JP2000353241A - Signal processing method and device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To prevent the deterioration of high frequency components or the blur of a picture at the time of operating linear interpolation processing. SOLUTION: In this signal processing method, a picture is read by a scanner 1 so that an actual sampled value S1 can be obtained, and linear interpolation processing is operated by a linear interpolation processing part 5 for correcting inclination at the time of reading a picture so that an interpolated sampled value pi can be obtained. Then, variable characteristic filter processing is operated to the interpolated sampled value pi by a filter for compensating the low pass characteristics of the interpolated sampled value pi according to position deviation between the sampled position and the interpolated position so that the blur correction processing of the interpolated sampled value pi can be realized. The corrected picture is transmitted to a picture outputting part 7 so that an inclination-corrected printed matter can be obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] 1. Field of the Invention [0002] The present invention relates to a signal processing method and apparatus, and more particularly, to a signal processing method and apparatus for correcting deterioration of a high-frequency component of a signal, which is a problem in digital signal processing involving linear interpolation processing. .

[0002]

2. Description of the Related Art When performing frame rate conversion of a sampled moving image signal, rotation and enlargement / reduction of an image, or pitch conversion of a sampled audio signal, a point (interpolation position) other than a sample point is used. A signal is needed. As a method for obtaining a signal at a point other than the sample point, for example,
94784, Journal of the Printing Society of Japan (Vol. 32, No. 5, No. 199
5), “Introduction to prepress”) proposes a method using linear interpolation.

[0003]

However, it is known that when linear interpolation is performed, a low-pass characteristic depending on the interpolation position occurs. The analysis of the low-pass characteristic generated by the linear interpolation processing will be described below by taking the interpolation of a one-dimensional signal as an example.

Consider a one-dimensional signal band-limited to -π / T <ω <π / T as shown in FIG. In FIG. 5, f
(T) is a one-dimensional signal serving as a model, and F (ω) is its frequency component. The operation of discretizing f (t) at the sampling period T corresponds to multiplying the original signal f (t) by an impulse train as shown in Expression (1).

[0005]

(Equation 1) Therefore, the signal fs (t) after being discretized is expressed as in Expression (2).

[0006]

(Equation 2) The frequency component of the signal after discretizing the original signal f (t) is obtained by the Fourier transform of fs (t) according to the equation (2), and is represented by the following equation (3).

[0007]

(Equation 3) As can be seen from equation (3), the spectrum of the signal obtained by discretizing the continuous signal f (t) is obtained by repeating the spectrum of the original signal indefinitely at a period of 2π / T as shown in FIG. Therefore, by extracting a frequency component in the range of -π / T <ω <π / T by an ideal low-pass filter, a signal Fsb (ω) shown in the following equation (4) is obtained, and this Fsb (ω) is It can be seen that the original continuous signal f (t) can be completely restored from the signal after discretization by performing the inverse Fourier transform. Here, the ideal low-pass filter outputs a signal in a frequency band satisfying | f | ≦ π / T, and |
A filter having a characteristic of not outputting a signal in a frequency band satisfying f |> π / T, and the characteristic is as shown in FIG.

[0008]

(Equation 4) Next, the influence of the linear interpolation operation on the frequency characteristics of the signal will be considered. In the following, a discrete signal obtained when the sampling timing of the original signal is delayed by τ · T,
Approximately obtained by linear interpolation of fs (t). And
The influence of the interpolation operation on the frequency characteristics of the signal will be considered by analyzing the frequency of the interpolation signal obtained by the linear interpolation. The interpolation signal is as shown in FIG. 8 and is represented by fs ′ (t) in equation (5).

[0009]

(Equation 5) When Equation (5) is Fourier-transformed, Equation (6) is obtained.

[0010]

(Equation 6) The signal of Expression (6) has a form in which a signal whose band is limited by -π / T <ω <π / T is infinitely repeated at a period of 2π / T. Therefore, -π / T <ω <
When a signal in the range of π / T is extracted by an ideal low-pass filter, the following equation (7) is obtained, and a signal close to the spectrum of the original continuous signal can be reproduced. However, unlike the case of Expression (4), the bandpass characteristic indicated by the filter characteristic of Expression (8) is applied to the spectrum of the original signal.

[0011]

(Equation 7)

(Equation 8) The gain characteristic of the filter of equation (8) is as shown in equation (9).

