JPH04326183A - Enlarging and reducing method for picture - Google Patents

Abstract

PURPOSE:To prepare an enlarged and reduced picture whose resolution is improved better than that of the picture enlarged and reduced by a conventional method by correcting the deterioration of the picture searched by the enlarging and reducing method of the picture, generated by an analog LPF executed at a D/A converting part. CONSTITUTION:The first discrete picture is prepared by operating a sampling at an equal interval in which sampling intervals in two directions orthogonally crossing the first picture on a continuous plane are defined as X and Y, and the second discrete picture is prepared by inserting the sampling whose value is 0 into the sampling except for that included in this first discrete picture, and operating the sampling at the equal interval in which the sampling intervals in the two directions are respectively defined as X/L1 and Y/L1, and the third discrete picture is prepared by executing a digital LPF to this discrete picture, and interpolating the first discrete picture. Then, the forth discrete picture is prepared by taking out the sampling of this discrete picture at an interval of L2-1 sampling in the two directions, the second picture on the continuous plane is prepared by operating a digital/analog conversion in which the sampling intervals in the two direction of this forth discrete picture are defined as L1/L2 times, higher frequency components included in the second picture are removed by executing the analog LPF, and the enlarged or reduced picture which is L1/L2 times as large as the above mentioned first picture on the continuous plane is prepared.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image enlargement/reduction method using a discrete image interpolation method in digital signal processing.

0002

2. Description of the Related Art A method of enlarging or reducing an image on a continuous plane (hereinafter referred to as a continuous image) by an integral number or a rational number is generally performed using a block diagram as shown in FIG. In other words, an analog low-pass filter (
After limiting the image band to below the Nyquist frequency using an analog LPF (hereinafter referred to as an analog LPF) 2, an analog-to-digital converter (hereinafter referred to as an A/D converter) 3 performs sampling and quantization to generate a discrete image. Next, in interpolation processing 5, samples required when enlarging or reducing the input discrete image (hereinafter referred to as the original image) are obtained by interpolation from the samples. Hereinafter, the sample interval of the original image is L times the sample interval of the discrete image after interpolation (L is an integer greater than 1) or L1 /L2
(L1, L2 are integers greater than 1).

The following FIGS. 4 and 5 show schematic diagrams explaining the concept of such an interpolation method. Regarding this, please refer to the magazine "
Proceedings of IEEE (PRO)
CEEDINGS OF IEEE)” in 1981
“Interpolati” in the March issue (Vol.69)
On and Decimation of
Digital Signals-AT
“Utorial Review” (author: Rona
ld E. Crochiere and Law
rence R. Rabiner). This document applies interpolation of one-dimensional signals to two-dimensional images.

FIG. 4 shows a case in which interpolation processing 5 is performed using oversampling (a) and a digital LPF (10), and FIGS. An example image is shown. The original image is a(m,n)(m
, n are integers representing coordinates in the horizontal direction and vertical direction, respectively), and the sample is represented by a circle in FIG. 4(a). By oversampling, the original image is oversampled by a factor of L and a sample with a value of 0 is inserted between the samples, as shown in Figure 4(b).Here, the inserted sample with a value of 0 is represented by ×. ing. Letting this image be b(m, n), b(m, n) becomes as shown in the following equation (1).

[0005]

Here, the Fourier transform of a(m, n) is expressed as A(
exp[jω1 ] , exp[jω2 ] ),
ω1 and ω2 are the angular frequencies normalized by the horizontal and vertical sampling intervals, respectively.If the horizontal and vertical sampling intervals are X and Y, respectively, the frequency of ω1 = 2π becomes 1/X, and ω2 = The frequency of 2π corresponds to 1/Y. From equation (1), the Fourier transform B(exp
[jω1 ′],exp[jω2 ′])(ω1 ′,
ω2' is the angular frequency normalized by the sampling interval in the horizontal and vertical directions, and the frequency of ω1'=2π corresponds to L/X, and the frequency of ω2'=2π corresponds to L/Y) is (2
) is as follows.

