CN107545549B - Method for estimating scattered focus point spread function based on one-dimensional spectrum curve - Google Patents
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Abstract
The invention discloses a method for estimating a scatter focus point spread function based on a one-dimensional spectrum curve, which comprises the following steps: (1) inputting a defocusing fuzzy picture, and performing Fourier transform on the defocusing fuzzy picture to obtain a spectrogram; (2) selecting a threshold value to carry out threshold value segmentation on the frequency spectrum image to obtain a binaryzation defocusing frequency spectrum image; (3) constructing a one-dimensional spectrum curve by using a statistical method; (4) eliminating the influence of burrs and micro-oscillation on the one-dimensional frequency spectrum curve obtained in the step (3) to obtain a smooth curve; (5) solving a minimum value between two levels of lobes to be used as a zero point estimated value to replace the radius of a dark ring; (6) calculating the defocusing radius according to the mathematical relationship between the dark ring radius and the defocusing radius; (7) and reconstructing a point spread function. The method has high processing accuracy, and can well estimate the defocus radius value; the operation speed is high, and no complex operation with long time consumption exists.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a method for estimating a defocusing point diffusion function based on a one-dimensional spectrum curve.
Background
In the optical imaging process, image blurring inevitably occurs due to the influences of focusing errors, air flow disturbance, system noise and the like. Defocusing blurring is a phenomenon of image blurring caused by inaccurate focusing, and is widely used in the imaging process of various optical instruments. High-frequency information of the defocused blurred image is lost, readability is reduced, and development of subsequent processes such as feature identification and information extraction is not facilitated. Therefore, restoration of a defocused blurred image is particularly necessary in practical engineering. In the image restoration process, the point spread function plays an important role, and whether the parameter estimation of the point spread function is correct or not directly influences the restoration result of the defocused blurred image. The defocus radius is an important parameter of the defocus point spread function, and the accuracy of the defocus radius estimate determines the correctness of the defocus point spread function. However, there is no method for accurately estimating the defocus point spread function.
The method for estimating the divergence point spread function by using the defocused blurred image spectrogram is an important way for researching the parameter estimation of the divergence point spread function. The defocused blurred image can be regarded as a convolution of a clear image and a defocused point diffusion function, light and dark alternating circular rings exist in a spectrogram, specific mathematical relations exist between corresponding radiuses of all levels of dark rings and defocused radiuses, and the defocused radius can be estimated according to the radius values of the dark rings. However, the defocused blurred image has less high-frequency information, so that the energy of the center position representing the low-frequency information in the spectrogram is stronger, the energy is rapidly attenuated from the central first-level bright spot to the surrounding energy, the visibility of the secondary bright ring is sharply reduced, and the difficulty in zero point estimation is increased. Meanwhile, due to the influence of noise, a large number of isolated points exist in the spectrogram, and the zero point solution is greatly influenced.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for estimating a defocusing point diffusion function based on a one-dimensional spectrum curve, which can well estimate a defocusing radius value and does not have complex operation with long time consumption.
In order to solve the above technical problem, the present invention provides a method for estimating a defocusing point spread function based on a one-dimensional spectrum curve, comprising the following steps:
(1) inputting a defocusing blurred picture, performing Fourier transform to obtain a spectrogram, and performing Fourier transform on the defocusing blurred picture to obtain a defocusing blurred picture with a size of L0×L0Performing discrete Fourier transform on the defocused blurred image G to obtain a frequency spectrum image G of the defocused blurred image G;
(2) selecting a threshold value to carry out threshold value segmentation on the frequency spectrum image to obtain a binaryzation defocusing frequency spectrum image;
(3) constructing a one-dimensional spectrum curve by using a statistical method;
(4) eliminating the influence of burrs and micro-oscillation on the one-dimensional frequency spectrum curve obtained in the step (3) to obtain a smooth curve; smoothing filtering is carried out on the one-dimensional frequency spectrum curve by using a smoothing filtering operator, burrs and micro-oscillation on the curve are eliminated, and a smoother curve is obtained;
(5) solving a minimum value between two levels of lobes to be used as a zero point estimated value to replace the radius of a dark ring;
(6) calculating the defocusing radius according to the mathematical relationship between the dark ring radius and the defocusing radius;
(7) and reconstructing a point spread function.