[0012]

(Equation 9) Here, when the expression in the square root on the right side in Expression (9) is modified, it becomes as shown in Expression (9a), and 2 (1-cosT)
ω) ≧ 0, it can be seen that equation (9) has a minimum when τ = １ ／ and a maximum when τ = 0,1. That is, when τ = １ ／, the amount of attenuation becomes maximum, and when τ = 0, 1, there is no attenuation.

[0013]

(Equation 10) Also,

[Equation 11] Since it is considered that 0 ≦ τ ≦ 1, it is understood that the amplitude ratio has a characteristic as shown in FIG. 9 when τ is fixed. It can be seen from FIG. 9 that the filter of equation (8) has low-pass characteristics and that the attenuation of high-frequency components (high-frequency components) changes depending on τ. In addition,
Equation (10) shows the filter characteristics when τ = １ ／.

[0014]

(Equation 12) As described above, the low-pass characteristic generated by the one-dimensional signal interpolation processing is analyzed.
It also occurs when interpolation of a dimensional sample signal is performed. Some 2
A low-pass characteristic generated when a sample signal obtained when the sample position of the two-dimensional signal is translated by (dx · Tx, dy · Ty) by linear interpolation approximation from the original two-dimensional sample signal is expressed by the following equation. This is shown in (11). Where Tx and Ty
Is the sampling period in the x-axis and y-axis directions, respectively. Therefore, (dx, dy) represents the translation amount of the sample position normalized by the sampling period.

[0015]

(Equation 13) However, the low-pass characteristic of equation (11) occurs when the sample value at the interpolation position is obtained from the sample values of the original four sample points surrounding the interpolation position by linear interpolation approximation of equation (12). is there.

[0016]

[Equation 14] As in the case of the one-dimensional signal, the filter of the equation (11)
The normalized position deviation (d between the original sample position and the interpolation sample position
(x, dy) has a low-pass characteristic in which the attenuation of the high-frequency component changes. The attenuation of the high frequency component is dx = 0 or dx =
1 and minimum (no attenuation) when dy = 0 or dy = 1. When dx = 1/2 and dy = 1/2, the amount of attenuation becomes maximum. Equation (13) shows the filter characteristics when dx = １ ／ and dy = １ ／.

[0017]

(Equation 15) As described above, when the linear interpolation processing is performed, high-frequency components are deteriorated depending on the interpolation position. Therefore, the frequency characteristic of the interpolated signal differs from the frequency characteristic of the original signal due to the difference in the amount of delay or movement between the case where the delay of the audio signal and the parallel movement of the image are performed by the linear interpolation processing. Problem.

Further, when the fine adjustment of the frame rate of the moving image signal, the fine angle rotation of the image, the fine adjustment of the enlargement / reduction ratio, or the fine adjustment of the voice pitch are performed by linear interpolation, a more complicated problem occurs. I do. If the adjustment amount is small,
When the signal is viewed locally, the positional deviation between the sample position and the interpolation position is kept substantially constant. However, when the signal is viewed globally, the positional deviation fluctuates greatly periodically.
There is a problem that blurring of an image occurs in an image signal and muffled sound occurs periodically in an audio signal.

The present invention has been made in view of the above circumstances, and it is an object of the present invention to provide a signal processing method and apparatus capable of preventing deterioration of a high frequency component and blurring of an image when performing the above-described linear interpolation processing. Is what you do.

[0020]

According to the present invention, there is provided a signal processing method for obtaining an interpolation signal at an interpolation position other than a sampling position from a discrete signal obtained by sampling an original signal by a linear interpolation process. A variable characteristic filter processing for compensating a low-pass characteristic of the linear interpolation processing according to a positional deviation between a position and the interpolation position is performed on the interpolation signal.

In the signal processing method of the present invention, it is preferable that the variable characteristic filter processing is a filter processing using a filter having a transfer function having an inverse function of a low-pass characteristic of the linear interpolation processing.

Further, it is preferable that the variable characteristic filter process is a filter process for changing an applied strength of a differential operator according to a positional deviation between the sample position and the interpolation position.

A signal processing apparatus according to the present invention is a signal processing apparatus for obtaining an interpolation signal at an interpolation position other than a sample position by linear interpolation from a discrete signal obtained by sampling an original signal. And a filter processing means for performing a variable characteristic filter process for compensating a low-pass characteristic of the linear interpolation process in accordance with the positional deviation of the interpolation signal with respect to the interpolation signal.