[0007]

In this way, B(exp[jω1 ′], e
In one period of xp[jω2 ′]), A(exp[jω2 ′])
1 ′], exp[jω2 ′]) for L periods. Next, when this is passed through the digital LPF 10 having the frequency characteristic of equation (3), it becomes one period, and the correct value of the sample inserted with the value as 0 can be found.

[0009]

Here, |ω1 ′|≦π, |ω2 ′|
The range is ≦π. This correctly determined sample is represented by a □ mark in FIG. 4(c), and interpolation can be performed by a factor of L in this way.

Next, examples of discrete images at each stage when L1 = 3 and L2 = 2 are shown in FIGS. 5(a) to 5(c), and FIGS. 2, an example of a discrete image when L2 =3 is shown. Let the original image be a(m, n), its sample is represented by a circle in Figure 5(a), and this is oversampled (9), which multiplies the original image by L1 as shown in Figures 5(b) and (e). A sample with a value of 0 is inserted between the samples by oversampling, and the sample inserted with a value of 0 is represented by an x here. Assuming that this image is b(m,n), b(m,n) can be obtained by replacing L with L1 in equation (1).

[0012] Next, if L1 > L2 > 1, (4)
When L2 > L1 > 1, the cutoff frequency of this formula is π/L2, and the digital L has the frequency characteristic of formula (5).
When passed through the PF, it becomes one period, and the correct value of the sample inserted with the value set to 0 can be found.

[0013]

[0014] Here, ω1' and ω2' are angular frequencies normalized by the horizontal and vertical sampling intervals, respectively, and the frequency of ω1'=2π becomes L1/X, and ω2'=
The frequency of 2π corresponds to L1/Y. Also (4), (
Equation 5) indicates the range of |ω1 ′|≦π and |ω2 ′|≦π. This correctly determined sample is shown in Figure 5(c).
, (f) are represented by □, and in this way, L1 times the interpolation can be performed. Furthermore, if this is down-sampled to 1/L2, interpolation times L1/L2 can be achieved as shown in FIGS. 5(d) and (g). Here, if L1 > L2 > 1, then 1
/L2 does not cause aliasing noise, and even when L2 > L1 > 1, the cutoff frequency is set to π/L.
Since frequency components of π/L2 or more are excluded as 2, aliasing noise does not occur.

[0015] Filter processing is realized by converting an oversampled image into a frequency domain sample using discrete Fourier transform, multiplying it by the frequency characteristics of a digital LPF, and performing discrete inverse Fourier transform. Furthermore, the impulse response is obtained by performing a discrete inverse Fourier transform on the frequency characteristics of the digital LPF, and is realized by convolving this with an oversampled image. Note that the above method assumes that an ideal filter can be constructed. However, in reality, it is not possible to construct an ideal filter, so the frequency characteristics of the digital LPF need only be sufficiently close to the frequency characteristics of equations (3) to (5).

In this way, oversampling and digital L
With PF, interpolation can be performed by L times or L1/L2 times. Next, a digital-to-analog converter (hereinafter referred to as a D/A converter) 6 converts the sample interval of the interpolated image into a D/A converter so that it is equal to the sample interval of the original image, that is, the sample interval of the A/D converter 3. By converting, it is possible to generate continuous images in which the input continuous images are enlarged by L times or L1/L2 times. This image contains unnecessary harmonics that occur when the D/A converter 6 converts from a discrete image to a continuous image, so it is necessary to remove this through the analog LPF 7. The final stage also includes the human eye lens system. In this way, enlarged/reduced images of the input continuous images are obtained.

