by increasing the quality of the artificial image second prediction means (e.g. a natural-image prediction unit 131 shown in Fig. 1) for predicting from the first image a third image which is obtained by increasing the quality of a natural image exhibiting a large number of grayscale levels and indistinct edges and synthesizing means (e.g. a synthesizer 133 shown in Fig. 1) for combining the second image and the third image on the basis of the degree of artificiality. The first prediction means may include first classification means (e.g. a classification portion 651 shown in Fig. 10) for classifying pixels of the second image into first classes first storage means (e.g. a prediction coefficient memory 654 shown in Fig. 10) for storing a first prediction coefficient for each of the first classes the first prediction coefficient being obtained by conducting learning by using a plurality of artificial images and first computation means (e.g. a prediction portion 655 shown in Fig. 10) for determining from the first image the second image having a higher quality than the first image by performing computation using the.first image and the first prediction coefficients for the first classes into which the pixels of the second image are classified. The second prediction means may include second classification means (e.g. a class tap extracting portion 551 or an adaptive dynamic range coding (ADRC) processor 552 shown in Fig. 3) for classifying pixels of the third image into second classes second storage means (e.g. a prediction coefficient memory 555 shown in Fig. 3) for storing a second prediction coefficient for each of the second classes the second prediction coefficient being obtained by conducting learning by using a plurality of natural images and second computation means (e.g. a prediction computation portion 557 shown in Fig. 3) for determining the third image from the first image by performing computation using the first image and the second prediction coefficients for the second classes into which the pixels of the third image are classified. The broad-range degree-of-artificiality calculation means (e.g. the broad-range degree-of-artificiality calculator 912 shown in Fig<. 20) may include broad-range artificial-image distribution range storage means (e.g. broad-range boundary memory 953 shown in Fig. 20) for storing the statistical distribution range of the artificial image of the first image in the multidimensional space represented by the plurality of types of broad-range features and the broad-range degree-of-artificiality calculation means may calculate the broad-range degree of artificiality from the positional relationship of the plurality of types of broad-range features extracted by the broad-range feature extraction means according to the statistical distribution range of the artificial image in the multidimensional space stored in the broad-range artificial-image distribution range storage means. The narrow-range degree-of-artificiality calculation means (e.g. the narrow-range degree-of-artificiality calculator 915 shown in Fig. 20) may include narrow-range artificial-image distribution range storage means (e.g. a narrow-range boundary memory 993 shown in Fig. 20) for storing the statistical distribution range of the artificial image of the first image in the multidimensional space represented by the plurality of types of narrow-range features and the narrow-range degree-of-artificiality calculation means may calculate the narrow-range degree of artificiality from the positional relationship of the plurality of types of narrow-range features extracted by the narrow-range feature extraction means according to the statistical distribution range of the artificial image in the multidimensional space stored in the narrow-range artificial-image distribution range storage means. The broad-range feature extraction means may include edge feature extraction means (e.g. a BEP extracting portion 931 shown in Fig. 20) for extracting a feature representing the presence of an edge from the pixels located in the predetermined area and flat feature extraction means (e.g. a BFP extracting portion.932 shown in Fig. 20) for extracting a feature representing the presence of a flat portion from the pixels located in the predetermined area. The edge feature extraction means (e.g. the BEP extracting portion 931 shown in Fig. 21) may extract as the feature representing the presence of an edge a difference dynamic range of the pixels located in the predetermined area by using a difference of pixel values between the subject pixel and each of the pixels located in the predetermined area. The edge feature extraction means (e.g. the BEP extracting portion 931 shown in Fig. 21) may extract as the feature representing the presence of an edge a difference dynamic range of the pixels located in the predetermined area by using a difference: of the pixel values between the subject pixel and each of the pixels located in the predetermined area after applying a weight to the difference of the pixel values in accordance with a distance therebetween. The edge feature extraction means (e.g. the BEP extracting portion 931 shown in Fig. 39) may extract as the feature representing the presence of an edge a predetermined order of higher levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area. The edge feature extraction means (e.g. the BEP extracting portion 931 shown in Fig. 39) may extract as the feature representing the presence of an edge the average of higher first through second levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area or the sum of the higher first through second levels of the difference absolute values after