KR101589719B1 - Method for detecting motion in low light level enviroment - Google Patents

Abstract

According to an embodiment of the present invention, a method for detecting motion in a low light level environment improves a detection error in monitoring equipment, and comprises: a step of receiving an image from a camera; a step of using a bilateral filter to remove noise of a first and a second frame image in the received image; a step of converting the first and the second frame image from which the noise is removed into a frequency domain; a step of filtering the first and the second frame image converted into the frequency domain using a contrast sensitivity function filter; a step of restoring the filtered first and second frame images in the frequency domain into a spatial domain; a step of calculating a difference image between the restored first and second frame images; and a step of comparing pixel values of the calculated difference image with a motion occurrence threshold to detect a motion occurrence.

Description

TECHNICAL FIELD [0001] The present invention relates to a motion detection method in a low-

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a motion detection method in a low-illuminance environment, and more particularly, to a motion detection method in which motion detection error is improved in a monitoring apparatus in a low-illuminance environment.

A general motion detection technique is a method of notifying that a motion has occurred when a pixel value difference between a first frame and a second frame in a closed circuit television (CCTV) system is higher than a threshold set by the user.

Specifically, the motion detection method used in the CCTV camera compares the pixel values of the current frame and the previous frame. If the motion detection method is higher than the threshold value set by the user, it is recognized as a motion occurrence. Next, the motion detection method mainly uses a method of giving a warning signal to the user.

The image sensor of CCTV camera used for security is changing rapidly from CCD (charge coupled device) to CMOS. This is because CMOS image sensors are easier to convert to digital signals than CCD image sensors. In addition, the CMOS image sensor is easy to increase the number of pixels and is inexpensive. In a CMOS image sensor, such a motion detection method is not problematic in a high-illuminance environment. However, in the case of a low-illuminance night or an indoor low-illuminance environment, a noise of a CMOS (Complementary Metal-Oxide Semiconductor) image sensor frequently occurs, resulting in an unexpected warning by a user.

That is, when a CMOS image sensor is used, if noise occurs in a low-illuminance environment, the noise is recognized as a motion. CMOS image sensors have the problem of frequent occurrence of noise at low illumination, and therefore there is a possibility of generating false alarms (unwanted) when detecting motion.

In a low-light environment, Salt-Pepper noise occurs in a low-frequency region, that is, a flat image. Then, the surveillance and reconnaissance device provided with the CMOS image sensor recognizes a motionless scene as a motion and notifies the user of a false alarm.

Embodiments of the present invention provide a motion detection method in a low illumination environment that can reduce errors in detection of motion due to noise by calculating an accurate motion generation value by performing image processing on a first frame and a subsequent frame for motion detection .

According to the present invention, there is provided an image processing method comprising: receiving an image from a camera; Removing noise of the first and second frame images from the input image using a bilateral filter, respectively; Transforming the noise-removed first and second frame images into a frequency domain, respectively; Filtering the first and second frame images of the transformed frequency domain through a Contrast Sensitivity Function filter; Restoring the first and second frame images of the filtered frequency domain into a spatial domain; Calculating a difference image between the restored first and second frame images; And comparing the pixel value of the calculated difference image with a motion occurrence threshold to detect motion occurrence.

The receiving of the image may be performed by acquiring an image from a camera equipped with a complementary metal-oxide semiconductor (CMOS) image sensor.

The method may further include the step of selecting a selected image region by the user in the input image, and the removing may remove noise of the first and second frame images in the selected selected image region .

The method includes: calculating an illuminance on the input image; And extracting a low-illuminance image region in which the calculated illuminance is less than a preset illuminance from the input image, wherein the removing includes removing noise of the first and second frame images in the extracted low- Can be removed.

The method of claim 1, wherein the step of removing the salt-pepper noise in the first and second frame images is performed by using a Fast-by-Letter filter in a low frequency region while maintaining a sharp edge component of the first and second frame images. Bilateral Filter), respectively.

The high-speed by-product filter converts the low-frequency noise into a low-frequency region in the first and second frame images according to Equation (1), which is weighted by a Gaussian filter of a spatial domain and a Gaussian filter of a light intensity domain, Pepper noise can be removed, respectively.

