Patent Publication Number: US-8537179-B2

Title: Image processing apparatus and method and image display apparatus

Description:
FIELD OF THE INVENTION 
     The present invention relates to an image processing apparatus and an image processing method that enhance an input image by, for example, generating and adding high-frequency components to an enlarged input image that is an enlargement of an original image, in order to obtain an output image with a high perceived resolution, and to an image display apparatus using the image processing apparatus and image processing method. 
     BACKGROUND ART 
     Images are generally reproduced and displayed after image signals representing the image have been subjected to appropriate image processing. 
     In the image processing apparatus disclosed in patent document 1, for example, following multiresolution decomposition, a desired frequency band is enhanced by specifying an enhancement coefficient for the image in the desired frequency band according to the signal of the image in a lower frequency band. 
     PRIOR ART REFERENCES 
     Patent Documents 
     
         
         Patent document 1: Japanese Patent Application Publication No. H9-44651 
       
    
     SUMMARY OF THE INVENTION 
     Problems to be Solved by the Invention 
     In the image processing apparatus in which an appropriate enhancement coefficient is specified for the constituent image in a desired frequency band of the decomposed multiresolution image, for some input images the enhancement processing is inappropriate or inadequate and output images with proper picture quality cannot be obtained. 
     If an image that has been subjected to enlargement processing is input as an input image, for example, part of the frequency spectrum of the image before the enhancement processing folds over and appears as a fold-over component on the high-frequency side of the frequency spectrum of the input image. Simply enhancing the high-frequency component is then inappropriate, because the fold-over component is enhanced. If the frequency band is limited so as to enhance only a frequency band excluding the fold-over component, however, then enhancement of the high-frequency side of the frequency spectrum must be avoided, and in consequence, the enhancement processing is inadequate. 
     In addition, if the input image includes noise, noise overlapping the frequency band of the constituent image is enhanced. 
     Furthermore, when the input image includes noise, if the noise included in the input image is eliminated by noise suppression in advance, the high-frequency side of the frequency spectrum is also eliminated by the noise suppression. Attempts to extract the high-frequency component therefore fail, which may make it impossible to carry out adequate image enhancement processing. 
     Means of Solution of the Problems 
     An image processing apparatus according to the invention includes: 
     a first intermediate image generating means for generating a first intermediate image by extracting components of an input image in a particular frequency band; 
     a second intermediate image generating means for generating a second intermediate image from the first intermediate image; 
     a first intermediate image processing means for generating a third intermediate image by suppressing low-level noise included in the first intermediate image; 
     a second intermediate image processing means for generating a fourth intermediate image by suppressing low-level noise included in the second intermediate image; and 
     an adding means for adding the input image and the third intermediate image and the fourth intermediate image together. 
     Effect of the Invention 
     According to the present invention, adequate image enhancement processing can be carried out without increasing or enhancing noise. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating the structure of an image processing apparatus according to a first embodiment of the invention. 
         FIG. 2  is a block diagram illustrating an exemplary structure of the first intermediate image generating means  1  in  FIG. 1 . 
         FIG. 3  is a block diagram illustrating an exemplary structure of the second intermediate image generating means  2  in  FIG. 1 . 
         FIG. 4  is a block diagram illustrating an exemplary structure of the first intermediate image processing means  3 M in  FIG. 1 . 
         FIG. 5  is a block diagram illustrating an exemplary structure of the second intermediate image processing means  3 H in  FIG. 1 . 
         FIG. 6  is a block diagram illustrating an exemplary structure of the horizontal non-linear processing means  2 Ah in  FIG. 3 . 
         FIG. 7  is a block diagram illustrating an exemplary structure of the vertical non-linear processing means  2 Av in  FIG. 3 . 
         FIGS. 8(A) and 8(B)  are diagrams showing the signal input to a coring process and the signal output from the coring process. 
         FIG. 9  is a block diagram illustrating an exemplary structure of an image display apparatus utilizing the image processing apparatus according to the present invention. 
         FIG. 10  is a block diagram illustrating an exemplary structure of the image enlarging means U 1  in  FIG. 9 . 
         FIGS. 11(A) to 11(E)  are pixel arrangement diagrams illustrating the operation of the image enlarging means U 1  in  FIG. 10 . 
         FIGS. 12(A) to 12(D)  are diagrams showing frequency spectra and a frequency response to illustrate the operation of the image enlarging means U 1  in  FIG. 10 . 
         FIGS. 13(A) to 13(E)  are diagrams showing frequency spectra and frequency responses to illustrate the operation of the first intermediate image generating means  1  in  FIG. 1 . 
         FIGS. 14(A) to 14(C)  are diagrams showing frequency spectra and a frequency response to illustrate the operation of the second intermediate image generating means  2  in  FIG. 1 . 
         FIGS. 15(A) to 15(C)  are diagrams illustrating a step edge and indicating values of consecutive pixel signals obtained when the step edge is sampled at a sampling interval S 1 . 
         FIGS. 16(A) to 16(C)  are diagrams illustrating a step edge and indicating values of consecutive pixel signals obtained when the step edge is sampled at a sampling interval S 2 . 
         FIGS. 17(A) to 17(F)  are diagrams indicating values of consecutive pixel signals to illustrate the operation of the first intermediate image generating means  1  and second intermediate image generating means  2  in  FIG. 1 . 
         FIGS. 18(A) to 18(E)  are diagrams indicating values of consecutive pixel signals to illustrate the operation of the first intermediate image generating means  1  and second intermediate image generating means  2 . 
         FIGS. 19(A) to 19(D)  are diagrams indicating values of consecutive pixel signals to illustrate the operation of the first intermediate image processing means  3 M and second intermediate image processing means  3 H. 
         FIG. 20  is a flowchart illustrating processing steps in an image processing method according to a second embodiment. 
         FIG. 21  is a flowchart illustrating processing in the first intermediate image generating step ST 1  in  FIG. 20 . 
         FIG. 22  is a flowchart illustrating processing in the second intermediate image generating step ST 2  in  FIG. 20 . 
         FIG. 23  is a flowchart illustrating processing in the horizontal non-linear processing step ST 2 Ah in  FIG. 22 . 
         FIG. 24  is a flowchart illustrating processing in the vertical non-linear processing step ST 2 Av in  FIG. 22 . 
         FIG. 25  is a flowchart illustrating processing in the first intermediate image processing step ST 3 M in  FIG. 20 . 
         FIG. 26  is a flowchart illustrating processing in the second intermediate image processing step ST 3 H in  FIG. 20 . 
     
    
    
     MODE FOR CARRYING OUT THE INVENTION 
     First Embodiment 
       FIG. 1  is a diagram illustrating an exemplary structure of an image processing apparatus according to the first embodiment of the invention; the illustrated image processing apparatus can be utilized as, for example, part of an image display apparatus. 
     The illustrated image processing apparatus includes a first intermediate image generating means  1 , a second intermediate image generating means  2 , a first intermediate image processing means  3 M, a second intermediate image processing means  3 H, and an adding means  4 . 
     The first intermediate image generating means  1  generates an intermediate image D 1  (the first intermediate image) by extracting components in a particular frequency band (components from a first frequency (a first predetermined frequency) to a second frequency (a second predetermined frequency)) from an input image DIN. 
     The second intermediate image generating means  2  generates an intermediate image D 2  (the second intermediate image) by carrying out certain processing, which will be described later, on intermediate image D 1 . 
     The first intermediate image processing means  3 M generates an intermediate image D 3 M (the third intermediate image) by carrying out certain processing, which will be described later, on intermediate image D 1 . 
     The second intermediate image processing means  3 H generates an intermediate image D 3 H (the fourth intermediate image) by carrying out certain processing, which will be described later, on intermediate image D 2 . 