[0017]

Although images can be enlarged/reduced using the conventional methods described above, it is generally difficult to create an analog LPF with flat passband characteristics and steep cutoff characteristics. Therefore, since the analog LPF 7 shown in FIG. 3 does not have a flat pass band or a sharp cutoff characteristic, the enlarged/reduced image is often degraded by the analog LPF 7. In particular, if the cutoff characteristics are not steep, the deterioration will be significant in the high frequency region, but conventional image enlargement/reduction methods do not correct this deterioration caused by the analog LPF 7. Therefore, images that have been enlarged/reduced using the conventional method have lower image quality because the resolution has not been increased, and in particular, images that have been enlarged have lower image quality because the resolution has not increased. Also, even if the image is reduced in size,
There was a noticeable drop in image quality when reducing the image by nearly twice as much.

An object of the present invention is to provide an image enlarging/reducing method that can solve such problems and correct image deterioration caused by the analog LPF applied after D/A conversion.

[0019]

[Means for Solving the Problems] The structure of the image enlargement/reduction method of the present invention is to perform sampling at equal intervals in two directions orthogonal to a first image on a continuous plane, with sampling intervals of X and Y, respectively. By doing so, a first discrete image is generated, and by inserting samples whose values are 0 except for the samples included in this first discrete image, the sample intervals in the two orthogonal directions are respectively set to X/L1.
, Y/L1 (L1 is an integer) to generate a second discrete image, and apply a digital low-pass filter to the second discrete image to obtain the first discrete image. A third discrete image is generated by performing interpolation of Then, a second image on a continuous plane is generated by performing digital-to-analog conversion to multiply the sample intervals in the two orthogonal directions of this fourth discrete image by L1/L2, and In the image enlarging/reducing method, the digital low-frequency The frequency characteristic of the band pass filter is characterized in that it has a characteristic that corrects the characteristic of the analog low pass filter.

[0020]

[Operation] The image enlargement/reduction method of the present invention is characterized by correcting image deterioration caused by an analog LPF applied after D/A conversion. This deterioration correction method is
This is done by emphasizing the frequency components that deteriorate in advance, using a technique called image restoration. This is a method of estimating the original image before deterioration from the deteriorated image and the impulse response representing the deterioration.

First, image restoration will be explained. D/
Since the analog LPF applied after A conversion is generally a linear, position-invariant filter, a method for restoring an image degraded by such a filter will be described.

[0022] The original image is f(x, y), the impulse response representing deterioration is k(x, y), the output image (degraded image) is g(x, y), and the noise added during the deterioration process is n. (x, y
) and a continuous system (assuming that x represents the horizontal direction and y represents the vertical direction coordinate), these relationships are expressed by the following equation (6).

[0023]

Image restoration g(x,y) is performed by applying a filter called a restoration filter. There are various configurations for this restoration filter, for example, the document “0 Pl
It is explained in detail in "Chapter 3: Image Restoration" in the USE special volume, "Latest Trends in Image Processing Algorithms", edited by Takagi, Toriwaki, and Tamura, New Technology Communications.

[0025] Here, Wiener (Wie
A restoration filter using a ner) filter will be explained. If the transfer function of this Wiener filter is W(u,v) (u is the horizontal frequency and v is the vertical frequency), then W(u,v) is the degradation transfer function (i.e., the impulse Fourier transform of the response k(x,y)) is expressed as K(u
, v), it is expressed as equation (7).

[0026]

Here, K*(u,v) represents the complex conjugate of K(u,v), and δ is a constant determined based on the relative magnitude of the original image and noise. This Wiener filter exhibits a characteristic of approximately 1/K(u,v) at frequencies where the absolute value of K(u,v) is large compared to δ, and K(u,v)
In addition, at frequencies where the absolute value of K(u,v) is smaller than δ, the gain of W(u,v) is suppressed by δ to avoid instability. are doing. Therefore, if the transfer function of the analog LPF to be applied after D/A conversion is K(u,v), we construct the Wiener filter of equation (7) from this, and apply this to the original image.
, v), thereby pre-emphasizing the frequency components that decrease, and the output image becomes an image close to the original image with the deterioration corrected.

The filter used for image interpolation according to the present invention is an LPF that is a combination of this restoration filter and an LPF with frequency characteristics expressed by equations (3) to (5). In other words, it is a filter that performs the same operation as performing image interpolation by correcting in advance the deterioration caused by the analog LPF applied after D/A conversion.