applying a weight to each of the difference absolute values. The flat feature extraction means (e.g. the BFP extracting portion 932 shown in Fig. 22) may extract as the feature representing the presence of a flat portion the number of difference absolute values between adjacent pixels of the pixels located in the predetermined area which are smaller than a predetermined threshold. The flat feature extraction means (e.g. the BFP extracting portion 932 shown in Fig. 22) may extract as the feature representing the presenceof a flat portion the sum of difference absolute values between adjacent pixels of the pixels located in the predetermined area after transforming the difference absolute values by a predetermined function. The flat feature extraction means (e.g. the.BFP extracting portion 932 shown in Fig. 22) may extract as the feature representing the presence of a flat portion the sum of difference absolute values between the adjacent pixels of the pixels located in the predetermined area after transforming the difference absolute values by a predetermined function and.after applying a weight to each of the transformed difference absolute values in accordance with a distance from the subject pixel to each of the pixels located in the predetermined area. The flat feature extraction means (e.g. the BFP extracting portion 932 shown in Fig. 42) may extract as the feature representing the presence of a flat portion a predetermined order of lower levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area. The flat feature extraction means (e.g. the BFP extracting portion 932 shown in Fig. 42) may extract as the feature representing the presence of a flat portion the average of lower first through second levels of difference absolute values between adjacent pixels of the pixels located in the predetermined area or the sum of the lower first through second levels of the .difference absolute values after applying a weight to each of the difference absolute values. The narrow-range feature extraction (e.g. the narrowrange feature extracting portion 914 shown in Fig. 20) means may extract from the pixels located in the predetermined area the narrow-range features including two types of features selected from features representing thin lines edges points flat portions in the vicinity of edges and gradation. The narrow-range feature extraction means (e.g. the narrow-range feature extracting portion 914 shown in Fig. 20) may include first narrow-range' feature extraction means (e.g. a PNDP extracting portion 971 shown in Fig. 20) for extracting as a first feature of the narrow-range features a pixel-value dynamic range obtained by subtracting a minimum pixel value from a maximum pixel value of pixels located in a first area included in the predetermined area and second narrow-range feature extraction means (e.g. an SNDP extracting portion 972 shown in Fig. 20) for extracting as a second feature of the narrow-range features a pixel-value dynamic range obtained by subtracting a minimum pixel value from a maximum pixel value of pixels located in a second area including the subject pixel and included in the first area. The second narrow-range feature extraction means (e.g. an SNDP extracting portion 972 shown in Fig. 24) may extract as the second feature a minimum pixel-value dynamic range of pixel-value dynamic ranges obtained from a plurality of the second areas. The first narrow-range feature extraction means (e.g. the PNDP extracting portion 971 shown in Fig. 45) may extract as the first feature of the narrow-range features a pixel-value dynamic range of the pixel values of the pixels located in the predetermined area. The second narrow-range feature extraction means (e.g. the SNDP extracting portion 972 shown in Fig. 47) may extract as the second feature of the narrow-range features the sum of t ; difference absolute values between the subject pixel and the pixels located in the predetermined area after transforming the difference absolute values by a predetermined function and after applying a weight to each of the transformed difference absolute values. The second narrow-range feature extraction means (e.g. the SNDP extracting portion 972 shown in Fig. 47) may include weight calculation means (e.g. a weight calculator 1165 shown in Fig. 47) for calculating the weight in accordance with the sum of the difference absolute values between adjacent pixels of all the pixels located on a path from the subject pixel to the pixels located in the first area. According to another embodiment of the present invention there is provided an image processing method including the steps of extracting broad-range features including a plurality of types of broad-range features from pixels located in a predetermined area in relation to a subject pixel of a first image (e.g. steps S831 and S832 in the flowchart in Fig. 25) calculating in a multidimensional space represented by the plurality of types of broad-range features included in the extracted broadrange features from a positional relationship of the plurality of types of broad-range features according to a statistical distribution range of an artificial image which exhibits a small number of grayscale levels and distinct edges of the first image a broad-range degree of artificiality representing a degree by which the plurality of types of broad-range features belong to the statistical distribution range of the artificial image (e.g. step S834 in the flowchart in Fig. 25) extracting narrow-range features including a plurality of types of narrow-range features from pixels located in the predetermined area in relation to the subject pixel of the first image (e.g. steps S835 and S836 