     The adding means  4  adds the input image DIN, intermediate image D 3 M, and intermediate image D 3 H together. The image obtained as the resulting sum by the adding means  4  is output as a final output image DOUT. 
       FIG. 2  is a diagram illustrating an exemplary structure of the first intermediate image generating means  1 . The illustrated first intermediate image generating means  1  includes a high-frequency component image generating means  1 A for generating an image D 1 A by extracting only the high-frequency component above the first frequency from the input image DIN and a low-frequency component image generating means  1 B for generating an image D 1 B by extracting only the low-frequency component below the second frequency from image D 1 A. The high-frequency component image generating means  1 A and the low-frequency component image generating means  1 B form a band-pass filter means for extracting the component in a particular frequency band. Image D 1 B is output from the first intermediate image generating means  1  as intermediate image D 1 . 
       FIG. 3  is a diagram illustrating an exemplary structure of the second intermediate image generating means  2 ; the illustrated second intermediate image generating means  2  includes a non-linear processing means  2 A for outputting an image D 2 A obtained by performing non-linear processing, which will be described later, on intermediate image D 1  and a high-frequency component image generating means  2 B for outputting an image D 2 B obtained by extracting only the high-frequency component above a third frequency (the third predetermined frequency) from image D 2 A. Image D 2 B is output from the second intermediate image generating means  2  as intermediate image D 2 . 
       FIG. 4  is a diagram illustrating an exemplary structure of the first intermediate image processing means  3 M; the illustrated first intermediate image processing means  3 M includes a horizontal low-level noise suppression means  3 Mh and a vertical low-level noise suppression means  3 Mv. The first intermediate image processing means.  3 M performs processing, which will be described later, on intermediate image D 1 . The result is output from the first intermediate image processing means  3 M as intermediate image D 3 M. 
       FIG. 5  is a diagram illustrating an exemplary structure of the second intermediate image processing means  3 H; the illustrated second intermediate image processing means  3 H includes a horizontal low-level noise suppression means  3 Hh and a vertical low-level noise suppression means  3 Hv. The second intermediate image processing means  3 H performs processing, which will be described later, on the intermediate image D 2 . The result is output from the second intermediate image processing means  3 H as intermediate image D 3 H. 
     The adding means  4  generates the final output image DOUT by adding intermediate image D 3 M and intermediate image D 3 H to the input image DIN. 
     The operation of the image processing apparatus in the first embodiment of this invention will be described in detail below. 
     First the detailed operation of the first intermediate image generating means  1  will be described. 
     In the first intermediate image generating means  1 , the high-frequency component image generating means  1 A generates image D 1 A by extracting only the high-frequency component of the input image DIN above the first frequency. The high-frequency component can he extracted by performing high-pass filter processing. The high-frequency component of the image is extracted in the horizontal direction and vertical direction separately. The high-frequency component image generating means  1 A includes a horizontal high-frequency component image generating means  1 Ah for generating an image D 1 Ah by performing horizontal high-pass filter processing on the input image DIN to extract a horizontal high-frequency component above a first horizontal frequency only in the horizontal direction and a vertical high-frequency component image generating means  1 Av for generating an image D 1 Av by performing vertical high-pass filter processing to extract a vertical high-frequency component above a first vertical frequency only in the vertical direction; image D 1 A includes image D 1 Ah and image D 1 Av. 
     Next, in the first intermediate image generating means  1 , the low-frequency component image generating means  1 B generates an image D 1 B by extracting only the low-frequency component of image D 1 A below the second frequency. The low-frequency component can be extracted by performing low-pass filter processing. The low-frequency component is extracted in the horizontal direction and the vertical direction separately. The low-frequency component image generating means  1 B includes a horizontal low-frequency component image generating means  1 B for generating an image D 1 Bh by performing horizontal low-pass filter processing on image D 1 Ah to extract a horizontal low-frequency component below a second horizontal frequency and a vertical low-frequency component image generating means  1 Bv for generating an image D 1 Bv by performing vertical low-pass filter processing on image D 1 Av to extract a vertical low-frequency component below a second vertical frequency; image D 1 B includes image D 1 Bh and image D 1 Bv. Image D 1 B is output from the first intermediate image generating means  1  as intermediate image D 1 . Intermediate image D 1  includes an image D 1   h  corresponding to image D 1 Bh and an image D 1   v  corresponding to image D 1 Bv. 
     Next the detailed operation of the second intermediate image generating means  2  will be described. 
     In the second intermediate image generating means  2 , the non-linear processing means  2 A generates image D 2 A by performing non-linear processing, which will be described later, on intermediate image D 1 . The non-linear processing is performed in the horizontal direction and vertical direction separately. The non-linear processing means  2 A includes a horizontal non-linear processing means  2 Ah for generating an image D 2 Ah by performing non-linear processing, which will be described later, on image D 1   h , and a vertical non-linear processing means  2 Av for generating an image D 2 Av by performing non-linear processing, which will be described later, on image D 1   v ; image D 2 A includes image D 2 Ah and image D 2 Av. 
     The operation of the non-linear processing means  2 A will now be described in further detail. The horizontal non-linear processing means  2 Ah and the vertical non-linear processing means  2 Av included in the non-linear processing means  2 A have the same structure. The horizontal non-linear processing means  2 Ah performs processing in the horizontal direction, and the vertical non-linear processing means  2 Av performs processing in the vertical direction. 
       FIG. 6  is a diagram illustrating an exemplary structure of the horizontal non-linear processing means  2 Ah. The illustrated horizontal non-linear processing means  2 Ah includes a zero-crossing decision means  311   h  and a signal amplifying means  312   h . The horizontal non-linear processing means  2 Ah receives image D 1   h  as an input image DIN 311   h.    
     The zero-crossing decision means  311   h  checks the pixel values in the input image DIN 311   h  for changes in the horizontal direction. A point where the pixel value changes from positive to negative or from negative to positive is identified as a zero-crossing point, and the positions of the pixels preceding and following the zero-crossing point (the adjacently preceding and following pixels) are reported to the signal amplifying means  312   h  by a signal D 311   h . Preceding and following herein means the preceding and following positions in the sequence in which signals are supplied: the positions to the left and right when the pixel signals are supplied from left to right in the horizontal direction, or the positions above and below when the pixel signals are supplied from top to bottom in the vertical direction. The zero-crossing decision means  311   h  in the horizontal non-linear processing means  2 Ah recognizes the pixels to the left and right of the zero-crossing point as the pixels preceding and following the zero-crossing point. 
     The signal amplifying means  312   h  identifies the pixels preceding and following the zero-crossing point (the adjacently preceding and following pixels) in accordance with the signal D 311   h  and generates a non-linear image D 312   h  by amplifying the pixel values (increasing the absolute values) of only the pixels preceding and following the zero-crossing point. The amplification factor for the pixel values of the pixels preceding and following the zero-crossing point is a value greater than 1; the amplification factor for the pixel values of other pixels is 1. 
     The non-linear image D 312   h  is output from the horizontal non-linear processing means  2 Ah as image D 2 Ah. 
       FIG. 7  is a diagram illustrating an exemplary structure of the vertical non-linear processing means  2 Av. The illustrated vertical non-linear processing means  2 Av includes a zero-crossing decision means  311   v  and a signal amplifying means  312   v . Image D 1   v  is input to the vertical non-linear processing means  2 Av as an input image DIN 311   v.    
     The zero-crossing decision means  311   v  checks the pixel values in the input image DIN 311   v  for changes in the vertical direction. A point where the pixel value changes from positive to negative or from negative to positive is identified as a zero-crossing point, and the positions of the pixels preceding and following the zero-crossing point (the adjacently preceding and following pixels) are reported to the signal amplifying means  312   v  by a signal D 311   v . The zero-crossing decision means  311   v  in the vertical non-linear processing means  2 Av recognizes the pixels above and below the zero-crossing point as the pixels preceding and following the zero-crossing point. 