[0029]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a block diagram illustrating an image enlargement method according to an embodiment of the present invention. The A/D converter 3 samples (the sampling intervals in the horizontal and vertical directions are X and Y, respectively) and quantizes the discrete images a(m,n)(m,n
is an integer). And oversample 9
Then, as in Figure 4(b), oversample by a factor of L to create a discrete image b(m,n), that is, b(m,n)
is expressed as equation (1).

Next, the digital LPF 11 is applied. This digital LPF11 is an analog L that is applied after D/A conversion.
This is a filter that combines a restoration filter that pre-compensates for the deterioration caused by PF7 and a digital LPF of equation (3) that calculates the correct value of the inserted sample with the value set to 0. When using a filter, this frequency characteristic H2 (exp[jω1 ′], ex
p[jω2']) is expressed as the following equation (8).

[0031]

Here, the frequency of ω1 ′=2π corresponds to L/X, and the frequency of ω2 ′=2π corresponds to L/Y, and equation (8) is expressed as |ω1 ′|≦π, |ω2 ′|≦π It shows the range. Also, W′(exp[jω1], exp[jω2
]) is a periodic function obtained by sampling W(u,v) in equation (7) at a period of 1/X and 1/Y in the horizontal and vertical directions, respectively, and |ω1 |≦π, |ω2 In the range |≦π, it can be expressed as equation (9).

[0033]

However, the frequency of ω1 = 2π corresponds to 1/X, and the frequency of ω2 = 2π corresponds to 1/Y. The operation of this digital LPF 11 is as follows. a(m,n)
The Fourier transform of A(exp[jω1 ], exp[j
ω2 ]) (ω1 and ω2 correspond to the frequency of ω1 = 2π corresponding to 1/X, and the frequency of ω2 = 2π to 1/Y)
Then, the Fourier transform B(exp[j
ω1 ′],exp[jω2 ′])(ω1 ′=2π
The frequency of ω2′=2π is L/Y, and the frequency of ω2′=2π is L/Y.
) corresponds to equation (2). Therefore, the image passing through the digital LPF 11 is c(m, n), and its Fourier transform is C(exp[jω1'], exp[jω
2']), this becomes equation (10).

[0035]

Here, W′(exp[jLω1′], e
xp[jLω2 ′])A(exp[jLω1 ′],
exp[jLω2']) is the Fourier transform of the image obtained by oversampling the image that has been pre-compensated for deterioration in the analog LPF 7 by a factor of L, and H1 (exp[j
Multiplying ω1 ′], exp[jω2 ′]) gives 1
The period is extracted and the correct value of the inserted sample is determined using oversampling. Therefore, digital LPF11
The interpolated image is one in which deterioration in the analog LPF 7 is corrected in advance. In this way, L-times interpolation of the discrete image can be performed. The discrete image obtained in this way has been corrected in advance for deterioration caused by the analog LPF 7.

Next, the sample interval of the discrete image interpolated by L times by the D/A converter 6 is made equal to the sample interval of the original image to generate continuous images, thereby making it possible to enlarge the image by L times. . Unnecessary harmonics generated when generating continuous images from discrete images are removed by analog LPF 7, and continuous images enlarged by L times can be generated. Furthermore, since the digital LPF 11 has the characteristic of pre-compensating the deterioration caused by the analog LPF 7, the continuous images obtained by this image enlarging method are enlarged images in which the deterioration caused by the analog LPF 7 has been corrected, and are larger than the enlarged images obtained by the conventional method. The resolution will also increase.

In the filter processing used here, as in the conventional example, the oversampled image is converted into a frequency domain sample using discrete Fourier transform, and the digital L of equation (8) is
This can be achieved by multiplying the frequency characteristics of the digital LPF 11 by discrete inverse Fourier transform, or by performing discrete inverse Fourier transform on the frequency characteristics of the digital LPF 11 to obtain an impulse response, and convolving the impulse response with an oversampled image. Note that this method assumes that an ideal filter can be constructed, but in reality it is not possible to construct an ideal filter, so the frequency characteristics of the digital LPF 11 are sufficiently similar to the frequency characteristics of equation (8). The closer the better.