Preferably, the step (2) is specifically: obtaining spectral image threshold T by using Otsu method1(ii) a Use publicFormula T2＝EG+gCalculating T2In which EGThe mean value of the spectral image G representing the defocus blur image,grepresents the variance of the defocused blurred image g; using T1And T2The weighted average of (a) obtains the final threshold T, T being 0.9T1+0.1T2(ii) a And (3) performing binary segmentation on the frequency spectrum image according to a threshold value T, setting the pixel value larger than the threshold value T as 1, and setting the pixel value smaller than the threshold value T as 0 to obtain a binary defocused frequency spectrum image.
Preferably, the step (3) is specifically: using the central point of the binarized frequency spectrum image as a reference original point, and counting the pixel value and the number of pixel points of which the Euclidean distance between the reference original point is d, wherein: d is 1 to RmaxWherein R ismax＝L0(ii)/2, calculating the average pixel value P over the distance ddConstruction of PdThe curve for d, i.e. the one-dimensional spectral curve.
Preferably, the step (5) is specifically: according to the constructed one-dimensional spectrum curve, d is 2,3, …, Rmax-1 calculation t1d＝Pd-Pd-1、t2d＝Pd+1-PdFind t1d＜0、t2dThe point of more than 0 is the minimum value point of the spectrum curve; in practice, due to the existence of micro-oscillation of the curve, in order to eliminate the influence of local minimum interference, the minimum judgment condition is changed to t1d＜σ，t2d> 0, where σ is a relatively small number, e.g. 10-2Ensuring the minimum value as the minimum point between lobes, and using the minimum value satisfying the conditionnReplacing the estimated value of the zero point of the frequency spectrum curve, and further replacing the nth zero point estimation with the nth dark ring radius r of the two-dimensional spectrogramn。
Preferably, in step (6), the mathematical relationship between the dark ring radius and the defocus radius is as follows: using the formula R ═ ZnL0/2πrnCalculating the defocus radius R, where ZnRepresenting the nth zero of the bessel function of the first kind.
Preferably, in step (7), the reconstructed point spread function is specifically: reconstructing the scatter focus point diffusion function according to the mathematical expression of the scatter focus point diffusion function, namely estimating the scatter focus point diffusion function, wherein the mathematical expression of the scatter focus point diffusion function is as follows:
where R represents the defocus radius.
The invention has the beneficial effects that: the method comprises the steps of constructing a one-dimensional spectrum curve based on a fuzzy degraded image spectrogram, solving curve minimum value points meeting requirements according to difference values of each point of the curve to replace defocusing fuzzy image spectrogram radius, and further estimating defocusing radius of a defocusing point diffusion function to reconstruct the defocusing point diffusion function; the defocused blurred image has more low-frequency information and less high-frequency information, so that the numerical value of a central area where low frequency is located in a shifted spectrogram is larger, the numerical value of an edge area where high frequency is located is small, the spectral energy is mainly concentrated at the central position and is rapidly decreased towards the periphery, the visibility is rapidly reduced, the numerical difference between secondary bright rings of the spectral image is small and is difficult to distinguish, the difficulty in solving a zero point by directly using the spectral image is larger, the contrast between light and dark rings of each level of the image after threshold segmentation is increased, the circular distribution with alternating light and dark can be clearly observed, and the determination of the zero point position is facilitated; the method has high processing accuracy, and can well estimate the defocus radius value; the operation speed is high, and no complex operation with long time consumption exists.