     The signal amplifying means  312   v  identifies the pixels preceding and following the zero-crossing point (the adjacently preceding and following pixels) from signal D 311   v  and generates a non-linear image D 312   v  by amplifying the pixel values (increasing the absolute values) of only the pixels preceding and following the zero-crossing point. The amplification factor for the pixel values of the pixels preceding and following the zero-crossing point is a value greater than 1, and the amplification factor for the pixel values of other pixels is 1. 
     The non-linear processing means  2 A operates as described above. 
     Next, in the second intermediate image generating means  2 , the high-frequency component image generating means  2 B generates image D 2 B by extracting only the high-frequency component of image D 2 A above the third frequency. The high-frequency component can be extracted by performing high-pass filter processing. The high-frequency component of the image is extracted in the horizontal direction and the vertical direction separately. The high-frequency component image generating means  2 B includes a horizontal high-frequency component image generating means  2 Bh for generating an image D 2 Bh by performing horizontal high-pass filter processing on image D 2 Ah to extract a horizontal high-frequency component above a third horizontal frequency only in the horizontal direction and a vertical high-frequency component image generating means  2 Bv for generating an image D 2 Bv by performing vertical high-pass filter processing on image D 2 Av to extract a vertical high-frequency component above a third vertical frequency only in the vertical direction; image D 2 B includes image D 2 Bh and image D 2 Bv. Image D 2 B is output from the second intermediate image generating means  2  as intermediate image D 2 . Intermediate image D 2  includes an image D 2   h  corresponding to image D 2 Bh and an image D 2   v  corresponding to image D 2 Bv. 
     Next the detailed operation of the first intermediate image processing means  3 M will be described. 
     Intermediate image processing means  3 M performs a process for suppressing low-level noise (a low-level noise suppression process) on the first intermediate image D 1 . Since the first intermediate image includes image D 1   h  and image D 1   v , the horizontal low-level noise suppression means  3 Mh performs a low-level noise suppression process on image D 1   h  to generate an image D 3 Mh, and the vertical low-level noise suppression means  3 Mv performs a low-level noise suppression process on image D 1   v  to generate an image D 3 Mv. Image D 3 Mh and image D 3 Mv are output from the first intermediate image processing means  3 M as intermediate image D 3 M. 
     The low-level noise suppression process will now be described in further detail with reference to  FIGS. 8(A) and 8(B) . 
     In  FIGS. 8(A) and 8(B) , a coring process is used as an exemplary low-level noise suppression process.  FIG. 8(A)  illustrates an input signal input to the coring process;  FIG. 8(B)  illustrates an output signal output by the coring process. If the input value to the coring process is DATAIN and the output value from the coring process is DATAOUT, the relationship between DATAIN and DATAOUT is given by: 
     
       
         
           
             
               
                 
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     THp denotes a threshold value that takes a positive value; THm denotes a threshold value that takes a negative value. 
     A comparison of  FIGS. 8(A) and 8(B)  shows that low-level noise (oscillation in the range from threshold value THp to threshold value THm) is clearly being suppressed by the coring process. That is, low-level noise can be suppressed by the coring process. 
     The low-level noise suppression process is not limited to the coring process described by Expression (1); any process that can suppress low-level noise may be used. 
     The first intermediate image processing means  3 M operates as described above. 
     Next the operation of the second intermediate image processing means  3 H will be described. A comparison of  FIGS. 4 and 5  indicates that the second intermediate image processing means has the same structure as the first intermediate image processing means except that the input signal is intermediate image D 2 ; the intermediate image D 3 H output by the second intermediate image processing means  3 H is obtained by performing, on intermediate image D 2 , the same processing as performed on intermediate image D 1  by the first intermediate image processing means  3 M. Since the details of the operation of the second intermediate image processing means  3 H are clear from the detailed description of the operation of the first intermediate image processing means  3 M given above, a description of the detailed operation of the second intermediate image processing means  3 H will be omitted. 
     Finally, the operation of the adding means  4  will be described. The adding means  4  generates an output image DOUT by adding the input image DIN, intermediate image D 3 M, and intermediate image D 3 H together. The output image DOUT of the adding means  4  is output from the image processing apparatus as the final output image. 
     Intermediate image D 3 M includes image D 3 Mh and image D 3 Mv, and intermediate image D 3 H includes image D 3 Hh and image D 3 Hv, so to add the input image DIN, intermediate image D 3 M, and intermediate image D 3 H together means to add images D 3 Mh, D 3 Mv, D 3 Hh, and D 3 Hv to the input image DIN. 
     The addition in the adding means  4  is not limited to simple addition; weighted addition may be performed. That is, images D 3 Mh, D 3 Mv, D 3 Hh, and D 3 Hv may be amplified by different amplification factors before being added to the input image DIN. 
     An example in which the image processing apparatus in this embodiment is utilized as part of an image display apparatus will be described below. The description will clarify the effects of the image processing apparatus in this embodiment. Unless otherwise specified, Fn will denote the Nyquist frequency of the input image DIN. 
       FIG. 9  illustrates an image display apparatus utilizing the image processing apparatus according to the invention; in the illustrated image display apparatus, an image corresponding to the original image DORG is displayed on a monitor U 3 . 
     If the image size of the original image DORG is smaller than the image size of the monitor U 3 , the image enlarging means U 1  outputs an image DU 1  obtained by enlarging the original image DORG. The image can be enlarged by the bicubic method, for example. 
     The image processing apparatus U 2  of this invention outputs an image DU 2  obtained by performing the processing described above on image DU 1 . Image DU 2  is displayed on the monitor U 3 . 
     The operation and effects of the image enlarging means U 1  will be described below on the assumption that the number of pixels in the original image DORG is half of the number of pixels in the monitor U 3  in both the horizontal and vertical directions. 
       FIG. 10  is a diagram illustrating the structure and operation of the image enlarging means U 1 . The image enlarging means U 1  includes a horizontal zero insertion means U 1 A, a horizontal low-frequency component passing means U 1 B, a vertical zero insertion means U 1 C, and a vertical low-frequency component passing means U 1 D. 
     The horizontal zero insertion means U 1 A generates an image DU 1 A by appropriately inserting pixels having a pixel value of 0 into the original image DORG in the horizontal direction (inserting a column of pixels having pixel values of 0 between each horizontally adjacent pair of pixel columns in the original image DORG). 
     The horizontal low-frequency component passing means U 1 B generates an image DU 1 B by performing low-pass filter processing to extract only a low-frequency component from image DU 1 A. 
     The vertical zero insertion means U 1 C generates an image DU 1 C by appropriately inserting pixels having a pixel value of 0 into image DU 1 B in the vertical direction (inserting a row of pixels having pixel values of 0 between each vertically adjacent pair of pixel rows in image DU 1 B). 
     The vertical low-frequency component passing means U 1 D generates an image DU 1 D by extracting only a low-frequency component from image DU 1 C. 
     Image DU 1 D, which is output from the image enlarging means U 1  as image DU 1 , is an enlargement of the original image DORG by a factor of two in both the horizontal direction and the vertical direction. 
       FIGS. 11(A) to 11(E)  are diagrams illustrating the operation of the image enlarging means U 1  in detail:  FIG. 11(A)  shows the original image DORG;  FIG. 11(B)  shows image DU 1 A;  FIG. 11(C)  shows image DU 1 B;  FIG. 11(D)  shows image DU 1 C;  FIG. 11(E)  shows image DU 1 D. In  FIGS. 11(A) to 11(E) , each box represents a pixel, and the characters or numbers in the box represent the pixel value of the corresponding pixel. 