in the flowchart in Fig. 25) calculating in a multidimensional space represented by the plurality of types of narrow-range features included in the extracted narrow-range features from a positional relationship of the plurality of types of narrow-range features according to a statistical distribution range of the artificial image of the first image a narrow-range degree of artificiality representing a degree by which the plurality of types of narrow-range features belong to the statistical distribution range of the artificial image (e.g. step S838 in the flowchart in Fig. 25) and calculating a degree of artificiality of the subject pixel by combining the broad-range degree of artificiality and the narrow-range degree of artificiality (e.g. step S839 in the flowchart in Fig. 25). Embodiments of the present invention are described in detail below with reference to the accompanying drawings. Fig. 1 is a block diagram illustrating an image conversion device 101 according to an embodiment of the present invention. The image conversion device 101 includes a cyclic interlace/progressive (IP) converter 111 an output phase converter 112 an image processor 113 and a naturalimage/ artificial-image determining unit 114. The cyclic IP converter 111 includes an IP converter 121 and a cyclic converter 122. The image processor 113 includes a naturalimage prediction unit 131 an artificial-image prediction unit 132 and a synthesizer 133. An interlace SD image to be processed is input into the IP converter 121 and the cyclic 'converter 122 of the cyclic IP converter 111. The IP converter 121 converts the input interlace SD image (hereinafter also referred to as an "input image") into a progressive SD image (hereinafter also referred to as an "intermediate image") according to a predetermined method and supplies the converted progressive SD image to the cyclic converter 122. The cyclic converter 122 determines motion vectors between the input image and the progressive SD image of the previous frame (one frame before) output from the cyclic converter 122 (such an image is also referred to as an "output image"). The cyclic converter 122 then adds the pixel values of the output image motion-compensated based on the determined motion vectors to the pixel values of the input image by using cyclic coefficients as weights thereby improving the intermediate image. That is the cyclic converter 122 converts the intermediate image into an output image which is a progressive SD image of a quality higher than the intermediate image and supplies the resulting output image to the output phase converter 112. The cyclic coefficients are set based on whether each pixel of the intermediate image exists in the original input image and also based on the magnitudes of the motion vectors in the vertical direction and the reliabilities representing the probabilities of the motion vectors. The output phase converter 112 interpolates the SD image having a first pixel number supplied from the cyclic converter 122 in the horizontal and vertical directions to generate an HD image having a second pixel number. The second pixel number is greater than the first pixel number. The output phase converter 112 supplies the HD image to the natural-image prediction unit 131 the artificial-image prediction unit 132 and the natural-image/artificial-image determining unit 114. The image processor 113 performs processing for converting the HD image into a high-quality image based on the degrees of artificiality supplied from the naturalimage/ artificial-image determining unit 114 and outputs the high-quality HD image. The natural-image/artificial-image determining unit 114 determines for each pixel of the HD image supplied from the output phase converter 112 whether it belongs to an artificial image area or a natural image area and outputs determination results to the image processor 113 as the degrees of artificiality. That is the degree of artificiality represents the ratio of artificial image components to natural image components in an intermediate area which is between the artificial image area and the natural image area by a value from 0 to 1. The natural-image prediction unit 131 predicts from the HD image supplied from the output phase converter 112 a high-quality HD image which can be obtained by increasing the quality of natural image components contained in the input HD image (such a high-quality HD image is hereafter referred to as a "high-quality natural image"). More specifically in accordance"with the features of the input HD image the natural-image prediction unit 131 allocates the subject pixels into classes optimal for the features of the natural image. Then the natural-image prediction unit 131 performs computation by using the input HD image and prediction coefficients corresponding to the classes which are used for predicting the high-quality natural image to predict the high-quality natural image from the input HD image. The natural-image prediction unit 131 supplies the computed high-quality natural image to the synthesizer 133. As in the natural-image prediction unit 131 the artificial-image prediction unit 132 predicts from the HD image supplied from the output phase converter 112 a highquality HD image which can be obtained by increasing the quality of artificial image components contained in the input HD image (such a high-quality HD image is hereafter referred to as a "high-quality artificial image"). More specifically in accordance with the features of the input HD image the artificial-image prediqtion unit 132 allocates the pixels forming the high-quality artificial image to be determined from the input HD image into classes optimal for the