JP2887805B2 - Image processing method - Google Patents

Description

Description: BACKGROUND OF THE INVENTION The present invention relates to an image processing method, and more particularly to an image processing method that enables highly accurate discrete image interpolation and image enlargement / reduction.

(Prior Art) An image on a continuous plane is multiplied by an integer (L times, L is an integer)
Or rational number times (L ₁ / L ₂ times, L ₁ and L ₂ are integers and L ₁ > L ₂ >
The process of expanding to 1) is generally performed using a circuit configuration as shown in FIG.

That is, the band of the image is limited to the Nyquist frequency or lower by an analog low-pass filter (hereinafter abbreviated as analog LPF) 2 so that aliasing noise does not occur at the time of sampling. Generate As an example of such an analog LPF2, for example, in a camera using a CCD that performs a sampling operation as an image sensor, a filter called an optical filter is used. Next, the image is converted into a digital signal by the analog-to-digital converter 4, the image is enlarged by a digital signal processing method in the enlargement processing 5, and the digital-to-analog converter 7 converts the image into an analog signal. Then, convert this analog signal to a continuous signal through analog LPF8,
We want a magnified image that is on a continuous plane. In the enlargement processing 5, a sample required when the discrete image is enlarged is obtained by interpolating from a sample of the discrete image before the enlargement, and the next obtained sample interval is made equal to the sample interval of the discrete image before the enlargement. It is expanding by that.

Further, rational multiple images that are on a continuous plane (L ₁ / L
_The process of reducing to ₂ times and L ₁ and L ₂ are integers and L ₂ > L ₁ > 1) is generally performed by performing a reduction process instead of the enlargement process 5 in FIG. This reduction process is performed by interpolating from the sample of the discrete image before reducing the sample required when the image is reduced to a rational number, and then obtaining the sample interval of the discrete image before reducing the obtained interval of the sample. And it has shrunk by being far away.

As a conventional example of such an interpolation process, a case where a sample interval of a discrete image before interpolation (hereinafter referred to as an original image) is an integer multiple (L times, L is an integer) of a sample interval of a discrete image after interpolation (hereinafter, referred to as an original image) integral multiple of abbreviated as interpolation) and rational multiple (L ₁ / L _2-fold, an example of L _1, L ₂ are abbreviated as _{L 1> 1, L 2>} 1) in the case (hereinafter rational multiple of the interpolation integer) These are shown in FIGS. 3 and 4, respectively. These processes are described in the literature “Interpolation and Decimation of Digital Signal.
s-A Tutorial Review ", Ronald E. Crochiere and Lawre
nce R. Rabiner, PROCEEDINGS OF IEEE, Vol. 69, No. 3, Marc
h 1981 ”, the one-dimensional signal interpolation process
This is applied to a two-dimensional image.

 First, the integral multiplication process will be described.

FIG. 4A shows the interpolation process, and FIGS.
(D) shows an example of an image at each stage when L = 2. Let the original image be a (m, n) (where m and n are integers representing horizontal and vertical coordinates, respectively),
It is represented by a circle in FIG. The original image is oversampled L times as shown in FIG. 4 (c) by an oversampling process 10, and a sample having a value of 0 is inserted between the samples. In FIG. 4 (c), a sample inserted with a value of 0 is represented by X. Assuming that this image is b (m, n), b (m, n) is represented by the following equation (1).

b (m, n) = a (m / L, n / L) (m, n = 0, ± L, 2L, ...) = 0 (m, n is other than the above) …… (1) where a Let the Fourier transform of (m, n) be A (exp [j
ω ₁ ], exp [jω ₂ ]), where ω ₁ and ω ₂ are angular frequencies normalized by the horizontal and vertical sample intervals, respectively, and the horizontal and vertical sample intervals are X and Y, respectively. ω
_{1 =} the frequency 1 / X of 2 [pi, frequency omega _{2 =} 2 [pi corresponds to 1 / Y. From equation (1), the Fourier transform B (e) of b (m, n)
xp [jω ₁ ′], exp [jω ₂ ′]) (ω ₁ ′, ω ₂ ′ are angular frequencies normalized by horizontal and vertical sample intervals, respectively, and the frequency of ω ₁ ′ = 2π is 1 / ( LX), ω ₂ ′ =
(2π frequency corresponds to 1 / (LY)) is as shown in equation (2).