[Equation 1]

(Wherein, p, q is the pixel location, I _p is p pixel values of the input image I, Ω is a pixel near the value of p, k _p is normalized (Normalizing) factor, f, g are Gaussian by σ _s, σ _r Function, J _p represents the filtered image.)

The filtering may filter the first and second frame images of the transformed frequency domain to compensate for edge components lost by the bi-lateral filter.

Wherein the filtering is performed using a contrast sensitivity function filter using a frequency of a low-frequency lobe, a frequency of a high-frequency lobe, and a weight of a low-frequency lobe according to Equation (2) ) ≪ / RTI >

&Quot; (2) "

( Where f ₀ is a lobe in a low frequency region, f ₁ is a lobe in a high frequency region, and ? Is a weight in a low frequency region).

Embodiments of the present invention can prevent a motion detection error in a low-illuminance environment in a camera using a CMOS image sensor, since accurate alerting in a security system is an important issue for a user.

Embodiments of the present disclosure can be used as precise motion detection methods for monitoring surveillance equipment and CCTV cameras used in low-light environments.

Embodiments of the present invention solve the problem of generating a false alarm due to noise in a low-illuminance environment because a function of giving a warning to a user when an event such as a motion occurs in a scene viewed by a camera.

1 is a block diagram of a motion detection apparatus in a low-illuminance environment according to an embodiment of the present invention.
2 is an explanatory diagram of the contrast sensitivity function of the Barton model applied to the present specification.
3 is an explanatory diagram of a contrast sensitivity function according to an embodiment of the present invention.
FIG. 4 is an explanatory diagram of a detection error in a conventional motion detection apparatus. FIG.
5 is an explanatory diagram of motion detection in a motion detection apparatus according to an embodiment of the present invention.
6 is an explanatory diagram of a motion generation event in the motion detection apparatus according to an embodiment of the present invention.
7 is a flowchart of a motion detection method in a low-illuminance environment according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

In describing the embodiments, descriptions of techniques which are well known in the technical field to which this specification belongs and which are not directly related to this specification are not described. This is for the sake of clarity without omitting the unnecessary explanation and without giving the gist of the present invention.

For the same reason, some of the components in the drawings are exaggerated, omitted, or schematically illustrated. Also, the size of each component does not entirely reflect the actual size. In the drawings, the same or corresponding components are denoted by the same reference numerals.

1 is a block diagram of a motion detection apparatus in a low-illuminance environment according to an embodiment of the present invention.

1, the motion detection apparatus 100 according to an exemplary embodiment of the present invention includes an image input unit 110, a bidirectional filter unit 120, an image conversion unit 130, a contrast sensitivity filter unit 140, An image restoration unit 150, a difference image calculation unit 160, and a motion detection unit 170.

Hereinafter, the specific configuration and operation of each component of the motion detection apparatus 100 according to the embodiment of the present invention will be described.

First, the motion detection apparatus 100 acquires an image in a low-illuminance environment, and divides the image for each frame. The surveillance apparatus to which the motion detection apparatus 100 is applied can use an image using only a luminance component rather than a color for obtaining a clear image signal at night.

More specifically, the image input unit 110 receives images from the camera. The image input unit 110 may acquire an image from a camera equipped with a CMOS (Complementary Metal-Oxide Semiconductor) image sensor and receive the image. That is, the image input unit 110 receives the image of the camera using the CMOS image sensor.

For example, the video input unit 110 may transmit the selected video region selected by the user to the bidirectional filter unit 120 in the input video. As another example, the image input unit 110 may calculate the illuminance on the input image, extract the low illuminance image region having the calculated illuminance less than the preset illuminance from the input image, and transmit the extracted low illuminance image region to the bidirectional filter unit 120.

The bidirectional filter unit 120 removes noise of the first and second frame images from the image input from the image input unit 110 using a bilateral filter. That is, the bidirectional filter unit 120 passes the first frame image of the image input from the image input unit 110 to the bilateral filter, thereby maintaining the high frequency part such as the edge of the image as much as possible, Salt-Pepper Noise can be removed. For example, the bidirectional filter unit 120 may be a bilateral filter. Here, to remove the noise of the first and second frame images, two bilateral filters may be used. However, the present invention is not limited to a specific number of binary filters. The bi-linear filter may be a non-linear filter. For example, the bifurcated filter may be composed of two Gaussian filters. The two Gaussian filters may be filters of a spatial domain and an intensity domain.