features of the artificial image. Then the artificialimage prediction unit 132 performs calculations by using the input HD image and prediction coefficients corresponding to the classes which are used for predicting the high-quality artificial image to predict the high-quality artificial image from the input HD image. The artificial-image prediction unit 132 supplies-the calculated high-quality artificial image to the synthesizer 133. The synthesizer 133 combines based on the determination results supplied from the naturalimage/ artificial-image determining unit 114 the pixel values of the pixels forming the high-quality natural image supplied from the natural-image prediction unit 131 with the pixel values of the pixels forming the high-quality artificial image supplied from the artificial-image prediction unit 132 in accordance with the degrees of artificiality of the individual pixels. The synthesizer 133 then outputs the synthesized HD image. The image conversion processing executed by the image conversion device 101 is described below with reference to the flowchart in Fig. 2. This processing is started for example when an interlace SD image is input from an external source into the image conversion device 101. In step SI the IP converter 121 performs IP conversion. More specifically the IP converter 121 converts an interlace input image into a progressive intermediate image according to a predetermined method and supplies the IP-:Converted intermediate image to the cyclic converter 122. In step S2 the cyclic converter 122 performs cyclic conversion processing. More specifically the cyclic converter 122 determines motion vectors between the input image and the output image of the previous frame (one frame before) output from the cyclic converter 122. The cyclic converter 122 then adds the pixel values of the motioncompensated output image based on the determined motion vectors to the pixel values of the input image by using cyclic coefficients as weights thereby improving the intermediate image. The cyclic converter 122 converts the intermediate image into an output image which is a progressive SD image of a quality higher than the intermediate image and supplies the resulting output image to the output phase converter 112. In step S3 the output phase converter 112 performs output phase conversion processing. More specifically the output phase converter 112- interpolates the SD image supplied from the cyclic converter 122 in the horizontal and vertical directions to generate an HD image. The output phase converter 112 then supplies the HD image to the natural-image prediction unit 131 the artificial-image prediction unit 132 and the natural-image/artificial-image determining unit 114. In step S4 the natural-image prediction unit 131 performs natural-image prediction processing. According to this processing a high-quality natural image is predicted from the HD image and is supplied to the synthesizer 133. Details of the natural-image prediction processing are discussed below with reference to Fig. 6. In step S5 the artificial-image prediction unit 132 performs artificial-image prediction processing. According to this processing a high-quality artificial image is predicted from the HD image and is supplied to the synthesizer 133. Details of the artificial-image prediction processing are discussed below with reference to Fig. 15. In step S6 the natural-image/artificial-image determining unit 114 performs natural-image/artificial-image determination processing. According to this processing the natural-image/artificial-image determining unit 114 determines whether each pixel of the HD image supplied from the output phase converter 112 belongs to an artificial image area or a natural image area and outputs determination results to the synthesizer 133 as the degrees of artificiality. Details of the natural-image/artificialimage determination processing are:discussed below with reference to Fig. 25. In step S7 the synthesizer 133 synthesizes an image. More specifically the synthesizer 133 combines based on determination results supplied from the naturalimage/ artificial-image determining unit 114 the pixel values of the pixels forming the high-quality natural image supplied from the natural-image prediction unit 131 with the pixel values of the pixels forming the high-quality artificial image supplied from:the artificial-image prediction unit 132 in accordance with the degrees of artificiality of the individual pixels. The synthesizer 133 outputs the synthesized HD image to a subsequent device. If the image conversion processing is continuously performed on a plurality of images steps SI through S7 are repeated. Fig. 3 is a block diagram illustrating the configuration of the natural-image prediction unit 131 shown in Fig. 1. The natural-image prediction unit 131 includes a class tap extracting portion 551 an adaptive dynamic range coding (ADRC) processor 552 a coefficient seed memory 553 a prediction coefficient generator 554 a prediction coefficient memory 555 a prediction tap extracting portion 556 and a prediction computation portion 557. The naturalimage prediction unit 131 predicts a high-quality natural image from the progressive HD image supplied from the output phase converter 112 shown in Fig. 1 after removing noise from the natural image A progressive HD image supplied from the output phase converter 112 shown in Fig. 1 is supplied to the naturalimage prediction unit 131 and more specifically to the class tap extracting portion 551 and the prediction tap extracting portion 556. The class tap extracting portion 551 sequentially selects the pixels forming the high-quality natural image determined from the