B (exp [jω ₁ ′], exp [jω ₂ ′]) = A (exp [jLω ₁ ′], exp [jLω ₂ ′]) (2) Thus, B (exp [jω ₁ ′], exp [jω ₂ '])
A (exp [jω ₁ ′], exp [j
ω ₂ ′]) for L periods. Next, this is expressed by the following equation (3): H ₁ (exp [jω ₁ ′], exp [jω ₂ ′]) = L ₂ (| ω ₁ ′ | ≦ π / L, | ω ₂ ′ | ≦ π / L) = 0 (ω ₁ ′, ω ₂ ′ are other than the above) .. When passed through a digital low-pass filter (hereinafter abbreviated as digital LPF) 11 having the frequency characteristic of (3), it becomes one cycle, and the value becomes 0
The correct value of the sample inserted as is obtained. This correctly determined sample is indicated by △ in FIG. 4 (d). In this way, L-times interpolation can be performed. As described above, the interpolation of the integral multiple is performed by the oversampling corresponding to the magnification and the digital LPF.

Next, the rational number multiplication process will be described. In FIG. 5, (a) shows the interpolation process, and (b) to (e) show L ₁ =
3 shows an example of an image at each stage when L ₂ = 2. In this case oversampled to L ₁ times an integer multiple of the interpolation as well as over-sample processing 12 described above the original image of FIG. 5 (b), a value between the specimen inserting a sample of 0. The image at this time is shown in FIG. 5 (c). Fig. 5 (c)
In X, a sample inserted with a value of 0 is represented by X. Next, if L ₁ > L ₂ > 1, equation (4) is used, and if L ₂ > L ₁ > 1, equation (5) is used to pass L ₁ through a digital LPF 13 having frequency characteristics of equation (5).
Do double interpolation.

_{H 2 (exp [jω 1 '} ], exp [jω 2']) = L 1 2 (| ω 1 '| ≦ π / L 1, | ω 2' | ≦ π / L 1) = 0 (ω 1 ' , Ω ₂ ′ are other than the above) (4) H ₃ (exp [jω ₁ ′], exp [jω ₂ ′]) = L ₁ ² (| ω ₁ ′ | ≦ π / L ₂ , | ω ₂ ′ | ≦ π / L ₂ ) = 0 (ω ₁ ′ and ω ₂ ′ are other than the above)... (5) where ω ₁ ′ and ω ₂ ′ are normalized by sample intervals in the horizontal and vertical directions, respectively. Ω ₁ ′ = 2π at angular frequency
Is 1 / (L ₁ X), and the frequency of ω ₂ ′ = 2π is 1 / (L
₁ corresponding to Y). (4) Equation (3) are those placed and L = L ₁ in formula, and (5) is a cut-off frequency of (4) π
/ L ₂ . The image at this time is shown in FIG.
Is shown in In FIG. 5 (d), △ represents a correctly determined sample. Then downsample this 14
In L ₁ / L as 1 / L ₂ when downsampling Figure 5 (e)
It is _twice the interpolation. Here, if L ₁ > L ₂ > 1, no aliasing noise occurs even if down-sampling to 1 / L ₂ is performed. Also L ₂ >
Also in the case of L ₁ > 1, since the cut-off frequency is π / L _{2 and} the frequency components equal to or higher than π / L ₂ are excluded, no aliasing noise occurs. As described above, the interpolation of the rational number is performed by the oversampling corresponding to the scaling factor, the digital LPF, and the downsampling.