Specifically, the bidirectional filter unit 120 may be configured to store the Salt-Pepper noise in the low frequency region in the first and second frame images while maintaining the sharp edge components of the first and second frame images, Can be removed using a filter (Fast-Bilateral Filter). At this time, the bidirectional filter unit 120 uses a fast by-product filter for image processing speed. Here, the high-speed by-productal filter is a low-speed, high-resolution filter that extracts low-frequency noise from a low-frequency region in the first and second frame images according to the following Equation 1 to which a weight according to a Gaussian filter of a spatial region and a Gaussian filter of a light intensity region is applied: Pepper noise can be removed, respectively.

Wherein, p, q is the pixel location, I _p is p pixel values of the input image I, Ω is close to the value of pixel p, k _p is normalized (Normalizing) factor, f, g is a Gaussian function by σ _s, σ _r , J _p represents the filtered image.

As shown in Equation (1), the bi-linear filter may be a non-linear filter for eliminating low-frequency noise while maintaining a sharp edge component. The bilateral filter can form a spatial smoothing kernel by multiplying the intensity of a pixel of an input image with a quadratic term. Here, the second term is generally expressed as a range term.

The image converting unit 130 converts the first and second frame images, from which noise has been removed, into the frequency domain through the bidirectional filter unit 120, respectively. The image transform unit 130 moves the first and second frame images into the FFT space. This is for applying the contrast sensitivity function filter in the contrast sensitivity filter unit 140.

For example, the image transforming unit 130 may be implemented by Fast Fourier Transform (FFT). Here, in order to convert the first and second frame images into the frequency domain, it may be composed of two FFTs, but is not limited to a specific number of FFTs.

Since the image passed through the fast by-product filter in the bidirectional filter unit 120 causes damage to the high frequency portion, an operation for compensating the high frequency portion is required.

For this compensation operation, the contrast sensitivity filter unit 140 filters the first and second frame images in the frequency domain converted by the image conversion unit 130 through a contrast sensitivity function (CSF) filter. Here, the contrast sensitivity function (CSF) filter is a filter considering human visual characteristics. The contrast sensitivity function (CSF) filter performs the function of improving only the region most sensitive to the non-noise component. Also, the contrast sensitivity can be referred to as a contrast sensitivity, and it means a sensitivity of brightness contrast or contrast. That is, it means a difference in intensity between bright and dark. Contrast refers to the difference in color or brightness or the intensity of contrast.

The contrast sensitivity filter unit 140 may filter the first and second frame images of the frequency domain converted by the image conversion unit 130 to compensate for the edge components lost by the bilateral filter. The contrast sensitivity filter unit 140 performs a contrast sensitivity function filter using a frequency of a low-frequency lobe, a frequency of a high-frequency lobe, and a weight of a low-frequency lobe according to Equation (2) Components can be compensated.

는 가우시안 함수를 나타낸다.Here, f ₀ is a lobe in a low frequency region, f ₁ is a lobe in a high frequency region, α is a weight in a low frequency region,

Represents a Gaussian function.

The image reconstruction unit 150 reconstructs the first and second frame images of the filtered frequency domain through the contrast sensitivity filter unit 140 into a spatial domain. The image restoring unit 150 is made of Inverse Fast Fourier Transform (IFFT). That is, the image restoring unit 150 restores the image of the FFT space to the original image by IFFT again. Here, in order to recover the first and second frame images into the spatial domain, they may be composed of two IFFTs, but are not limited to a specific number of IFFTs.

The difference image calculating unit 160 calculates a difference image between the first and second frame images reconstructed by the image reconstructing unit 150. The difference image calculating unit 160 calculates the difference image of the first frame and the second frame image-processed through the bidirectional filter unit 120, the image conversion unit 130, the contrast sensitivity filter unit 140, (Difference image). Here, as shown in FIG. 1, the motion detection apparatus 100 may process the first and second frame images separately for each frame and simultaneously process them. As another example, the motion detection apparatus 100 may perform image processing on the first frame image, and may perform image processing on the second frame image when the image processing of the first frame image is completed. Then, the difference image calculation unit 160 of the motion detection apparatus 100 calculates a difference image between the first and second frame images processed at the same time or sequentially.