     The horizontal zero insertion means U 1 A generates the image DU 1 A shown in  FIG. 11(B)  by inserting a pixel having a pixel value of 0 for each pixel in the original image DORG shown in  FIG. 11(A)  in the horizontal direction (inserting a column of pixels having pixel values of 0 between each horizontally adjacent pair of pixel columns in the original image DORG). The horizontal low-frequency component passing means U 1 B generates the image DU 1 B shown in  FIG. 11(C)  by performing low-pass filter processing on the image DU 1 A shown in  FIG. 11(B) . 
     The vertical zero insertion means U 1 C generates the image DU 1 C shown in  FIG. 11(D)  by inserting a pixel having a pixel value of 0 for each pixel in the image DU 1 B shown in  FIG. 11(C)  in the vertical direction (inserting a row of pixels having pixel values of 0 between each vertically adjacent pair of pixel rows in image DU 1 B). The vertical low-frequency component passing means U 1 D generates the image DU 1 D shown in  FIG. 11(E)  by performing low-pass filter processing on the image DU 1 C shown in  FIG. 11(D) . The image DU 1 D generated by this processing is twice as large as the original image DORG in both the horizontal and vertical directions. 
       FIGS. 12(A) to 12(D)  represent the effect of processing by the image enlarging means U 1  in the frequency domain:  FIG. 12(A)  represents the frequency spectrum of the original image DORG;  FIG. 12(B)  represents the frequency spectrum of image DU 1 A;  FIG. 12(C)  represents the frequency response of the horizontal low-frequency component passing means U 1 B;  FIG. 12(D)  represents the frequency spectrum of image DU 1 B. In  FIGS. 12(A) to 12(D) , the horizontal axis is a frequency axis representing spatial frequency in the horizontal direction, and the vertical axis represents the intensity value of the frequency spectrum or frequency response. 
     The number of pixels in the original image DORG is half the number of pixels in the input image DIN; in other words, the sampling interval of the original image DORG is twice the sampling interval of the input image DIN. Consequently, the Nyquist frequency of the original image DORG is half the Nyquist frequency of the input image DIN, i.e., Fn/2. 
     For the sake of simplicity, a single frequency axis is used in  FIGS. 12(A) to 12(D) . Image data in general, however, assign pixel values to pixels arranged in a two-dimensional array, and their frequency spectra are described in a plane determined by a horizontal frequency axis and a vertical frequency axis. Accordingly, both the horizontal frequency axis and the vertical frequency axis should be indicated to represent the frequency spectra of images such as DORG accurately. Since frequency spectra are generally isotropic about the origin of the frequency axes, if a frequency spectrum is given in a space with a single frequency axis, those skilled in the art can easily imagine how the frequency spectrum appears in a space with two frequency axes. Therefore, unless otherwise specified, spaces with a single frequency axis will be used in the descriptions related to the frequency domain. 
     First the frequency spectrum of the original image DORG will be described. The image input as the original image DORG is generally a natural image, in which case its spectral intensity is concentrated around the origin of the frequency space. The frequency spectrum of the original image DORG is accordingly like spectrum SPO in  FIG. 12(A) . 
     Next the spectral intensity of image DU 1 A will be described. Image DU 1 A is generated by inserting a pixel having a pixel value of 0 for each pixel in the original image DORG in the horizontal direction. This processing causes the frequency spectrum to fold over at the Nyquist frequency of the original image DORG. Because a spectrum SPM is generated by fold-over of the spectrum SPO at frequencies of ±Fn/2, the frequency spectrum of image DU 1 A is represented as shown in  FIG. 12(B) . 
     Next the frequency response of the horizontal low-frequency component passing means U 1 B will be described. The horizontal low-frequency component passing means is implemented by a low-pass filter, and its frequency response decreases as the frequency increases, as shown in  FIG. 12(C) . 
     Finally, the frequency spectrum of image DU 1 B will be described. The image DU 1 B shown in  FIG. 12(D)  is obtained by performing low-pass filter processing, with the frequency response shown in  FIG. 12(C) , on the image DU 1 A having the frequency spectrum shown in  FIG. 12(B) . 
     As shown in image DU 1 B, the frequency spectrum of image DU 1 B includes a spectrum SP 2  having a somewhat lower intensity than spectrum SPM and a spectrum SP 1  having a somewhat lower intensity than spectrum SPO. The frequency response of a low-pass filter generally decreases as the frequency increases. In comparison with spectrum SPO, spectrum SP 1  accordingly has an intensity lowered by the horizontal low-frequency component passing means U 1 B on the high-frequency side, at frequencies near ±Fn/2. 
     Among the processing by the image enlarging means U 1 , the effects in the frequency domain of the processing performed by the vertical zero insertion means U 1 C and the vertical low-frequency component passing means U 1 D will not be described, but from the content of the processing it can be easily understood that the effects are the same as described with reference to  FIGS. 12(A) to 12(D) , though in the direction of the vertical spatial frequency axis. The frequency spectrum of image DU 1 D becomes a two-dimensional expansion of the frequency spectrum shown in  FIG. 12(D) . 
     In the subsequent description, spectrum SP 2  will be referred to as the fold-over component. The fold-over component appears on an image as a spurious signal or noise having relatively high-frequency components. This type of noise or spurious signal includes overshoot, jaggies, ringing, and the like. 
     The effects of the image processing apparatus according to the invention will now be described. 
       FIGS. 13(A) to 13(E)  are diagrams schematically representing the effect of generating intermediate image D 1  from the input image DIN when an image DU 1 D obtained by enlarging the original image DORG is input as the input image DIN (or image DU 1 ):  FIG. 13(A)  represents the frequency spectrum of the input image DIN;  FIG. 13(B)  represents the frequency response of the high-frequency component image generating means  1 A;  FIG. 13(C)  represents the frequency response of the low-frequency component image generating means  1 B;  FIG. 13(D)  represents the frequency response of the first intermediate image generating means  1 ;  FIG. 13(E)  represents the frequency spectrum of intermediate image D 1 .  FIGS. 13(A) to 13(E)  use just a single frequency axis, for the same reason as in  FIGS. 12(A) to 12(D) . 
     In  FIGS. 13(A) to 13(E) , the intensity value of the frequency spectrum or frequency response is shown only in the range where the spatial frequency is zero or greater, but the frequency spectrum or frequency response described below is symmetrical about the origin on the frequency axis. Therefore, the diagrams used in the description, showing only the range in which the spatial frequency is zero or greater, are sufficient. 
     First the frequency spectrum of the input image DIN will be described. Because an image DU 1 D generated by enlargement processing in the image enlarging means U 1  is input as the input image DIN, the frequency spectrum of the input image DIN, shown in  FIG. 13(A) , has the same shape as shown in  FIG. 12(D) , including a spectrum SP 1  which has a lower intensity than the spectrum SPO of the original image DORG and a spectrum SP 2 , which is a fold-over component. 
     Next the frequency response of the high-frequency component image generating means  1 A will be described. Since the high-frequency component image generating means  1 A is implemented by a high-pass filter, its frequency response decreases as the frequency decreases, as shown in  FIG. 13(B) . 
     Next the frequency response of the low-frequency component image generating means  1 B will be described. Since the low-frequency component image generating means  1 B is implemented by a low-pass filter, its frequency response decreases as the frequency increases, as shown in  FIG. 13(C) . 