The filtering process transforms the oversampled image into a frequency domain sample using the discrete Fourier transform,
This is realized by multiplying the frequency characteristics of the LPF 11 or the digital LPF 13 and performing a discrete inverse Fourier transform. Or
The frequency characteristic of the digital LPF 11 or the digital LPF 13 is obtained by performing a discrete inverse Fourier transform to obtain an impulse response, and convolving it with an oversampled image. Note that the method described above assumes that an ideal filter can be constructed. However, since an ideal filter cannot actually be constructed, the frequency characteristics of the digital LPF 11 or the digital LPF 13 need only be sufficiently close to the frequency characteristics of the equations (3), (4) and (5).

By making the sample interval of the image interpolated in this way equal to the sample interval of the original image, the discrete image is enlarged / reduced, and is converted into an analog signal by the digital / analog converter 7. Then, the signal is converted into a continuous signal through the analog LPF 8 to obtain an enlarged image / reduced image on a continuous plane.

(Problems to be Solved by the Invention) Although the interpolation and enlargement / reduction of an image can be performed by the above-described conventional processing, it is generally difficult to produce an analog LPF having a flat passband characteristic and a steep cutoff characteristic. Therefore, the analog LPF2 shown in FIG. 3 has a non-flat passband or a steep cutoff characteristic, so that the image is often deteriorated by the analog LPF2 before being sampled. In particular, if the cutoff characteristic is not steep, it is significantly deteriorated in a high frequency region. In the conventional image interpolation and enlargement / reduction processing, the deterioration due to the analog LPF 2 is not corrected. As a result, the resolution of the image interpolated by the conventional method has not been sufficiently increased. In particular, in the case of the enlarged image, the image quality deteriorated because the resolution did not increase. Further, even in the case of a reduced image, especially when the reduction is performed close to one time, the image quality is remarkably reduced.

An object of the present invention is to interpolate an image in which the degradation of an image caused by an analog LPF before sampling is corrected, and to enlarge / enlarge an image.
An object of the present invention is to provide an image processing method for performing reduction.

(Means for Solving the Problems) The interpolation processing in the image processing method of the present invention is a processing of correcting image degradation due to an analog LPF before being sampled and an enlargement / reduction processing using this interpolation reason. The image processing method of the present invention performs the following processing.

That is, after an image on a continuous plane is band-limited by an analog low-pass filter, a first discrete image is generated by equally-spaced sampling in which sampling intervals in two orthogonal directions are X and Y, respectively. And the value is 0 except for the sample of the first discrete image.
Is inserted into the first discrete image, and the sample interval in two orthogonal directions is X / L and Y / L (L is an integer), and the first discrete image is sampled. The generated second discrete image is subjected to digital low-pass filter processing having a frequency characteristic for correcting the characteristic of the analog low-pass filter, thereby interpolating the first discrete image.

The sample intervals in the two orthogonal directions are X and Y, respectively.
Generating a second discrete image having sample intervals X / L and Y / L (L is an integer) in two orthogonal directions from the first discrete image of
The second discrete image is subjected to digital low-pass filter processing having a frequency characteristic for correcting the characteristic of the analog low-pass filter to perform interpolation of the first discrete image, and the interpolated second discrete image Are respectively multiplied by L, and an L-times enlarged image of the first discrete image is generated.

Further, the sample intervals in the two orthogonal directions are X and Y, respectively.
Generates a second discrete image having sample intervals in two orthogonal directions of X / L ₁ and Y / L ₁ (L ₁ is an integer), respectively, from the first discrete image of Digital low-pass filter processing having a frequency characteristic for correcting characteristics of an analog low-pass filter is performed to perform interpolation of the first discrete image,
The samples of the interpolated second discrete image are taken out at every L ₂ −1 (L ₂ is an integer) samples in two orthogonal directions,
Generate a third discrete image, and generate orthogonal 2
Direction of the sampling interval is _doubled L ₁ / L, respectively, to generate the L ₁ / L ₂ times the image of the first discrete image.