The motion detecting unit 170 compares the pixel value of the difference image calculated by the difference image calculating unit 160 with a motion occurrence threshold to detect motion occurrence. At this time, the low frequency noise in the low frequency region is removed from the difference image, and only the motion in the high frequency region remains. Therefore, the motion detector 170 can compare the pixel value of the difference image with a threshold value to determine the occurrence of motion.

That is, the motion detector 170 compares the pixel value of the difference between the two images calculated by the difference image calculating unit 160 with a threshold preset by the user. If the pixel value of the difference image is equal to or larger than the threshold value, the motion detector 170 can inform the user of the motion occurrence. On the other hand, if the pixel value of the difference image is less than the threshold value, the motion detector 170 determines that the motion event does not occur and does not warn the user. Here, the motion generation threshold value may be preset in advance by the motion generation threshold desired by the user. In addition, the motion generation threshold may be preset to an initial value of the motion detection apparatus 100 and stored in the motion detection unit 170. [

2 is an explanatory diagram of the contrast sensitivity function of the Barton model applied to the present specification.

The Contrast Sensitivity Function of the Barton model was developed in two models. One model is relatively complex and physiologically inspirational. Other models are relatively simple and empirically fit for psychophysical data. The latter model is expressed by the following equation (3).

, here,

,

,

를 나타낸다.

,

.

Where f is the spatial frequency of the stimulus [cycle / degree], w is the stimulus size in degrees of visual angle, L is mean luminance [cd / m ² ].

The contrast sensitivity function consists of the spatial frequency of the X axis and the contrast sensitivity of the Y axis. An example of the case where the stimulus size is 10 [cycle / degree] and the average luminance is 50 (dashed line), 2.5 (dash line), 0.025 (thick solid line) [cd / m ² ] Respectively.

3 is an explanatory diagram of a contrast sensitivity function according to an embodiment of the present invention.

The Contrast Sensitivity Function applied to the contrast sensitivity filter unit 140 according to an embodiment of the present invention is expressed by Equation (2).

The contrast sensitivity function filter can be made of a discrete digital finite impulse response (FIR) generated by sampling a one-dimensional CSF in a two-dimensional discrete Fourier transform (DFT) domain.

The contrast sensitivity filter unit 140 may use an oblique effect filter (OEF) for sharpness compensation. The slope effect means that the contrast sensitivity decreases in the oblique directions. Model-fest data does not include sufficient oblique patterns at varying frequencies to effectively limit this effect. Thus, the contrast sensitivity function filter according to one embodiment of the present disclosure is based on a slope effect model.

As shown in FIG. 3, the contrast sensitivity function is composed of the spatial frequency of the X-axis and the gain of the Y-axis.

Here, the contrast sensitivity function filters according to one embodiment of the disclosure is a lobe of the low frequency f ₀ to 0.3 region, and the lobe of the high frequency f ₁ of the area 2, the weight of α in the low frequency area 0.688. An example of such a case is shown in Fig.

FIG. 4 is an explanatory diagram of a detection error in a conventional motion detection apparatus. FIG.

The conventional motion detection apparatus receives the first frame image 401 and the second frame image 402 in a low-illuminance environment. At this time, low-frequency noise in a low-illuminance environment may occur in the first frame image 401 or the second frame image 402.

Then, the conventional motion detection apparatus calculates the difference image 403 between the first frame image 401 and the second frame image 402.

Then, the conventional motion detection apparatus compares the pixel value of the calculated difference image 403 with a preset motion occurrence threshold value.

In the conventional motion detection apparatus, as a result of the comparison, the pixel value of the calculated difference image 403 is determined to be equal to or greater than the motion occurrence threshold, and the user is alerted to the motion occurrence.

In the conventional motion detection apparatus, as shown in FIG. 4, even in the case where no motion occurs in the first frame image 401 and the second frame image 402 in a low-illuminance environment, it is determined that motion is generated through low- .

5 is an explanatory diagram of motion detection in a motion detection apparatus according to an embodiment of the present invention.