input HD image as subject pixels and extracts some of the pixels forming the HD image as class taps which are used for classifying the subject pixels. The class tap extracting portion 551 then supplies the extracted class taps to the ADRC processor 552. The ADRC processor 552 performs ADRC processing on the pixel values of the pixels forming the class taps supplied from the class tap extracting portion 551 to detect the ADRC code as the feature of the waveform of the class taps. In K-bit ADRC processing the maximum value MAX and the minimum value MIN of the pixel values of the pixels forming the class taps are detected and DR=MAX-MIN is set as the local dynamic range of a set and then the pixel values of the pixels forming the class taps are re-quantized into K bits based on the dynamic range. That is the minimum value MIN is subtracted from the pixel value of each pixel forming the class taps and the resulting value is divided by DR/2K. Then the K-bit pixel values of the pixels forming the class taps are arranged in a predetermined order resulting in a bit string which is then output as the ADRC code. Accordingly if one-bit ADRC processing is performed on the class taps the pixel value of each pixel forming the class taps is divided by the average of the maximum value MAX and the minimum value MIN so that it is re-quantized into one bit with the decimal fractions omitted. That is the pixel - 43 - alue of each pixel is binarized. Then a bit string of the one-bit pixel values arranged in a predetermined order is output as the ADRC code. The ADRC processor 552 determines the class based on the detected ADRC code to classify each subject pixel and then supplies the determined class to the prediction coefficient memory 555. For example the ADRC processor 552 directly supplies the ADRC code to the prediction coefficient memory 555 as the class. The coefficient seed memory 553 stores a coefficient seed which is obtained by learning discussed below with reference to Figs. 7 through 9 for each class. The prediction coefficient generator 554 reads a coefficient seed from the coefficient seed memory 553. The prediction coefficient generator 554 then generates a prediction coefficient from the read coefficient seed by using a polynomial containing a parameter h and a parameter v which are input by a user for determining the horizontal resolution and the vertical resolution respectively and supplies the generated prediction coefficient to the prediction coefficient memory 555. The prediction coefficient memory 555 reads out the prediction coefficient according to the class supplied from ADRC processor 552 and supplies the read prediction coefficient to the prediction computation portion 557. The prediction taps and the class taps may have the same tap structure or different tap structures. The prediction tap extracting portion 556 extracts from the input HD image as prediction taps some of the pixels forming the HD image used for predicting the pixel value of a subject pixel. The prediction tap extracting portion 556 supplies the extracted prediction taps to the prediction computation portion 557. The prediction computation portion 557 performs prediction computation such as linear expression computation for determining the prediction value of the true value of the subject pixel by using the prediction taps supplied from the prediction tap extracting portion 556 and the prediction coefficient supplied from the prediction coefficient memory 555. Then the prediction computation portion 557 predicts the pixel value of the subject pixel i.e. the pixel value of a pixel forming the high-quality natural image and outputs the predicted pixel value to the synthesizer 133. Fig. 4 illustrates an example of the tap structure of class taps extracted by the class tap extracting portion 551 shown in Fig. 3. In Fig. 4 among the pixels forming the HD image supplied from the output phase converter 112 the white circles indicate the pixels forming the class taps the circles represented by broken curves represent the pixels that do not form the class taps and the black circle designates the subject pixel. The same applies to Fig. 5. In Fig. 4 nine pixels form the class taps. More specifically around a pixel p64 forming the HD image corresponding to a subject pixel q6 five pixels p60 p61 p64 p67 and p68 aligned every other pixel in the vertical direction and four pixels p62 p63 p65 and p66 aligned every other pixel except for the pixel p64 in the horizontal direction are disposed as the class taps i.e. a so-called "cross-shaped" class tap structure is formed. Fig. 5 illustrates an example of the tap structure of prediction taps extracted by the prediction tap extracting portion 556 shown in Fig. 3. In Fig. 5 13 pixels form the prediction taps. More specifically among the pixels forming the HD pixel supplied from the output phase converter 112 around a pixel p86 forming the HD image corresponding to a subject pixel q8 five pixels p80 p82 p86 p90 and p92 aligned every other pixel in the vertical direction four pixels p84 p85 p87 and p88 aligned every other pixel except for the pixel in the vertical direction two pixels p81 and p89 aligned every other pixel except for the pixel p85 in the vertical direction around the pixel p85 and two pixels p83 and p91 aligned every other pixel except for the pixel p87 in the • - 46 - vertical direction around the pixel p87 are disposed as the prediction taps i.e. a generally rhomboid prediction tap structure is formed. In Figs. 4 and 5 the nine pixels p60 through p68 forming the class taps and the 13 pixels p80 through p92 forming the prediction taps respectively are arranged in the vertical direction or