(Operation) In the image processing method of the present invention, the process of correcting the image deterioration caused by the analog LPF before being sampled is a process called image restoration, and the original image before the deterioration is obtained from the deteriorated image and the impulse response of the deterioration. This is a process of estimating an image.

Since an analog filter for applying aliasing noise before sampling is generally a linear and position-invariant filter, a process of restoring an image deteriorated by such a filter will be described.

The original image is represented by f (x, y), and the impulse response of degradation is represented by k (x, y).
y), the degraded image is represented by g (x, y), the noise added during the degradation process is represented by n (x, y) and a continuous system (x represents the horizontal direction, and y represents the vertical direction). , These relationships are expressed by equation (6).

Image restoration is performed by applying a filter called a restoration filter to g (x, y). There are various ways to construct the restoration filter. For example, see the document "O Plus E separate volume,
This is described in detail in "Latest Trends in Image Processing Algorithms", edited by Takagi, Toriwaki and Tamura, Chapter 3 Image Restoration by New Technology Communications. Here, a restoration filter using a Wiener filter will be described. The transmission relationship of the Wiener filter is represented by W (u, v) (u
Is the horizontal frequency and v is the vertical frequency), W (u, v) is the transfer function of degradation (ie, the Fourier transform of the impulse response k (x, y)) to k (u, v
When v), it is expressed as in equation (7).

here Represents the complex conjugate of K (u, v). δ is a constant determined based on the relative magnitude of the original image and noise. This Wiener filter shows a characteristic of approximately 1 / K (u, v) at a frequency where the absolute value of K (u, v) is larger than δ, and shows K (u, v).
A characteristic that corrects the characteristic of v) and suppresses the increase in the gain of W (u, v) by δ at a frequency where the absolute value of K (u, v) is smaller than δ to avoid instability. have. The image estimated by this Wiener filter is denoted by f ′
(X, y) and its Fourier transform is F '(u, v),
F ′ (u, v) is the Fourier transform G of the degraded image g (x, y)
It can be obtained from (u, v) and W (u, v) as in equation (8).

F ′ (u, v) = W (u, v) G (u, v) (8) f ′ (x, y) can be obtained by performing an inverse Fourier transform on F ′ (u, v). .

As described above, the deteriorated image can be corrected. Degradation of an image can be similarly restored by using another restoration filter of the Wiener filter.

The filter used for the interpolation in the image processing method of the present invention is an LPF obtained by synthesizing the restoration filter and the LPF having the frequency characteristic represented by the equation (3) or the equations (4) and (5). That is, the filter performs the same operation as that of performing image interpolation after correcting deterioration due to the analog LPF.

(Example) Next, the present invention will be described with reference to the drawings.

FIG. 1 shows a first embodiment of the interpolation processing in the image processing method of the present invention. This embodiment is an embodiment in which an image on a continuous plane is sampled and is interpolated by an integral multiple (L times), and is configured as follows.

An image on a continuous plane is input to an input terminal 1. Before being sampled, the image is band-limited by an analog LPF so that aliasing does not occur in the sampling. Then, sampling is performed (sample intervals in the horizontal and vertical directions are set to X and Y, respectively) in a sampling process 3 to generate a discrete image.

Further, the signal is converted into a digital signal by an analog / digital converter (hereinafter abbreviated as A / D converter) 4. Let this discrete image be a (m, n) (m and n are integers). This is oversampled L times in an oversampling process 12 in the same manner as in FIG. 4 (c) to create a discrete image b (m, n). That is, b (m, n) is as shown in equation (1).

Next, apply digital LPF15. The digital LPF 15 has a restoration filter for correcting the deterioration caused by the analog LPF 2 and a value of 0.
A filter that combines the digital LPF of equation (3) to find the correct value of the sample inserted as
When the Wiener filter represented by the equation is used, the frequency characteristic H of this digital LPF 15 (exp [jω ₁ ′], exp
[Jω ₂ ′]) is expressed as in equation (9).