The motion detection apparatus 100 according to an embodiment receives a first frame image 501 and a second frame image 502 in a low-illuminance environment. The motion detection apparatus 100 compensates for edge components while removing noise through the bidirectional filter unit 120, the image transformation unit 130, the contrast sensitivity filter unit 140, and the image reconstruction unit 150. At this time, low-frequency noise in a low-illuminance environment may occur in the first frame image 501 or the second frame image 502.

Then, the motion detection apparatus 100 according to the present invention calculates a difference image 503 between the first frame image 501 and the second frame image 502 subjected to image processing.

Subsequently, the motion detection apparatus 100 compares the pixel value of the calculated difference image 503 with a predetermined motion generation threshold.

As a result of the comparison, the motion detection apparatus 100 according to the present invention does not warn the user because motion is not generated because the pixel value of the calculated difference image 503 is determined to be less than the motion occurrence threshold value.

5, in the low-illuminance environment, the motion detection apparatus 100 according to the present invention can remove noise through image processing even if low-frequency noise occurs in the first frame image 401 or the second frame image 402 Detection error can be prevented.

4 and 5, the signal-to-noise ratio (SNR) between the conventional motion detection apparatus and the motion detection apparatus 100 according to the present invention is measured. same.

를 나타낸다.here,

.

The signal-to-noise ratio (SNR) is calculated according to Equation (4). The calculated signal-to-noise ratio (SNR) is shown in Table 1 below.

division SNR [dB] The motion detection device (conventional) 1.10 The motion detection apparatus of FIG. 5 (present invention) 1.59

As shown in Table 1, it can be seen that the signal-to-noise ratio of the difference image calculated by the conventional motion detection apparatus is 1.10, so that the low-frequency noise is not removed. In contrast, the signal-to-noise ratio of the difference image calculated by the motion detection apparatus 100 according to the present invention is 1.59, which indicates that the low-frequency noise is reduced compared to the conventional method.

6 is an explanatory diagram of a motion generation event in the motion detection apparatus according to an embodiment of the present invention.

The motion detection apparatus 100 according to an embodiment receives a first frame image 601 and a second frame image 602 in a low-illuminance environment. Here, low-frequency noise in a low-illuminance environment may occur in the first frame image 601 or the second frame image 602. [ Also, in the second frame image 602, motion is identified as occurring.

5, the motion detection apparatus 100 compensates for edge components while eliminating low-frequency noise.

The motion detection apparatus 100 according to the present invention calculates the difference image 603 between the first frame image 601 subjected to the image processing and the second frame image 502 where motion occurs.

Subsequently, the motion detection apparatus 100 compares the pixel value of the calculated difference image 603 with a preset motion occurrence threshold value.

As a result of the comparison, the motion detection apparatus 100 according to the present invention determines that the pixel value is greater than or equal to the motion generation threshold due to the motion generation region 604 of the calculated difference image 603, thereby alerting the user of the motion generation event .

Therefore, the motion detection apparatus 100 according to the present invention can accurately detect a motion occurrence event while eliminating low-frequency noise in a low-illuminance environment, as shown in FIG.

7 is a flowchart of a motion detection method in a low-illuminance environment according to an embodiment of the present invention.

The motion detection apparatus 100 according to the present invention acquires an image of the camera (S702).

Then, the motion detection apparatus 100 sets a threshold value of motion generation (S704). Here, the threshold value of motion generation may be preset by the user or may be set at motion detection.

Thereafter, the motion detection apparatus 100 performs image processing according to steps S706 to S712 for the first frame image (first frame image).

Referring to steps S706 to S712, the motion detection apparatus 100 removes noise of an image of the first frame using a bidirectional filter (a bilateral filter) (S706).

In operation S706, the motion detection apparatus 100 converts the image of the noise-removed first frame into a frequency space.

Subsequently, the motion detection apparatus 100 filters the image of the first frame converted in step S708 through a contrast sensitivity function (CSF) filter (step S710).

Then, the motion detection apparatus 100 restores the original image of the first frame of the filtered frequency space (S712).

On the other hand, the motion detection apparatus 100 performs image processing according to steps S714 to S720 for the image of the second frame (second frame image).

Referring to steps S714 to S720, the motion detection apparatus 100 removes noise of the image of the second frame using a bidirectional filter (a bilateral filter) (S714).

In operation S716, the motion detection apparatus 100 converts the image of the noise-removed second frame into a frequency space.