Drawings
FIG. 1 is a schematic flow chart of the method for estimating a diffuse focus point spread function based on a one-dimensional spectrum curve according to the present invention.
FIG. 2 is a schematic diagram of a simulated defocused blurred image of the present invention.
FIG. 3 is a schematic diagram of logarithmic display of a spectrogram of a defocused blurred image according to the present invention.
Fig. 4 is a schematic diagram of the spectrum after threshold segmentation in accordance with the present invention.
Fig. 5 is a schematic diagram of a one-dimensional spectral curve constructed after threshold segmentation of a spectrogram in the present invention.
Fig. 6 is a schematic diagram of a smoothed one-dimensional spectral curve of the present invention.
FIG. 7 is a schematic diagram of a defocus radius estimate versus true value fitting curve according to the present invention.
Fig. 8 is a diagram illustrating the results of restoring a defocused blurred lena image using two methods according to the present invention.
Detailed Description
As shown in fig. 1, a method for estimating a defocusing point spread function based on a one-dimensional spectrum curve includes the following steps:
step 2: and (4) selecting a threshold value to carry out threshold value segmentation on the frequency spectrum image to obtain a binary defocused frequency spectrum image. Obtaining spectral image threshold T by using Otsu method1(ii) a Using the formula T2＝EG+gCalculating T2In which EGThe mean value of the spectral image G representing the defocus blur image,grepresents the variance of the defocused blurred image g; using T1And T2The weighted average of (a) obtains the final threshold T, T being 0.9T1+0.1T2(ii) a Performing binary segmentation on the frequency spectrum image according to a threshold value T, setting the pixel value larger than the threshold value T as 1, and setting the pixel value smaller than the threshold value T as 0 to obtain a binary defocusing frequency spectrum image;
and step 3: a one-dimensional spectral curve is constructed using statistical methods. Using the central point of the binarized frequency spectrum image as a reference original point, and counting the pixel value and the number of pixel points of which the Euclidean distance between the reference original point is d, wherein: d is 1 to RmaxWherein R ismax＝L0/2. Calculating the average pixel value P over the distance dd. Construction of PdA curve for d, i.e. a one-dimensional spectral curve;
and 4, step 4: the smooth curve eliminates the effects of glitches and micro-oscillations. Smoothing filtering is carried out on the one-dimensional frequency spectrum curve by using a smoothing filtering operator, burrs and micro-oscillation on the curve are eliminated, and a smoother curve is obtained;
and 5: and solving a minimum value between the two levels of lobes as a zero point estimation value. According to constructionFrom d 2,3, …, Rmax-1 calculation t1d＝Pd-Pd-1、t2d＝Pd+1-PdFind t1d＜0、t2dThe point of > 0, i.e. the spectral curve minimum point. In practice, due to the existence of micro-oscillation of the curve, in order to eliminate the influence of local minimum interference, the minimum judgment condition is changed to t1d＜σ，t2d> 0, where σ is a relatively small number, e.g. 10-2To ensure that the minimum is the minimum point between lobes. Using minimum values satisfying conditionsnReplacing the estimated value of the zero point of the frequency spectrum curve, and further replacing the nth zero point estimation with the nth dark ring radius r of the two-dimensional spectrogramn；
Step 6: the defocus radius is calculated from a mathematical relationship between the dark ring radius and the defocus radius. Using the formula R ═ ZnL0/2πrnCalculating the defocus radius R, where ZnRepresents the nth zero of the Bessel function of the first type, as detailed in Table 1;
TABLE 1 first order zero of the first 5 th order Bessel function
And 7: and reconstructing a point spread function. And reconstructing the scatter focus point diffusion function according to the mathematical expression of the scatter focus point diffusion function, namely estimating the scatter focus point diffusion function. The mathematical expression of the defocusing point diffusion function is as follows:
where R represents the defocus radius.