in the horizontal direction every other pixel i.e. at regular intervals of two pixels. However the intervals of the pixels forming the class taps or the prediction taps are not restricted to two pixels and may be changed in accordance with the ratio of the number of pixels of the converted HD image to the number of pixels of the SD image before conversion i.e. the interpolation factor employed in the output phase converter 112. It is now assumed for example that the output phase converter 112 converts the SD image so that the numbers of pixels in the horizontal and vertical directions are doubled. In this case if class taps or prediction taps are formed of the pixels arranged at intervals of two pixels in the horizontal or vertical'direction as shown in Fig. 4 or 5 either of the interpolated pixels or the pixels that are not interpolated can form the class taps or the prediction taps. Thus the precision of the prediction processing performed by the natural-image prediction unit 131 can be improved compared to that for example in the case where both the interpolated pixels and the pixels that are not interpolated form class taps or prediction taps i.e. the class taps or the prediction taps could be arranged adjacent to each other. Details of the natural-image prediction processing in step S4 in Fig. 2 performed by the natural-image prediction unit 131 shown in Fig. 3 are discussed below with reference to Fig. 6. In step S551 the class tap extracting portion 551 selects as a subject pixel one of the pixels forming the high-quality natural image determined from the HD image supplied from the output.phase converter 112 shown in Fig. In step S552 the class tap extracting portion 551 then extracts as class taps some of the pixels forming the input HD image such as those shown in Fig. 4 used for classifying the subject pixel selected in step S551 and supplies the extracted class taps to the ADRC processor 552. In step S553 the ADRC processor 552 performs ADRC processing on the pixel values of the pixels forming the class taps supplied from the class tap extracting portion 551 and sets the resulting ADRC code as the feature of the class taps. In step S554 the ADRC processor 552 determines the class based on the ADRC code to classify the subject pixel and then supplies the determined class to the prediction coefficient memory 555. In step S555 the prediction coefficient generator 554 reads out the corresponding coefficient seed from the coefficient seed memory 553. In step S556 the prediction coefficient generator 554 generates the prediction coefficient from the coefficient seed read from the coefficient seed memory 553 by using the polynomial containing the parameters h and v input by the user and supplies the generated prediction coefficient to the prediction coefficient memory 555. Details of the processing for generating a prediction coefficient from a coefficient seed are discussed below. In step S557 the prediction coefficient memory 555 reads out the prediction coefficient on the basis of the class supplied from the ADRC processor 552 and supplies the read prediction coefficient to the prediction computation portion 557. In step S558 the prediction tap extracting portion 556 extracts as prediction taps some of the pixels forming the input HD image such as those shown in Fig. 5 used for predicting the pixel value of the subject pixel. The prediction tap extracting portion 556 supplies the extracted prediction taps to the prediction computation portion 557. In step S559 the prediction computation portion 557 performs prediction computation for example linear expression computation for determining the prediction value of the true value of the subject pixel by using the prediction taps supplied from the prediction tap extracting portion 556 and the prediction coefficient supplied from the prediction coefficient memory 555. In step S560 the prediction computation portion 557 outputs the predicted pixel value of the subject pixel as a result of the prediction computation i.e. the pixel value of the corresponding pixel forming the high-quality natural image to the synthesizer 133. In step S561 the class tap extracting portion 551 determines whether all the pixels forming the high-quality natural image determined from the input HD image have been selected as the subject pixels. If it is determined in step S561 that not all the pixels forming the high-quality natural image have been selected as the subject pixels the process proceeds to step S562. In step S562 the class tap extracting portion 551 selects a pixel which has not been selected as the subject pixel arid returns to step S552. Steps S552 and the subsequent steps are then repeated. If it is determined in step S561 that all the pixels forming the high-quality natural image have been selected as the subject pixels the natural-image prediction processing is completed. As discussed above the natural-image prediction unit 131 predicts a high-quality natural image from the HD image supplied from the output phase converter 112 and outputs the predicted high-quality natural image. That is the naturalimage prediction unit 131 converts the HD image into the high-quality natural image and outputs it. As described above in the image conversion device 101 shown in Fig. 1 the output phase converter 112 converts an SD image supplied from the cyclic converter 122 into an HD image and then supplies the converted HD image to the natural-image prediction unit 131. Accordingly the number of pixels forming the image after prediction is the same as that before prediction and the positions of the pixels forming the image after prediction are not displaced from those of the pixels