Subsequently, the motion detection apparatus 100 filters the image of the second frame converted in step S708 through a contrast sensitivity function (CSF) filter (step S710).

Then, the motion detection apparatus 100 restores the original image of the image of the second frame of the filtered frequency space (S712).

Here, with respect to the image of the first frame (the first frame image), the image processing according to the steps S706 to S712 and the image processing according to the steps S714 to S720 with respect to the image of the second frame (the second frame image) And may be performed sequentially.

After all the image processing processes for the images of the first and second frames are completed, the motion detection apparatus 100 obtains difference images of the images of the first and second frames subjected to the image processing (S722).

The motion detection apparatus 100 compares the pixel value of the difference image with a predetermined threshold value of motion generation to recognize motion occurrence (S724). That is, when the low frequency noise is removed through the image processing even if the low frequency noise occurs, the motion detection apparatus 100 does not warn the user when the pixel value of the difference image is less than the motion generation threshold, . On the other hand, when the pixel value of the difference image is equal to or larger than the motion occurrence threshold value, the motion detection apparatus 100 determines that motion has occurred and warns the user.

It will be understood by those skilled in the art that the present specification may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. It is therefore to be understood that the above-described embodiments are illustrative in all aspects and not restrictive. The scope of the present specification is defined by the appended claims rather than the foregoing detailed description, and all changes or modifications derived from the meaning and scope of the claims and their equivalents are included in the scope of the present specification Should be interpreted.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, It is not intended to limit the scope of the specification. It will be apparent to those skilled in the art that other modifications based on the technical idea of the present invention are possible in addition to the embodiments disclosed herein.

100: Motion detection device
110:
120: bidirectional filter unit
130:
140: Contrast sensitivity filter section
150:
160: car image calculation unit
170:

Claims (8)

Receiving an image from a camera;
Receiving a selected image region from the input image by a user;
Removing noise of the first and second frame images in the selected image region by using a bilateral filter, removing noises of the first and second frame images in the selected image region, respectively, ;
Transforming the noise-removed first and second frame images into a frequency domain, respectively;
Filtering the first and second frame images of the transformed frequency domain through a Contrast Sensitivity Function filter;
Restoring the first and second frame images of the filtered frequency domain into a spatial domain;
Calculating a difference image between the restored first and second frame images; And
Detecting a motion occurrence by comparing the calculated pixel value of the difference image with a motion occurrence threshold value
Gt; The method according to claim 1,
The step of receiving the image
A motion detection method for acquiring and inputting an image from a camera equipped with a CMOS (Complementary Metal-Oxide Semiconductor) image sensor. delete The method according to claim 1,
Calculating illuminance from the input image; And
Further comprising extracting a low-illuminance image region in which the calculated illuminance is less than a preset illuminance from the input image,
Wherein the eliminating step removes noise of the first and second frame images in the extracted low-illuminance image area. The method according to claim 1,
The step of removing
The Salt-Pepper noise of the low-frequency region in the first and second frame images while maintaining a sharp edge component of the first and second frame images using a Fast-Bilateral Filter Respectively. 6. The method of claim 5,
The high speed by-product filter
In the first and second frame images according to the following Equation (1), the low-frequency noise is weighted according to the Gaussian filter of the spatial domain and the Gaussian filter of the intensity domain of the light, and the Salt-Pepper noise Respectively.
[Equation 1]

(Wherein, p, q is the pixel location, I _p is p pixel values of the input image I, Ω is a pixel near the value of p, k _p is normalized (Normalizing) factor, f, g are Gaussian by σ _s, σ _r Function, J _p represents the filtered image.) The method according to claim 1,
The filtering step
And filtering the first and second frame images of the transformed frequency domain to compensate for edge components lost by the bidirectional filter. 8. The method of claim 7,
The filtering step
The edge component lost by the bidirectional filter is compensated by the contrast sensitivity function filter using the frequency of the low-frequency lobe, the frequency of the high-frequency lobe, and the weight of the low-frequency lobe according to Equation (2) A motion detection method.
&Quot; (2) "

( Where f ₀ is a lobe in a low frequency region, f ₁ is a lobe in a high frequency region, α is a weight in a low frequency region,

Represents a Gaussian function.)

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