     Next the frequency response of the first intermediate image generating means  1  will be described. Among the frequency components of the input image DIN, the frequency components in a low-frequency region RL 1  (the frequency band lower than the first frequency FL 1 ) shown in  FIG. 13(D)  are weakened by the high-frequency component image generating means  1 A in the first intermediate image generating means  1 . The frequency components in a high-frequency region RH 1  (the frequency band higher than the second frequency FL 2 ) shown in  FIG. 13(D)  are weakened by the low-frequency component image generating means  1 B in the first intermediate image generating means  1 . Therefore, as shown in  FIG. 13(D) , the frequency response of the first intermediate image generating means  1  has a peak in an intermediate region (specific frequency band) RM 1  limited by the low-frequency region RL 1  and the high-frequency region RH 1 . 
     Next the frequency spectrum of intermediate image D 1  will be described. The intermediate image D 1  shown in  FIG. 13(E)  is obtained by passing the input image DIN having the frequency spectrum shown in  FIG. 13(A)  through the first intermediate image generating means  1  having the frequency response shown in  FIG. 13(D) . Since the frequency response of the first intermediate image generating means  1  peaks in the intermediate region RM 1  limited by the low-frequency region RL 1  and the high-frequency region RH 1 , the frequency spectrum of intermediate image D 1  is the frequency spectrum of the input image DIN with attenuation of the parts included in the low-frequency region RL 1  and high-frequency region RH 1 . Therefore, spectrum SP 2 , which would become a fold-over component, is removed from the high-frequency component of input image DIN in intermediate image D 1 . In other words, the first intermediate image generating means  1  has the effect of generating intermediate image D 1  by removing spectrum SP 1 , which becomes a fold-over component, from the high-frequency component of the input image DIN. 
       FIGS. 14(A) to 14(C)  are diagrams representing the effect of the second intermediate image generating means  2 :  FIG. 14(A)  represents the frequency spectrum of non-linearly processed image D 2 A;  FIG. 14(B)  represents the frequency response of the high-frequency component image generating means  2 B;  FIG. 14(C)  represents the frequency spectrum of image D 2 B.  FIGS. 14(A) to 14(C)  represent the frequency spectra and frequency response only in regions where the spatial frequency is 0 or greater, for the same reason as  FIGS. 13(A) to 13(E) . 
     A high-frequency component corresponding to the high-frequency region RH 2  is generated in non-linearly processed image D 2 A, as described later.  FIG. 14(A)  expresses this schematically. The image D 2 B shown in  FIG. 14(C)  is generated by passing the non-linearly processed image D 2 A through the high-frequency component image generating means  2 B. The high-frequency component image generating means  2 B includes a high-pass filter that passes components higher than the third frequency FL 3 , and its frequency response increases as the frequency increases as shown in  FIG. 14(B) . Accordingly, the frequency spectrum of image D 2 B is obtained by removing a component corresponding to the low-frequency region RL 2  (the frequency component lower than the third frequency FL 3 ) from the frequency spectrum of the non-linearly processed image D 2 A, as shown in  FIG. 14(C) . In other words, the non-linear processing means  2 A has the effect of generating a high-frequency component corresponding to the high-frequency region RH 2 , and the high-frequency component image generating means  2 B has the effect of extracting only the high-frequency component generated by the non-linear processing means  2 A. In the illustrated example, the third frequency FL 3  is substantially equal to Fn/2. 
     The effects will now be described in further detail. 
       FIGS. 15(A) to 15(C)  and  FIGS. 16(A) to 16(C)  are diagrams illustrating signals obtained when a step edge is sampled. 
       FIG. 15(A)  shows a step edge and a sampling interval S 1 ;  FIG. 15(B)  shows the signal obtained when the step edge is sampled at sampling interval S 1 ;  FIG. 15(C)  shows the high-frequency component of the signal shown in  FIG. 15(B) .  FIG. 16(A)  shows a step edge and a sampling interval S 2 , which is longer than sampling interval S 1 ;  FIG. 16(B)  shows the signal obtained when the step edge is sampled at sampling interval S 2 ;  FIG. 16(C)  shows the high-frequency component of the signal shown in  FIG. 16(B) . In the description below, the length of sampling interval S 2  is twice the length of sampling interval S 1 . 
     As shown in  FIGS. 15(C) and 16(C) , the center of the step edge appears as a zero-crossing point Z in the signal representing the high-frequency component. The slope of the signal representing the high-frequency component near the zero-crossing point Z increases as the length of the sampling interval decreases, and the positions of the points that give the local maximum and local minimum values near the zero-crossing point Z approach the zero-crossing point Z as the length of the sampling interval decreases. 
     That is, a change in sampling interval does not change the position of the zero-crossing point in the signal representing the high-frequency component near the edge, but as the sampling interval decreases (or the resolution increases), the slope of the high-frequency component near the edge increases, and the position of the points that give the local maximum and minimum values approach the zero-crossing point. 
       FIGS. 17(A) to 17(F)  are diagrams illustrating effects when the signal obtained by sampling the step edge at sampling interval S 2  is enlarged to twice its size and then input to the image processing apparatus in this invention, and more specifically the effects of the first intermediate image generating means  1  and second intermediate image generating means  2 . As described earlier, the processing in the first intermediate image generating means  1  and second intermediate image generating means  2  is performed in the horizontal direction and the vertical direction separately, and the processing is carried out one-dimensionally. Accordingly, in  FIGS. 17(A) to 17(F) , the content of the processing is represented by using a one-dimensional signal. 
     Like  FIG. 16(B) ,  FIG. 17(A)  shows the signal obtained when the step edge is sampled at sampling interval S 2 .  FIG. 17(B)  shows a signal obtained by twofold enlargement of the signal shown in  FIG. 17(A) . If the original image DORG contains an edge like the one shown in  FIG. 17(A) , a signal like the one shown in  FIG. 17(B)  is input as the input image DIN. When the signal is enlarged twofold, the sampling interval becomes half of what it was before the enlargement, so the sampling interval of the signal shown in  FIG. 17(B)  is the same as sampling interval S 1  in  FIGS. 14(A) to 14(C) . In  FIG. 17(A) , the position denoted by coordinate P 3  is on the boundary of the low luminance region (low level side) of the edge signal, and the position denoted by coordinate P 4  is on the boundary of the high luminance region (high level side) of the edge signal. 
       FIG. 17(C)  shows a signal representing the high-frequency component of the signal shown in  FIG. 17(B) , that is, a signal corresponding to the image D 1 A output from the high-frequency component image generating means  1 A. Since image D 1 A is obtained by extracting the high-frequency component of the input image DIN, it also includes a fold-over component. 
       FIG. 17(D)  shows a signal representing the low-frequency component of the signal shown in  FIG. 17(C) , that is, a signal corresponding to the image D 1 B output from the low-frequency component image generating means  1 B. Since, as described earlier, image D 1 B is output as intermediate image D 1 ,  FIG. 17(D)  also corresponds to intermediate image D 1 . In the vicinity of the zero-crossing point Z in intermediate image D 1 , a local minimum value appears at coordinate P 3 , and a local maximum value appears at coordinate P 4 , as shown in  FIG. 17(D) , matching the form of the high-frequency component extracted from the signal obtained by sampling the step edge at sampling interval S 2  as shown in  FIG. 16(C) . The fold-over component is removed from image D 1 A by the low-pass filtering process performed by the low--frequency component image generating means  1 B. 