The filter processing means may be means for performing filter processing using a filter having a transfer function that is an inverse function of the low-pass characteristic of the linear interpolation processing, or may apply an applied strength of a differential operator to the sample position and the interpolation position. It is preferable to use a means for performing a filter process of changing the position in accordance with the positional deviation from.

[0025]

According to the present invention, the variable filter processing for compensating for the low-pass characteristic of the linear interpolation processing is performed on the interpolation signal in accordance with the positional deviation between the sample position and the interpolation position. It is possible to effectively correct deterioration of a high-frequency component of a signal, which is a problem in digital signal processing involving interpolation processing. In addition, by applying the present invention to image processing and audio signal processing, periodic adjustments that occur when fine adjustment of the frame rate of a moving image signal, fine angle rotation of an image, and fine adjustment of an enlargement / reduction ratio are performed. It is possible to improve the blurring of an image and the periodic muffled sound that occurs when the sound pitch is finely adjusted.

[0026]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a schematic block diagram showing a configuration of a copying apparatus having a function of correcting the inclination of a document to which a signal processing apparatus according to an embodiment of the present invention is applied. The skew correction function of the present apparatus corrects a slight skew angle within several degrees, such as a skew of printing on a manuscript sheet and an angle error between the scanner and the manuscript sheet that occurs when reading the manuscript.

A sample value S1 (hereinafter, referred to as an actual sample value) of an image read and sampled by the scanner 1 is temporarily stored in an image memory 2, and a tilt angle of an input image, that is, a tilt of the image, is detected by a tilt angle detector 3. Rotation angle θ to correct
1 is detected. Note that the tilt angle detection unit 3 may be configured so that the operator directly inputs the tilt angle. The tilt angle detection unit 3 outputs the detected rotation angle θ1 to the oblique scanning coordinate calculation unit 4.

The rotation of the image is performed by obliquely scanning the original image at an inclination equal to the rotation angle θ1 and re-sampling the original image. This principle will be described with reference to an example of inclination correction of a character string image having an inclination of an angle θ0 as shown in FIG. In FIG. 2A, the horizontal direction is the x-axis, and the vertical direction is y.
For the axis, the center of the image is the coordinate origin. A position where sampling is performed by the scanner (hereinafter referred to as an actual sample position) (x
m, yn) is

(Equation 16) Becomes Here, Tx and Ty in Expression (14) are sampling periods in the x and y directions, respectively, and (m, n)
Is

[Equation 17] It is. Therefore, the size of the image captured by the scanner 1 is as shown in Expression (16).

[0030]

(Equation 18) In order to correct the tilt by rotating the image of FIG. 2A by an angle −θ0, the main scanning is performed at an angle of θ0 as shown in FIG. What is necessary is just to resample the image data in the indicated area. That is, xy
The new coordinate system obtained by rotating the coordinate system by θ0 is x'-y '
When an image is viewed on this coordinate system as a coordinate system, FIG.
The inclination of the image is corrected.

The coordinates of the m-th sample point on the n-th main scanning line in the x'-y 'coordinate system are (x'm, y'n)
And The position (x'm, y ') on the x'-y' coordinates
n) corresponds to the position of (x "m, y" n) in the xy coordinate system, the coordinate between (x "m, y" n) and the coordinate (xm, yn) is The relationship shown in Expression (17) exists.

[0032]

[Equation 19] Then, by re-sampling the original image using the coordinates (x "m, y" n) as a new sample point, the image can be rotated.

However, in general, the coordinates (x "m, y")
n) does not match the actual sample position. Further, since only the sample values at the actual sample position S1 having the coordinates (xm, yn) of Expression (14) as the sample points are stored in the image memory 2 of FIG. 1, the coordinates (x In order to obtain the sample value at "m, y" n), it is necessary to perform some pixel value restoration processing. Here, from the sample values of the four actual sample points surrounding the coordinates (x ″ m, y ″ n), the coordinates (x ″ m,
A method of approximately restoring the pixel value at y "n) will be described.

The coordinates of the four actual sample points surrounding the coordinates (x "m, y" n) are (xa, yb) and (xa + Tx, y
b), (xa, yb + Ty), (xa + Tx, yb + T
y). The oblique scanning coordinate calculator 4 in FIG. 1 calculates memory addresses corresponding to these four points, and outputs them as read addresses of the image memory 2. The sample values S2 of the four actual sample points are read from the image memory 2, and the read sample values S2 are sent to the linear interpolation processing unit 5.