The invention is described in detail below with reference to the attached drawing figures:
selecting the size of L0×L0As shown in fig. 2, a lena diagram blurred by a defocus point spread function with a radius of 5 is combined with the step flow shown in fig. 1 to describe the method of the present invention, which specifically includes the following steps:
step 1: and solving a Fourier transform spectrum image. Performing discrete Fourier transform on the defocused blurred image G to obtain a frequency spectrum image G thereof, as shown in FIG. 3;
step 2: and carrying out threshold segmentation on the frequency spectrum image to obtain a binary frequency spectrum image. The spectrum image G is subjected to threshold segmentation processing to obtain a spectrum image after threshold segmentation, as shown in fig. 4. The specific method of the threshold segmentation processing is as follows: obtaining spectral image threshold T by using Otsu method1(ii) a Using the formula T2＝EG+gCalculating T2In which EGRepresents the mean value of the spectrum of the defocused blurred image,grepresenting the variance of the defocused blurred image; using T1And T2The weighted average of (a) obtains the final threshold T, T being 0.9T1+0.1T2(ii) a And performing binary segmentation on the frequency spectrum image according to a threshold value T, setting the pixel value larger than the threshold value T as 1, and setting the pixel value smaller than the threshold value T as 0. The threshold segmentation processing algorithm can accurately segment the frequency spectrum image into a foreground part and a background part, and the contrast of a bright ring and a dark ring in a segmentation result is strong, as shown in fig. 4, the boundary is clear, the problems that the signal intensity of the central area of the image frequency spectrum image is too large and secondary ripple information is covered are solved, and the subsequent numerical statistics is facilitated;
and step 3: and constructing a one-dimensional spectrum curve by a statistical method. Taking the center of the frequency spectrum image as a reference original point, and counting the pixel value and the number of pixel points of each pixel point with the Euclidean distance d between the reference original point and the reference original point, wherein: d is 1 to RmaxWherein R ismax＝L0/2. Calculating the average pixel value P over the distance dd. According to the distance d and the average pixel value PdConstructing a one-dimensional curve of the mean value varying with the distance, as shown in fig. 5; and 4, step 4: smoothing the image by using a smoothing filter operator to remove smaller burrs, so that the zero point of the next step can be conveniently solved, and the smoothed curve is shown in FIG. 6;
and 5: and calculating the minimum value between two adjacent stages of lobes according to the difference value. According to the constructed one-dimensional spectrum curve, d is 2,3, …, Rmax-1 calculation t1d＝Pd-Pd-1、t2d＝Pd+1-PdLooking fort1d＜0、t2dThe point of > 0, i.e. the spectral curve minimum point. In practice, because the image has micro-oscillation, in order to eliminate the influence of local minimum interference, the minimum judgment condition is changed to: t1d＜σ，t2d> 0, where σ is a relatively small number, e.g. 10-2. The threshold σ is set to further eliminate the disturbance of the minor oscillation. The resulting zero point estimates are marked in fig. 6 using "". Using minimum values satisfying conditionsnReplacing the estimated value of the zero point of the frequency spectrum curve, and further replacing the estimated value of the nth zero point with the radius r of the nth dark ring of the two-dimensional frequency spectrum graphn；
Step 6: the defocus radius is calculated from a mathematical relationship between the dark ring radius and the defocus radius. According to the formula R ═ ZnL0/2πrnThe defocus radius R is calculated with the zero values of the first order bezier function n in table 1. The estimated value of the defocus radius obtained in this example was 5.19;
and 7: and reconstructing a point spread function. And reconstructing the defocusing point diffusion function according to the mathematical expression of the defocusing point diffusion function by using the defocusing radius obtained by estimation, so as to obtain the estimated value of the defocusing point diffusion function.
In the simulation test, the image is blurred by using a defocusing point diffusion function with a defocusing radius R of 3:0.5:10, then point diffusion function estimation is performed to obtain a fitting curve of an estimated value and a true value shown in fig. 7, through statistical analysis, the variance between the two is 0.0337, and the pearson correlation coefficient is 0.9965.