       FIG. 17(E)  shows the signal output when the signal shown in  FIG. 17(D)  is input to the non-linear processing means  2 A, that is, it illustrates the image D 2 A output from the non-linear processing means  2 A when intermediate image D 1  is input. In the non-linear processing means  2 A, the signal values at the coordinates P 1  and P 2  preceding and following (adjacently preceding and following) the zero-crossing point are amplified. Therefore, the magnitudes of the signal values at coordinates P 1  and P 2  in image D 2 A become greater than the other values, as shown in  FIG. 17(E) ; the position where the local minimum value appears near the zero-crossing point Z changes from coordinate P 3  to coordinate P 1 , which is closer to the zero-crossing point Z; and the position where the local maximum value appears changes from coordinate P 4  to coordinate P 2 , which is closer to the zero-crossing point Z. This means that the high-frequency component is generated by a non-linear process that amplifies the values of the pixels preceding and following the zero-crossing point Z in the non-linear processing means  2 A. A high-frequency component can be generated in this way by changing the amplification factor appropriately for each pixel or by changing the content of the processing appropriately for each pixel. The non-linear processing means  2 A has the effect of generating a high-frequency component which is not included in intermediate image D 1 , that is, a high-frequency component corresponding to the high-frequency region RH 2  shown in  FIG. 14(A) . 
       FIG. 17(F)  shows a signal representing the high-frequency component of the signal shown in  FIG. 17(E) , that is, a signal corresponding to the image D 2 B output from the high-frequency component image generating means  2 B. The more precise form of image D 2 B will be described later, but in the vicinity of the zero-crossing point Z in image D 2 B, the local minimum value (negative peak) appears at coordinate P 1  and the local maximum value (positive peak) appears at coordinate P 2 , as shown in  FIG. 17(F) , matching the form of the high-frequency component extracted from the signal obtained by sampling the step edge at sampling interval S 1 , shown in  FIG. 15(C) . This means that the high-frequency component generated in the non-linear processing means  2 A is extracted by the high-frequency component image generating means  2 B and output as image D 2 B. 
     It could also be said that the extracted image D 2 B is a signal including a frequency component corresponding to the sampling interval S 1 . In other words, the high-frequency component image generating means  2 B has the effect of extracting only the high-frequency component generated by the non-linear processing means  2 A. 
     To put it another way, shifting the positions of the peaks in the vicinity of the zero-crossing point Z to the positions represented by coordinates P 1  and P 2  by performing the process described above is equivalent to generating a frequency component corresponding to the sampling interval S 1 . 
     The above-described effects of the second intermediate image generating means  2  can be summarized as follows: the non-linear processing means  2 A in the second intermediate image generating means  2  has the effect of generating the high-frequency component corresponding to the high-frequency region RH 2 ; the high-frequency component image generating means  2 B in the second intermediate image generating means  2  has the effect of extracting only the high-frequency component generated by the non-linear processing means  2 A. Since image D 2 B is output as intermediate image D 2 , the second intermediate image generating means  2  can output an intermediate image D 2  having a high-frequency component corresponding to sampling interval S 1 . 
     Image enhancement processing could be carried out at this point by adding intermediate image D 1  and intermediate image D 2  to the input image DIN. 
     Although this invention does not add the first intermediate image D 1  and second intermediate image D 2  to the input image DIN, the effects that would be obtained by adding the first and second intermediate images will be described below; then the effects of adding the third intermediate image D 3 M and fourth intermediate image D 3 H instead of the first intermediate image D 1  and second intermediate image D 2  will be described. 
     First, the effect of adding intermediate image D 1  will be described. As described earlier, intermediate image D 1  is obtained by excluding the fold-over component from the high-frequency component of the input image DIN, and corresponds to the high-frequency component near the Nyquist frequency of the original image DORG, as shown in  FIG. 13(E) . The spectral intensity near the Nyquist frequency of the original image DORG is weakened by the enlargement processing in the image enlarging means U 1 , as described with reference to  FIG. 12(D) . The spectral intensity weakened by the enlargement processing can be made up for by adding intermediate image D 1 . Since the fold-over component has been excluded from intermediate image D 1 , spurious signals such as overshoot, jaggies, and ringing are not enhanced. 
     Next the effect of adding intermediate image D 2  will be described. As described above, intermediate image D 2  is the high-frequency component corresponding to sampling interval S 1 . Adding intermediate image D 2  can supply a high-frequency component in the band above the Nyquist frequency of the original image DORG, so the perceived image resolution can be increased. 
     To summarize, by adding intermediate image D 1  and intermediate image D 2  to the input image DIN, high-frequency components can be added without enhancing the fold-over component, and the perceived image resolution can be improved. 
     The addition of high-frequency components generated as described above to the input image can sharpen the image and can improve its image quality, but if the input image includes much noise, the noise is enhanced and the image quality may be lowered instead. 
       FIGS. 18(A) to 18(E)  are diagrams illustrating the lowering of image quality by the addition of high-frequency components. 
       FIG. 18(A) , like  FIG. 17(B) , shows an image enlarged twofold after a step-edge signal is sampled. Unlike  FIG. 17(B) , however,  FIG. 18(A)  has noise in the intervals denoted by SEC 1  and SEC 2 . Coordinate Z 0  represents the central part of the step edge signal. A case in which the image shown in  FIG. 18(A)  is input as input image DIN will be considered below. 
     For convenience,  FIG. 18(A)  depicts low-level noise (two-pixel cyclic low-level noise), which alternately increases and decreases at each pixel as noise in the intervals SEC 1  and SEC 2 , but the noise is not limited to this form. That is, the low-level noise period is not limited to two pixels, or to one specific form. In other words, it may be a combination of a plurality of frequencies. An exemplary combinatorial noise form including all frequencies is white noise. The noise is also not limited to periodic noise; it may occur sporadically, as in salt-and-pepper noise. 
       FIG. 18(B)  is a diagram showing the image D 1 A obtained this time. This image D 1 A has substantially the same form as described with reference to  FIG. 17(C) , but differs from  FIG. 17(C)  in that low-level noise is present in intervals SEC 1  and SEC 2 , due to the noise included in intervals SEC 1  and SEC 2  in the input image. DIN. In other words, low-level noise occurs in intervals SEC 1  and SEC 2  because part of the noise included in the input image DIN passes through the high-pass filter in the high-frequency component image generating means  1 A. 
       FIG. 18(C)  is a diagram illustrating the intermediate image D 1  obtained this time. This intermediate image D 1 A has substantially the same form as described with reference to  FIG. 17(D) , but differs from  FIG. 17(D)  in that low-level noise is present in intervals SEC 1  and SEC 2 . This is because part of the low-level noise included in image D 1 A passes through the low-pass filter in the low-frequency component image generating means  1 B. 
     In other words, image D 1  includes the part of the noise included in image D 1 A that has passed through the frequency band shown as region RM 1  in  FIG. 13(D) . 
       FIG. 18(D)  is a diagram illustrating the intermediate image D 2 A obtained this time. This intermediate image D 2 A has substantially in the same form as described with reference to  FIG. 17(E) , but differs from  FIG. 17(E)  in that low-level noise is present in intervals SEC 1  and SEC 2 . This arises from the low-level noise included in intermediate image D 1 . Since the low-level noise present in intervals SEC 1  and SEC 2  in intermediate image D 1  includes many zero-crossing points at which the low-level noise value changes from positive to negative or from negative to positive, the low-level noise is amplified by the non-linear processing in the non-linear processing means  2 A. 
       FIG. 18(E)  is a drawing illustrating the intermediate image D 2  obtained this time. This intermediate image D 2  has substantially the same form as described with reference to  FIG. 17(F) , but differs from  FIG. 17(F)  in that low-level noise is present in intervals SEC 1  and SEC 2 . This is because part of the low-level noise included in intermediate image D 2 A passes through the high-pass filter in the high-frequency component image generating means  2 B. 
     The step-edge signal centered on coordinate Z 0  can be enhanced by adding the intermediate image D 1  shown in  FIG. 18(C)  and the intermediate image D 2  shown in  FIG. 18(E)  to the input image DIN shown in  FIG. 18(A) , whereby the perceived image resolution can be improved. In intervals SEC 1  and SEC 2 , however, low-level noise is also added from intermediate image D 1  and intermediate image D 2 , and as a result, the noise originally included in intervals SEC 1  and SEC 2  is increased. 