H (exp [jω ₁ ′], exp [jω ₂ ′]) = W ′ (exp [jLω ₁ ′], exp [jLω ₂ ′]) × H ₁ (exp [jω ₁ ′], exp [jω ₂ ′) ]) = L ² × W ′ (exp [jLω ₁ ′], exp [jLω ₂ ′]) (| ω ₁ ′ | ≦ π / L and | ω ₂ ′ | ≦ π / L) = 0 (ω ₁ ′) , Ω ₂ ′ except above) (9) where the frequency of ω ₁ ′ = 2π is 1 / (LX),
It corresponds to the frequency 1 / (LY) of ω ₂ ′ = 2π. W '
(Exp [jω ₁ ], exp [jω ₂ ]) is W (u,
v) is sampled at a period of 1 / X and 1 / Y in the horizontal and vertical directions to form a periodic function, and | ω ₁ | ≦ π, | ω ₂ | ≦
In the range of π, it can be expressed as in equation (10).

W ′ (exp [jω ₁ ], exp [jω ₂ ]) = W (ω ₁ / (2πX), ω ₂ / (2πY)) (| ω ₁ | ≦ π and | ω ₂ | ≦ π) 10) However, the frequency of ω ₁ = 2π corresponds to 1 / X, and the frequency of ω ₂ = 2π corresponds to 1 / Y.

The operation of the digital LPF 15 is as follows. a (m,
n) to the Fourier transform A (exp [jω ₁ ], exp [j
ω ₂ ]) (ω ₁ and ω ₂ have the frequency of ω ₁ = 2π equal to 1 / X,
Assuming that the frequency of ₂ = 2π corresponds to 1 / Y), b (m,
n) Fourier transform B (exp [jω ₁ '], exp [j
ω ₂ ′]) (the frequency of ω ₁ ′ = 2π becomes 1 / (LX),
(the frequency of ω ₂ ′ = 2π corresponds to 1 / (LY)) is (2)
Because it is like the formula, the image that passed through the digital LPF15 is c
(M, n) and its Fourier transform to C (exp [jω ₁ ′], exp
[Jω ₂ ′], C (exp [jω ₁ ′], exp
[Jω ₂ ′]) is as shown in equation (11).

C (exp [jω ₁ ′], exp [jω ₂ ′]) = H (exp [jω ₁ ′], exp [jω ₂ ′]) × B (exp [jω ₁ ′], exp [jω ₂ ′]) _{= W '(exp [jLω 1} '], exp [jLω 2 ']) × A (exp [jLω 1'], exp [jLω 2 ']) × H 1 (exp [jω 1'], exp [jω 2 ']) ... (11) _{where, W' (exp [jLω 1} '], exp [jLω 2'])
× A (exp [jLω ₁ ′], exp [jLω ₂ ′]) is a Fourier transform of an image obtained by oversampling the image corrected for degradation in the analog LPF ₂ L times, and therefore, H ₁ (exp
[Jω ₁ ′], exp [jω ₂ ′]), the correct value of the sample inserted by oversampling is obtained. Therefore, in the image interpolated by applying the digital LPF 15, the deterioration in the analog LPF 2 is interpolated.

In this manner, the interpolation processing according to the present invention enables the interpolation of an integral multiple of the discrete image. The discrete image obtained in this manner is corrected for deterioration in the analog LPF2. As in the conventional example, the filter processing can be realized by converting the oversampled image into the frequency domain using the discrete Fourier transform, applying the digital LPF 15 of the equation (9), and performing the discrete inverse Fourier transform. Alternatively, it can be realized by performing a discrete inverse Fourier transform on the frequency characteristic of the digital LPF 15 to obtain an impulse response, and convolving it with an oversampled image.