FIG. 2 is a block diagram illustrating another embodiment of the image enlarging method of the present invention. This is the discrete image L1
A case is shown in which after performing double interpolation, downsampling is performed by 1/L2 times (L1, L2 are integers, L1 > L2 > 1) and the original image is enlarged by L1/L2 times. 1st
Similar to the embodiment, the A/D converter 3 performs sampling and quantization to generate a discrete image a(m,n), which is multiplied by L1 using the oversampling 9 as in FIG. 4(b). After oversampling, a discrete image b(m,
n) and apply digital LPF11. The digital LPF 11 is a filter that combines a restoration filter that pre-compensates for the deterioration caused by the analog LPF 7 that is applied after D/A conversion, and a digital LPF of equation (3) that calculates the correct value of the inserted sample with the value set to 0. When using the Wiener filter expressed by equation (7), this frequency characteristic H3 (exp[jω1 ′] , exp[j
ω2 ′]) is expressed in the same way as the above-mentioned equation (8). However, in equation (8), H2 may be replaced by H3 and L may be replaced by L1. Further, its Fourier transform is similarly expressed in the same manner as the above-mentioned equation (10).

Here, W′(exp[jL1 ω1′]
,exp[jL1 ω2 ′])A(exp[jL1
ω1 ′], exp[jL1 ω2 ′]) is the L1
It is the Fourier transform of the image oversampled twice, and H1 (exp[jω1 ′] , exp[j
By multiplying by ω2 ′] ), one period is extracted, and the correct value of the inserted sample is obtained by oversampling. Therefore, the image interpolated by applying the digital LPF 11 has the deterioration caused by the analog LPF 7 corrected in advance. This is downsampled to 1/L2 by 12 as in Figure 5(a).
Downsample by a factor of 2 and perform interpolation by a factor of L1/L2. Here, L1 > L2 > 1, so 1/L2
No aliasing noise occurs even if the sample is down-sampled twice. In this way, the deterioration in analog LPF7 is corrected in advance.
Interpolation can be performed by a factor of 1/L2.

Next, the D/A converter 6 converts L1/L
By generating continuous images by making the sample interval of the double interpolated discrete image equal to the sample interval of the original image, it is possible to enlarge the image by a factor of L1/L2. By removing unnecessary high frequencies generated when continuous images are generated from discrete images using the analog LPF 7, continuous images enlarged by L1/L2 times can be generated.

Next, an embodiment of the image reduction method of the present invention will be described. This is calculated by interpolating the discrete image by L1 times, then by 1/L2 (L1, L2 are integers, L2 > L1
>1) Downsample and L1/L2 of the original image
This is a method of doubling the reduction, and the digital LPF 1 in Fig. 2
This can be achieved by changing the characteristic of 1 to a reduction method.

In this embodiment, similarly to the image enlargement method,
The A/D converter 3 performs sampling (sample intervals in the horizontal and vertical directions are X and Y, respectively) and quantization to generate a discrete image a(m, n) (m, n are integers). This is oversampled by a factor of L1 using oversampling 9, as in FIG. 4(e), to create a discrete image b(m,n). That is, b(m, n) becomes as shown in equation (1).

Next, the digital LPF 11 is applied. This digital LPF 11 is a restoration filter that corrects in advance the deterioration caused by the analog LPF 7 applied after D/A conversion, and a restoration filter that calculates the correct value of the sample inserted with the value set to 0 (
When the Wiener filter expressed by equation (7) is used as the restoration filter in a filter that synthesizes the digital LPF of equation (3), this frequency characteristic H4 (exp[jω1 ′
] , (exp[jω2′]) is expressed as in equation (11).