     As described above, noise included in the input image DIN appears as low-level noise in intermediate images D 1  and D 2 . The low-level noise is added to the input image DIN, thereby increasing the noise. 
     Therefore, to carry out image enhancement processing without increasing noise, the low-level noise present in intermediate images D 1  and D 2  is suppressed before they are added to the input image DIN. 
     In the image processing apparatus according to the first embodiment of the invention, the first intermediate image processing means  3 M suppresses low-level noise by a low-level noise suppression process in intermediate image D 1 , and the second intermediate image processing means  3 H suppresses low-level noise by a low-level noise suppression process in intermediate image D 2 . 
     The effects of the image processing apparatus according to the first embodiment of the invention will now be described with reference to  FIGS. 19(A) to 19(D) , in which a coring process used as an exemplary low-level noise suppression process. 
     The intermediate image D 1  shown in  FIG. 18(B)  is shown again in  FIG. 19(A) .  FIG. 19(A)  also shows the threshold values THp 1  and THm 1  used for the coring process by the first intermediate image processing means  3 M. 
       FIG. 19(B)  shows the intermediate image D 3 M generated by the coring process of the first intermediate image processing means  3 M. It can be seen that since low-level noise in the range limited by the threshold values THp 1  and THm 1  is suppressed by the coring process, the low-level noise included in intervals SEC 1  and SEC 2  has been suppressed. The peaks positioned at coordinates P 3  and P 4  remain intact, so adding this intermediate image D 3 M to the input image DIN enables the image enhancement processing to be carried out without increasing noise. 
     The intermediate image D 2  shown in  FIG. 18(E)  is shown again in  FIG. 19(C) .  FIG. 19(C)  also shows the threshold values THp 2  and THm 2  used for the coring process by the second intermediate image processing means  3 H. 
       FIG. 19(D)  shows the intermediate image D 3 H generated by the coring process in the second intermediate image processing means  3 H. It can be seen that since the low-level noise in the range indicated by the threshold values THp 2  and THm 2  is suppressed by the coring process, the low-level noise included in intervals SEC 1  and SEC 2  in intermediate image D 2  has been suppressed. The peaks positioned at coordinates P 1  and P 2  remain intact, so it is also possible to carry out image enhancement processing by adding intermediate image D 3 H to the input image DIN. As described above, the peaks present at coordinates P 1  and P 2  in the vicinity of the zero-crossing point are a high-frequency component corresponding to sampling interval S 1 , so adding intermediate image D 3 H can supply a high-frequency component in the frequency band above the Nyquist frequency of the original image DORG, increasing the perceived resolution of the image. 
     As described above, in the image processing apparatus according to the first embodiment of the invention, the perceived image resolution is improved without increasing noise included in the input image DIN. 
     To summarize, adding intermediate images D 3 M and D 3 H to the input image DIN can improve the perceived image resolution without increasing noise. 
     In the image processing apparatus in the invention, the first intermediate image generating means  1  and the second intermediate image generating means  2  perform image processing in the horizontal direction and the vertical direction in parallel. Accordingly, the effects described above can be obtained not just in the horizontal or vertical direction but in any direction. 
     Considered in the frequency domain, the image processing apparatus in this invention generates an image D 2 B corresponding to high-frequency components near the Nyquist frequency ±Fn of the input image DIN on the basis of the components in the input image DIN near half of the Nyquist frequency of the original image DORG, ±Fn/2, (or in a particular frequency band), in a frequency band from the origin to Fn. Even if the frequency components near the Nyquist frequency ±Fn are lost in the input image DIN, frequency components near the Nyquist frequency ±Fn can be supplied by image D 2 B. In other words, since the input image DIN is given frequency components on the high-frequency side, the perceived image resolution of the output image DOUT can be increased. 
     The location used as the particular frequency band is not limited to the vicinity of ±Fn/2. The frequency band to be used can be changed by changing the frequency response of the high-frequency component image generating means  1 A and low-frequency component image generating means  1 B appropriately. 
     In the description given above, an image enlargement process was given as an exemplary process in which frequency components near the Nyquist frequency Fn are lost, but that is not the only cause of the loss of frequency components near the Nyquist frequency Fn in the input image DIN; noise suppression and various other causes can also be considered. Therefore, the use of the image processing apparatus of the invention is not limited to processing following image enlargement processing. 
     The low-level noise suppression process carried out in the first intermediate image processing means  3 M and the second intermediate image processing means  3 H is not limited to the process described in this embodiment; any type of process capable of suppressing low-level noise may be carried out. 
     Second Embodiment 
       FIG. 20  is a flowchart illustrating an image processing method according to the second embodiment of the invention; the image processing method according to the second embodiment of the invention includes a first intermediate image generating step ST 1 , a second intermediate image generating step ST 2 , a first intermediate image processing step ST 3 M, a second intermediate image processing step ST 3 H, and an adding step ST 4 . 
     The first intermediate image generating step ST 1  includes, as shown in  FIG. 21 , a high-frequency component image generating step ST 1 A and a low-frequency component image generating step ST 1 B. 
     The high-frequency component image generating step ST 1 A includes a horizontal high-frequency component image generating step ST 1 Ah and a vertical high-frequency component image generating step ST 1 Av, and the low-frequency component image generating step ST 1 B includes a horizontal low-frequency component image generating step ST 1 Bh and a vertical low-frequency component image generating step ST 1 Bv. 
     As illustrated in  FIG. 22 , the second intermediate image generating step ST 2  includes a non-linear processing step ST 2 A and a high-frequency component image generating step ST 2 B. 
     The non-linear processing step ST 2 A includes a horizontal non-linear processing step ST 2 Ah and a vertical non-linear processing step ST 2 Av, and the high-frequency component image generating step ST 2 B includes a horizontal high-frequency component passing step ST 2 Bh and a vertical high-frequency component passing step ST 2 Bv. 
     The horizontal non-linear processing step ST 2 Ah includes, as shown in  FIG. 23 , a zero-crossing decision step ST 311   h  and a signal amplification step ST 312   h , and the vertical non-linear processing step ST 2 Av includes, as shown in  FIG. 24 , a zero-crossing decision step ST 311   v  and a signal amplification step ST 312   v.    
     The first intermediate image processing step ST 3 M includes, as shown in  FIG. 25 , a horizontal low-level noise suppression step ST 3 Mh and a vertical low-level noise suppression step ST 3 Mv. 
     The second intermediate image processing step ST 3 H includes, as shown in  FIG. 26 , a horizontal low-level noise suppression step ST 3 Hh and a vertical low-level noise suppression step ST 3 Hv. 
     First the operation in the first intermediate image generating step ST 1  will be described with reference to the flowchart in  FIG. 21 . 
     In the high-frequency component image generating step ST 1 A, the following processing is performed on an input image DIN input in an image input step, which is not shown. 
     In the horizontal high-frequency component image generating step ST 1 Ah, horizontal high-pass filter processing is performed to generate an image D 1 Ah by extracting horizontal high-frequency components from the input image DIN. 
     In the vertical high-frequency component image generating step ST 1 Av, vertical high-pass filter processing is performed to generate an image D 1 Av by extracting vertical high-frequency components from the input image DIN. 
     The high-frequency component image generating step ST 1 A performs the same processing as performed by the high-frequency component image generating means  1 A, generating an image D 1 A including image D 1 Ah and image D 1 Av from the input image DIN. The operations performed are equivalent to the operations performed by the high-frequency component image generating means  1 A. 