Although the above-described method assumes that an ideal filter can be constructed, it is not possible to actually construct an ideal filter. Therefore, the frequency characteristic of the digital LPF 15 is represented by the frequency characteristic of equation (9). It should be close enough to

By making the sample interval of the discrete image interpolated by the integral multiple equal to the sample interval of the original image, a discrete image enlarged to the integral multiple is obtained. Enlarged discrete image is analog LPF2
, The resolution is higher than that of the image enlarged by the conventional method. If this is converted into a digital-to-analog signal in the same manner as in FIG. 3 and converted into an image on a continuous plane by the analog LPF, an enlarged image in which the deterioration due to the analog LPF 2 has been corrected can be generated.

FIG. 2 shows a second embodiment of the interpolation processing of the image processing method of the present invention.

This embodiment, by sampling the image that is on a continuous plane to generate a discrete image, after L ₁ × (L ₁ are the L _1> 1 integer) was performed interpolation, 1 / L ₂ times (L ₂ is a interpolation integer L _2> 1) of the down-sampling processing is performed to L ₁ / L ₂ times the interpolation of the original image, on the first embodiment and a continuous input terminal 1 similarly plane Enter an image. Before the image is sampled, an analog LP is used to avoid aliasing in the sampling.
Bandwidth is limited by F2. Then, it is sampled (sample intervals in the horizontal and vertical directions are set to X and Y, respectively) in a sampling process 3 and further converted into a digital signal by an A / D converter 4.
This digital signal is the same as the oversampled to _1x L and of FIG. 5 in the over-sample processing 12 (c), is input to the digital LPF 16. The frequency characteristic of the digital LPF 16 is expressed by equation (12) when L ₁ > L ₂ > 1, and when L ₂ > L ₁ > 1 (1
3) It is expressed by the equation.

_{H 5 (exp [jω 1 '} ], exp [jω 2']) = W '(exp [jL 1 ω 1'], exp [jL 1 ω 2 ']) × H 2 (exp [jω 1'], _{exp [jω 2 ']) =} L 1 2 × W' (exp [jL 1 ω 1 '], exp [jL 1 ω 2']) (| ω 1 '| ≦ π / L 1 and | ω _2' | ≦ π / L ₁ ) = 0 (ω ₁ ′ and ω ₂ ′ are other than the above)... (12) H ₆ (exp [jω ₁ ′], exp [jω ₂ ′]) = W ′ (exp [jL ₁ ω ₁ ′], exp [jL ₁ ω ₂ ′]) × H ₃ (exp [jω ₁ ′], exp [jω ₂ ′]) = L ₁ ² × W ′ (exp [jL ₁ ω ₁ ′], exp [JL ₁ ω ₂ ′]) (| ω ₁ ′ | ≦ π / L ₂ and | ω ₂ ′ | ≦ π / L ₂ ) = 0 (ω ₁ ′ and ω ₂ ′ are other than the above) (13) Here, ω ₁ ′ and ω ₂ ′ are angular frequencies normalized by horizontal and vertical sample intervals, respectively, and ω ₁ ′ = 2
The frequency of π is 1 / (L ₁ X), and the frequency of ω ₂ ′ = 2π is 1 /
(L ₁ Y). (12) Equation (11) are those placed and L = L ₁ in formula, and (13) is obtained by the a [pi / L ₂ cut-off frequency of (12).

The discrete image that has passed through the digital LPF 16 is corrected for deterioration in the analog LPF 2 as in the first embodiment. This was similarly in downsampling process 14 1 / L _2-fold downsampling processing of FIG. 5 (e) performing L ₁ / L _2-fold interpolation. Here, when L ₁ > L ₂ > 1, no aliasing noise occurs even if down-sampling is performed by 1 / L ₂ times. In the case of L ₂ > L ₁ > 1, since the cutoff frequency is π / L ₂ and frequency components equal to or higher than π / L ₂ are excluded, aliasing noise does not occur even if the sample is downsampled by a factor of 1 / L ₂ .

In this way, L ₁ / L ₂ corrected for degradation in analog LPF2
Double interpolation can be performed. Since this filtering process can be performed in the same manner as in the first embodiment, the description is omitted.