The linear interpolation processing unit 5 uses the sample value S2 of the four actual sample points and the positional deviation between the interpolated sample position and the actual sample position to calculate the interpolated sample value pi at the coordinates (x "m, y" n). (X "m, y" n) is obtained by linear interpolation. At this time, the positional deviation between the interpolation sample position and the actual sample position (dx · T
x, dy · Ty) is represented by equation (18).

[0036]

(Equation 20) From equation (18), (x ″ m, y ″ n) = (xa + dx · T
x, yb + dy · Ty), the interpolation sample value pi can be obtained by setting x = xa and y = yb in equation (12).
(X "m, y" n) can be obtained. Equation (12)
The position deviation (dx, dy) normalized by the sampling period used in is output from the oblique scanning coordinate calculator 4. As described above, the apparatus according to the present embodiment aims to correct a small tilt angle, and under the condition that the tilt correction angle is small, the normalized position deviation ( dx, dy) is substantially constant. To verify this, in the following, the interpolation sample point (x ″
m, y "n) and (x" m + i, y "n + j)
The respective normalized position deviations (dx, dy) and (d
x ', dy'). Where (x "m + i, y" n
+ J) is the position (x'm, y ') on the x'-y' coordinate.
Interpolated sample points (x'm + i, y'n + j) separated by i samples in the x'-axis direction and j samples in the y'-axis direction from n)
In the xy coordinate system. The relationship shown in equation (19) exists between the normalized position deviations (dx, dy) and (dx ', dy').

[0037]

(Equation 21) In Expression (19), θ1 represents a tilt correction angle. Since the apparatus according to the present embodiment is intended to correct a slight tilt angle, θ1 is a very small angle. Therefore, if there is no significant difference between the sampling periods in the main scanning direction and the sub-scanning direction, when i and j in Expression (19) are small integers, the normalized position deviations of the two interpolation sample points become substantially equal. That is, the normalized position deviation between neighboring interpolation sample points is substantially constant. Conversely, when i or j is a large integer, the normalized position deviations of the two interpolation sample points are significantly different. In other words, the normalized position deviation between interpolation sample points that are far apart greatly differs.

On the other hand, it can be seen from the above equation (11) that the low-pass characteristic generated by interpolation is determined by (dx, dy). From this, when the minute inclination angle is corrected by the linear interpolation processing, the normalized position deviation (dx, dy) is locally substantially constant, so that the low-pass characteristic generated by the interpolation processing is also locally. It can be understood from the above that it can be considered substantially constant. In general, the size of a two-dimensional FIR filter used in digital image processing is often as small as about 3 × 3 or 5 × 5 because of the ease of circuit configuration. From the above, since the low-pass characteristic in a local region of about 3 × 3 or 5 × 5 may be considered to be substantially constant, blur caused by linear interpolation is corrected by ordinary correction filter processing using an inverse filter or the like. be able to. However, since the low-pass characteristics, which are almost constant within the local area, vary greatly depending on the location when viewed globally, the blur correction of the entire image must be properly performed with the correction filter processing of a single characteristic. Can not. Therefore, a correction filter process with variable characteristics is required.

In the variable characteristic filter processing section 6 shown in FIG. 1, the interpolation sample value p output from the linear interpolation processing section 5 is used.
For i (x ″ m, y ″ n), a process of correcting blurring of an image caused by the linear interpolation process is performed. As shown in Expression (11), the characteristic of the generated blur changes due to the positional deviation between the interpolation position and the sample position. Therefore, the variable characteristic filter processing unit 6 sets the band according to the value of (dx, dy). A blur correction process using filters having different pass characteristics is performed. In the following, two ways of realizing the variable characteristic filter processing will be described.

One of the methods for implementing the variable characteristic filter processing is to apply an inverse filter having an inverse function of a low-pass characteristic generated by interpolation as a transfer characteristic to the interpolated image. As shown in equation (11), since the low-pass characteristic generated by interpolation differs depending on the position deviation between the interpolation position and the sample position, the transfer function of the inverse filter must also be variable according to the position deviation. . Especially when high-speed processing is not required, DSP (Digital Signal Processor)
The digital filter having the above-described variable characteristics can be configured by signal processing by software using the above-described method.