     In the low-frequency component image generating step ST 1 B, the following processing is performed on image D 1 A. In the horizontal low-frequency component image generating step ST 1 Bh, horizontal low-pass filter processing is performed to generate an image D 1 Bh by extracting horizontal low-frequency components from image D 1 Ah. 
     In the vertical low-frequency component image generating step ST 1 Bv, vertical low-pass filter processing is performed to generate an image D 1 Bv by extracting vertical low-frequency components from image D 1 Av. 
     The low-frequency component image generating step ST 1 B performs the same processing as performed by the low-frequency component image generating means  1 B, generating an image D 1 B including image D 1 Bh and image D 1 Bv from image D 1 A. The operations performed are equivalent to the operations performed by the low-frequency component image generating means  1 B. 
     The first intermediate image generating step ST 1  operates as described above, using image D 1 Bh as an image D 1   h , using image D 1 Bv as an image D 1   v , and outputting an intermediate image D 1  including image D 1   h  and image D 1   v . The above operations are equivalent to the operations performed by the first intermediate image generating means  1 . 
     Next the operation of the second intermediate image generating step ST 2  will be described with reference to the flowcharts in  FIGS. 22 to 24 . 
     In the non-linear processing step ST 2 A, the following processing is performed on intermediate image D 1 . 
     In the horizontal non-linear processing step ST 2 Ah, processing is performed according to the flowchart shown in  FIG. 23  to generate an image D 2 Ah from image D 1   h . The processing according to the flowchart shown in  FIG. 23  is as follows. The pixel values in image D 1   h  are checked for changes in the horizontal direction in the zero-crossing decision step ST 311   h . A point where the pixel value changes from positive to negative or from negative to positive is identified as a zero-crossing point, and the pixels to the left and right of the zero-crossing point are reported to the signal amplification step ST 312   h . In the signal amplification step ST 312   h , the pixel values of the pixels reported as being to the left and right of the zero-crossing point are amplified in image D 1   h , and the image is output as image D 2 Ah. That is, image D 2 Ah is generated in the non-linear processing step ST 2 Ah by performing on image D 1   h  the same processing as performed in the horizontal non-linear processing means  2 Ah. 
     In the vertical non-linear processing step ST 2 Av, processing is performed according the flowchart shown in  FIG. 24  to generate an image D 2 Av from image D 1   v . The processing according to the flowchart shown in  FIG. 24  is as follows. The pixel values in image D 1   v  are checked for changes in the vertical direction in the zero-crossing decision step ST 311   v . A point where the pixel value changes from positive to negative or from negative to positive is identified as a zero-crossing point, and the pixels immediately above and below the zero-crossing point are reported to the signal amplification step ST 312   v . In the signal amplification step ST 312   v , the pixel values of the pixels reported as being immediately above and below the zero-crossing point are amplified in image D 1   v , and the image is output as image D 2 Av. That is, image D 2 Av is generated in the non-linear processing step ST 2 Av by performing on image D 1   v  the same processing as performed in the vertical non-linear processing means  2 Av. 
     The non-linear processing step ST 2 A operates as described above to generate an image D 2 A including images D 2 Ah and D 2 Av. The above operations are equivalent to the operations performed by the non-linear processing means  2 A. 
     Next, in the high-frequency component image generating step ST 2 B, the following processing is performed on image D 2 A. 
     First an image D 2 Bh is generated by performing horizontal high-pass filter processing on image D 2 Ah in the horizontal high-frequency component image generating step ST 2 Bh. The horizontal high-frequency component image generating step ST 2 Bh performs processing similar to that performed in the horizontal high-frequency component image generating means  2 Bh. 
     Next, an image D 2 Bv is generated by performing vertical high-pass filter processing on image D 2 Av in the vertical high-frequency component image generating step ST 2 Bv. The vertical high-frequency component image generating step ST 2 Bv thus performs processing similar to that performed in the vertical high-frequency component image generating means  2 Bv. 
     The high-frequency component image generating step ST 2 B operates as described above to generate an image D 2 B including image D 2 Bh and image D 2 Bv. The above operations are equivalent to the operations performed by the high-frequency component image generating means  2 B. 
     The second intermediate image generating step ST 2  operates as described above, outputting image D 2 B as an intermediate image D 2 . That is, it outputs an intermediate image D 2  including image D 2 Bh as image D 2   h  and image D 2 Bv as image D 2   v . The above operations are equivalent to the operations performed by the second intermediate image generating means  2 . 
     Next the operation of the first intermediate image processing step ST 3 M will be described with reference to the flowchart in  FIG. 25 . 
     The first intermediate image processing step ST 3 M performs low-level noise suppression processing on intermediate image D 1  to generate intermediate image D 3 M. Since intermediate image D 1  includes images D 1   h  and D 1   v , first an image D 3 Mh is generated by performing low-level noise suppression processing on image D 1   h  in the horizontal low-level noise suppression step ST 3 Mh, and then an image D 3 Mv is generated by performing low-level noise suppression processing on image D 1   v  in the vertical low-level noise suppression step ST 3 Mv. An intermediate image D 3 M including images D 3 Mh and D 3 Mv is also generated. The details of the low-level noise suppression processing are as described in the first embodiment, so a description will be omitted. 
     By operating as described above, the first intermediate image processing step ST 3 M operates in the same way as the first intermediate image processing means  3 M. 
     Next, the operation in the second intermediate image processing step ST 3 H will now be described with reference to the flowchart in  FIG. 26 . 
     The second intermediate image processing step ST 3 H performs low-level noise suppression processing on intermediate image D 2  to generate intermediate image D 3 H. Since intermediate image D 2  includes images D 2   h  and D 2   v , first an image D 3 Hh is generated by performing low-level noise suppression processing on image D 2   h  in the horizontal low-level noise suppression step ST 3 Hh, and then an image D 3 Hv is generated by performing low-level noise suppression processing on image D 2   v  in the vertical low-level noise suppression step ST 3 Hv. An intermediate image D 3 H including images D 3 Hh and D 3 Hv is also generated. The details of the low-level noise suppression processing are as described in the first embodiment, so a description will be omitted. 
     By operating as described above, the second intermediate image processing step ST 3 H operates in the same way as the second intermediate image processing means  3 H. 
     In the adding step ST 4 , the input image DIN, intermediate image D 3 M, and intermediate image D 3 H are added together to generate the output image DOUT. Intermediate image D 3 M includes image D 3 Mh and image D 3 Mv, and intermediate image D 3 H includes image D 3 Hh and image D 3 Hv, so images D 3 Mh, D 3 Mv, D 3 Hh, and D 3 Hv are added to the input image DIN in the adding step ST 4 . The addition of images D 3 Mh, D 3 Mv, D 3 Hh, and D 3 Hv to the input image DIN may be simple addition or weighted addition. The output image DOUT is output as a final output image by the image processing method in this embodiment. By operating as described above, the adding step ST 4  operates equivalently to the adding means  4 . 
     The image processing method in this invention operates as described above. 
     As is clear from the preceding description, the image processing method in this embodiment and the image processing apparatus in the first embodiment operate equivalently. Therefore, the image processing method in this invention has the same effects as the image processing apparatus in the first embodiment. If the image processing method described above is carried out in the image processing apparatus U 2  in the image display apparatus shown in  FIG. 9 , for example, the image processed by the image processing method can be displayed by the image display apparatus shown in  FIG. 9 . 
     EXPLANATION OF REFERENCE CHARACTERS 
       1  first intermediate image generating means,  2  second intermediate image generating means,  3 M first intermediate image processing means,  3 H second intermediate image processing means,  4  adding means, DIN input image, D 1  intermediate image, D 2  intermediate image, D 3 M intermediate image, D 3 H intermediate image, DOUT output image.