L ₁ / L _2-fold enlargement / reduced discrete images are obtained if equal sampling interval of the sampling interval original image of the discrete images interpolated as described above L ₁ / L _2-fold. Since the discrete image enlarged / reduced in this manner is corrected for the deterioration due to the analog LPF2, the resolution is higher than that of the image enlarged / reduced by the conventional method. If this is converted into a digital-to-analog signal in the same manner as in FIG. 3 and converted to an image on a continuous plane by the analog LPF, an enlarged image / reduced image in which the deterioration due to the analog LPF 2 is corrected can be generated.

(Effects of the Invention) As described above, in the image obtained by the interpolation processing by the image processing method of the present invention, the deterioration caused by the analog LPF applied before sampling is corrected. Therefore, an image having a higher resolution than the image interpolated by the conventional processing is required. In addition, by performing enlargement / reduction by image enlargement / reduction processing using the image interpolation processing of the present invention, an enlarged image / reduced image having a higher resolution than before can be generated.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an example of a process of interpolating an image at an integral multiple in the image processing method according to the present invention, and FIG. 2 is a block diagram showing an example of a process of interpolating an image at a rational number in the image processing method according to the present invention. FIG. 3, FIG. 3 is a block diagram of a process for enlarging an image on a continuous plane, FIG. 4 is a diagram for explaining a process of interpolating an image to an integral multiple of the conventional image, and FIG. FIG. 6 is a diagram for explaining a process of interpolating. 1 input terminal, 2, 8 analog LPF, 3 sampling processing, 4 A / D converter, 5 enlargement processing, 7 D / A converter, 9 output terminal , 10,12 …… Oversampling processing, 11,13,15,16 …… Digital LPF, 14 …… Downsampling processing.

Claims (3)

(57) [Claims] An image on a continuous plane is band-limited by an analog low-pass filter, and then sampled at equal intervals where sampling intervals in two orthogonal directions are X and Y, respectively. An image is generated, and a sample whose value is 0 is inserted except for the sample of the first discrete image, and the sample intervals in the two orthogonal directions are X / L and Y / L (L is a positive integer). A first discrete image is sampled at a certain interval to generate a second discrete image, and the second discrete image is converted to a digital low-frequency signal having a frequency characteristic for correcting the characteristic of the analog low-pass filter. An image processing method, wherein the first discrete image is interpolated by band-pass filtering. 2. An image lying on a continuous plane is band-limited by an analog low-pass filter, and then sampled at equal intervals in two orthogonal sample intervals X and Y to perform first discrete sampling. An image is generated, and a sample whose value is 0 is inserted except for the sample of the first discrete image, and the sample intervals in the two orthogonal directions are X / L and Y / L (L is a positive integer). A first discrete image is sampled at a certain interval to generate a second discrete image, and the second discrete image is converted to a digital low-frequency signal having a frequency characteristic for correcting the characteristic of the analog low-pass filter. The first discrete image is interpolated by a band-pass filter processing to generate a discrete image, and the interpolated discrete image sample interval in each of the two orthogonal directions is multiplied by L, and the first discrete image is multiplied by L. Generating an L-times enlarged image of the discrete image; Processing method. 3. An image on a continuous plane is band-limited by an analog low-pass filter, and then sampled at equal intervals where sampling intervals in two orthogonal directions are X and Y, respectively. An image is generated, and a sample having a value of 0 is inserted except for the sample of the first discrete image, and the sample intervals in the two orthogonal directions are X / L ₁ and Y / L ₁ (L ₁ is positive. (Integer) is performed on the first discrete image to generate a second discrete image, and the second discrete image is subjected to frequency characteristics for correcting the characteristics of the analog low-pass filter. Digital low-pass filter processing to generate a discrete image in which the first discrete image has been interpolated. From the interpolated discrete image, L ₂ -1 (L ₂
Is an integer greater than or equal to 2) taking a sample every other sample to generate a third discrete image, and
Image processing method characterized in that by way of the sampling interval by _doubling L ₁ / L, respectively, to generate the L ₁ / L _2-fold enlarged image of the first discrete image.