On the other hand, in applications requiring high speed, FIG.
By constructing dedicated hardware of the filter bank type as shown in (1), a filter with variable characteristics can be realized. According to the filter bank method shown in FIG.
Since a desired inverse filter characteristic can be accurately realized, highly accurate blur correction can be performed. However, in order to increase the accuracy of the correction, a filter bank including a large number of filters must be used, and there is a problem that the circuit scale becomes large.

Another way to implement variable characteristic filtering is to use a differential operator as shown in FIG.
This is a method of changing the applied strength by weighting.
In this method, the accuracy of the blur correction is lower than in the filter bank method, but the variable characteristic filter processing can be approximately realized with simpler hardware.

In the example of FIG. 4, a Laplacian operator is used as a differential operator. The interpolated sample values and the filter output in FIG. 4 are represented by pi (x ', y') and p
If if (x ', y', dx, dy), the filter output is as shown in equation (20).

[0044]

(Equation 22) The function k () in equation (20) determines the applied strength of the Laplacian operator. As described above, the blur generated by the interpolation processing is such that the normalized position deviation (dx, dy) of the interpolation position from the sample position is (dx, dy) = (1
/ 2, 1/2), and becomes smaller as the interpolation position approaches the sample position. If the interpolation position matches the sample position, no blur occurs. Therefore, the function k () takes the maximum value when (dx, dy) = (1/2, 1/2), becomes smaller as the interpolation position approaches the sample position, and furthermore, the interpolation position and the sample position match. In this case, if a function that becomes zero is selected, a variable characteristic filter process that approximately compensates for the low-pass characteristic by the interpolation process can be realized. An example of such a function k () is shown in Expression (21).

[0045]

(Equation 23) The gain determination circuit in FIG. 4 outputs a gain adjustment signal having a magnitude as shown in Expression (21).

As described above, the process of correcting the blur generated in the image by the interpolation process is performed, and the image after the correction is sent to the image output unit 7 in FIG. 1 to obtain a printed material subjected to the tilt correction process. Can be

[Brief description of the drawings]

FIG. 1 is a schematic block diagram showing a configuration of a copying apparatus with a document skew correction function to which a signal processing device according to an embodiment of the present invention is applied.

FIG. 2 is a diagram for explaining the principle of tilt correction.

FIG. 3 is a diagram showing a variable characteristic filter using a filter bank;

FIG. 4 is a diagram showing a variable characteristic filter using a differential operator.

FIG. 5 is a diagram illustrating frequency characteristics of a one-dimensional signal to be evaluated;

FIG. 6 is a diagram showing discretization of f (t).

FIG. 7 is a diagram showing characteristics of an ideal low-pass filter.

FIG. 8 is a diagram showing a state in which a discrete signal obtained by adding a delay τT to a sampling timing is approximated by linear interpolation.

FIG. 9 is a diagram showing characteristics of the filter of Expression (8).

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Scanner 2 Image memory 3 Tilt angle detection part 4 Oblique scanning coordinate calculation part 5 Linear interpolation processing part 6 Variable characteristic filter processing part 7 Image output part

Claims (6)

[Claims] 1. A signal processing method for obtaining an interpolation signal at an interpolation position other than a sample position from a discrete signal obtained by sampling an original signal by a linear interpolation process, wherein the interpolation signal is obtained according to a positional deviation between the sample position and the interpolation position. A signal processing method, wherein a variable characteristic filter process for compensating for a low-pass characteristic of the linear interpolation process is performed on the interpolation signal. 2. The signal processing method according to claim 1, wherein the variable characteristic filter processing is filter processing using a filter having a transfer function having an inverse function of a low-pass characteristic of the linear interpolation processing. 3. The signal processing according to claim 1, wherein the variable characteristic filter processing is a filter processing that changes an applied strength of a differential operator according to a positional deviation between the sample position and the interpolation position. Method. 4. A signal processing apparatus for obtaining an interpolation signal at an interpolation position other than a sample position from a discrete signal obtained by sampling an original signal by a linear interpolation process, according to a positional deviation between the sample position and the interpolation position. A signal processing apparatus comprising: a filter processing unit that performs a variable characteristic filter process for compensating a low-pass characteristic of the linear interpolation process on the interpolation signal. 5. The signal processing apparatus according to claim 4, wherein said filter processing means is a means for performing a filter processing by a filter having an inverse function of a low-pass characteristic of said linear interpolation processing as a transfer function. . 6. The filter processing means according to claim 4, wherein said filter processing means is a means for performing filter processing for changing an applied strength of a differential operator according to a positional deviation between said sample position and said interpolation position. Signal processing device.