[0045]

Here, ω1' and ω2' are the angular frequencies normalized by the horizontal and vertical sampling intervals, respectively.
The frequency of 1 ′=2π becomes L1 /X, ω2 ′=2π
The frequency of corresponds to L1 /Y, |ω1 ′|≦π, |
The range of ω2 ′|≦π is shown. This formula | ω1 ′
The range of |≦π/L2 and |ω2 ′|≦π/L2 corresponds to one cycle of equation (10). Therefore, in this case, the digital LPF 11 calculates the correct value of the inserted sample by oversampling L1 times, and then converts it to the analog LPF.
The operation is the same as applying a digital filter that has the characteristic of pre-compensating for the deterioration in 7. Therefore, digital LP
The discrete image that has passed through the F11 has been corrected in advance for deterioration caused by the analog LPF 7.

Similar to FIG. 4(g), downsample 12 is used to downsample 1/L2 times, resulting in L1/L.
Performs double interpolation. Here, in equation (11), the cutoff frequency is set to π/L2 and frequency components higher than this are excluded, so no aliasing noise occurs even if downsampled to 1/L2. In this way, it is possible to perform interpolation times L1/L2 in which deterioration in the analog LPF 7 is corrected in advance. This filter processing can be performed in the same way as the image conversion method, so a description thereof will be omitted.

Next, as in FIG. 2, continuous images are generated by making the sample interval of the discrete image interpolated by L1/L2 times by the D/A converter 6 equal to the sample interval of the original image. , can be reduced by a factor of L1/L2. Then, unnecessary harmonics that occur when generating continuous images from discrete images are removed by analog LPF 7, and L1/L2
It is possible to generate continuous images reduced in size. Digital LPF1
1 has the characteristic of pre-compensating the deterioration caused by the analog LPF 7, so the continuous images obtained by this image reduction method have higher resolution than the reduced images by the conventional method.

[0049]

As explained above, the present invention corrects the deterioration caused by the analog LPF applied to the image obtained by the image enlargement/reduction method after D/A conversion, so that the image obtained by the image enlargement/reduction method can be enlarged/reduced using the conventional method. This has the effect of generating an enlarged/reduced image with higher resolution than the reduced image.

[Brief explanation of drawings]

FIG. 1 is a block diagram of an embodiment of the present invention in which an image is enlarged by an integral number of times.

FIG. 2 is a block diagram of an embodiment of the present invention in which an image is enlarged by a rational number of times.

FIG. 3 is a block diagram illustrating a conventional method for enlarging/reducing images on a continuous plane.

FIG. 4 is a schematic diagram illustrating a conventional method of interpolating an image to an integral multiple.

FIG. 5 is a schematic diagram illustrating a conventional method of interpolating an image by a rational number.

[Explanation of symbols]

1 Input terminal 2 Analog LPF 3 A/D converter 5 Interpolation section 6 D/A converter 7 Analog LPF 8 Output terminal 9 Oversample 11 Digital LPF 12 Down sample

Claims (3)

[Claims] Claim 1: A first discrete image is generated by sampling at equal intervals in two directions orthogonal to a first image on a continuous plane, with sample intervals of X and Y, respectively. By inserting samples with a value of 0 other than the samples included in the discrete image, the sample intervals in the two orthogonal directions are respectively set to X/L1.
, Y/L1 (L1 is an integer) to generate a second discrete image, and apply a digital low-pass filter to the second discrete image to generate the first discrete image. A third discrete image is generated by performing interpolation of Then, a second image on a continuous plane is generated by performing digital-to-analog conversion to multiply the sample intervals in the two orthogonal directions of this fourth discrete image by L1/L2, and In the image enlarging/reducing method, the digital A method for enlarging/reducing an image, characterized in that the frequency characteristics of the low-pass filter have characteristics that correct the characteristics of the analog low-pass filter. [Claim 2] L1 /L2 is an integer L, and the third
2. The image enlarging method according to claim 1, wherein the second image is generated by digital-to-analog conversion with the sample interval of the discrete image multiplied by L. 3. The image reduction method according to claim 1, wherein L1 is smaller than L2.