forming the image before prediction. Accordingly the natural-image prediction unit 131 can predict the pixel value of a subject pixel of the highquality natural image by using the prediction taps formed of the pixels of the HD image which are in phase with the subject pixel. As a result the natural-image prediction unit 131 can accurately predict the high-quality natural image to perform high-precision image conversion. That is the output phase converter 112 and the natural-image prediction unit 131 can accurately convert an SD image supplied from the cyclic converter 122 into a high-quality natural image which is a high-quality HD image having the number of pixels different from that of the SD image. Additionally the natural-image prediction unit 131 determines the feature of the waveform of the pixels forming the class taps and then classifies the subject pixel by using the determined feature. Accordingly the subject pixel can be suitably classified according to the feature of a natural image having relatively a small number of flat portions. As a result the natural-image prediction unit 131 can enhance the quality of the natural image components contained in the HD image. A description is now given of the prediction computation performed by the prediction computation portion 557 shown in Fig. 3 and learning for prediction coefficients used for the prediction computation. It is now assumed that linear prediction computation is conducted as predetermined prediction computation for predicting the pixel value of a pixel forming a high-quality natural image (hereinafter such a pixel is sometimes referred to as a "high-quality natural image pixel") by using prediction taps extracted from an input HD image and a prediction coefficient. In this case the pixel value y of the high-quality natural image pixel can be determined by the following linear expression: where xn represents the pixel value of the n-th pixel of the HD image (hereinafter sometimes referred to as an "HD image pixel") forming the prediction taps for the high-quality natural image pixel having the pixel value y and Wn designates the n-th prediction coefficient to be multiplied by the n-th pixel value of the HD image. It should be noted that the prediction taps are formed of N HD image pixels xlr x2 . . . and XN in equation (1) . The pixel value y of the high-quality natural image pixel may be determined from a higher-order expression instead of the linear expression represented by equation (1) If the true value of the pixel value of the k- sample high-quality natural image pixel is represented by yk and the prediction value of the true : value yk obtained by equation (1) is represented by yk' the prediction error ek can be expressed by the following equation. (2) The prediction value yk' in equation (2) can be obtained by equation (1) . Accordingly if equation (1) is substituted into equation (2) the following equation can be where xn/k designates the n-th HD image pixel forming the prediction taps for the k-sample high-quality natural image pixel. The prediction coefficient Wn that reduces the prediction error ek in equation (3) or (2) to 0 or statistically minimizes the prediction error ek is the optimal prediction coefficient Wn for predicting the highquality natural image pixel. Generally however it is difficult to obtain such a prediction coefficient Wn for all high-quality natural image pixels. If for example the method of least squares is employed as the standard for representing that the prediction coefficient Wn is optimal the optimal prediction coefficient Wn can be obtained by minimizing the total error E of square errors expressed by the following equation: where K is the number of samples of sets of the true values yk of the pixel values of a high-quality image and the HD image pixels x1(k x2(k ... xN;k forming the prediction taps for the true values yk i.e. the number of samples for conducting learning. The minimum value of the total error E of the square errors in equation (4) can be given by the prediction coefficient Wn that allows the value obtained by partially differentiating the total error E with respect to the prediction coefficient Wn to be 0 as expressed by equation (5) . (5) Then if equation (3) is partially differentiated with respect to the prediction coefficient Wn the following equation can be found. (6) The following equation can be found from equations (5) and (6). The normal equations in equation (8) can be solved with respect to the prediction coefficient Wn by using for example a sweeping-out method (Gauss-Jordan elimination method). By solving the normal equations in equation (8) for each class the optimal prediction coefficient Wn that minimizes the total error E of the least squares can be found for each class. Polynomials used for generating prediction coefficients by the prediction coefficient generator 554 shown in Fig. 3 and learning for coefficient seeds used for the polynomials are discussed below. If for example a polynomial is used as an expression for generating a prediction coefficient by using input parameters h and v and a coefficient seed the prediction coefficient Wn for each class and for each set of the parameters h and v can be found by the following equation: where wnm) indicates a reference pixel range. In Fig. 34 the pixels P(ij) forming the long tap are indicated by the white circles on the two-dimensional coordinates in the x direction and in the y direction around the subject pixel P(00) indicated by the hatched portion in the.image. The pixels P(ij) contained in the area surrounded by the broken lines (mxm) around the subject pixel Q(00) forming the long tap can be represented by - (m-1) /2