The defocus-point spread function is reconstructed using the defocus radius estimated value, and image restoration processing is performed by using a wiener filter restoration algorithm (deconvwnr) and a blind deconvolution restoration algorithm (deconvbind) in Matlab, and the result is shown in fig. 8. Therefore, the defocusing radius can be accurately estimated, and the quality of an image restoration processing result can be obviously improved.
The invention provides a method for solving defocusing radius, and provides a method for accurately calculating the dark ring radius of a frequency spectrum image. Replacing the dark ring radius with a one-dimensional spectral curve zero; because the defocusing blurred image spectrogram has good circular symmetry and the zero point of the dark ring is distributed on the circular ring taking the central point as the center point, the zero point of the one-dimensional spectrum curve can approximately replace the radius of the dark ring to estimate the defocusing radius. Searching a method capable of accurately constructing a one-dimensional spectrum curve; the one-dimensional spectrum curve needs to contain light and dark ring distribution information of a spectrum image as much as possible, the method for constructing the spectrum curve by counting pixel values of all points on a straight line of a central point of a certain over-frequency spectrum image does not fully utilize the information of the image, the fault tolerance is small, almost all pixel points are brought into a statistical sample space by adopting the method for constructing the spectrum curve by counting the average value of the pixel points with the same Euclidean distance with the central point, and the fault tolerance is greatly improved. Searching a curve smoothing method; the burr and the micro-oscillation existing in the curve can cause minimum value misjudgment to influence the estimation of the defocusing radius of the defocusing point diffusion function, and the influence of the burr can be reduced or even eliminated by using the mean filtering operator to carry out smooth filtering. Selecting a proper zero point solving method; the influence of the burrs can be reduced by using smooth filtering, but under some extreme conditions, the influence of the burrs still exists in the curve, the difference value change is used for solving the minimum value, the minimum value between two adjacent stages of lobes is used as a zero point estimation value, the influence of the burrs can be further eliminated by a threshold setting method, and the accuracy of zero point estimation is improved.
While the invention has been shown and described with respect to the preferred embodiments, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the scope of the invention as defined in the following claims.
Claims (5)
1. A method for estimating a defocusing point spread function based on a one-dimensional spectral curve is characterized by comprising the following steps of:
(1) inputting a defocusing blurred picture, performing Fourier transform to obtain a spectrogram, and performing Fourier transform on the defocusing blurred picture to obtain a defocusing blurred picture with a size of L0×L0Performing discrete Fourier transform on the defocused blurred image G to obtain a frequency spectrum image G of the defocused blurred image G;
(2) selecting a threshold value to carry out threshold value segmentation on the frequency spectrum image to obtain a binaryzation defocusing frequency spectrum image;
(3) construction of a one-dimensional frequency using statistical methodsA spectral curve; using the central point of the binarized frequency spectrum image as a reference original point, and counting the pixel value and the number of pixel points of which the Euclidean distance between the reference original point is d, wherein: d is 1 to RmaxWherein R ismax＝L0(ii)/2, calculating the average pixel value P over the distance ddConstruction of PdA curve for d, i.e. a one-dimensional spectral curve;
(4) eliminating the influence of burrs and micro-oscillation on the one-dimensional frequency spectrum curve obtained in the step (3) to obtain a smooth curve; smoothing filtering is carried out on the one-dimensional frequency spectrum curve by using a smoothing filtering operator, burrs and micro-oscillation on the curve are eliminated, and a smoother curve is obtained;
(5) solving a minimum value between two levels of lobes to be used as a zero point estimated value to replace the radius of a dark ring;
(6) calculating the defocusing radius according to the mathematical relationship between the dark ring radius and the defocusing radius;
(7) and reconstructing a point spread function.
2. The method for estimating a defocus point spread function based on a one-dimensional spectrum curve as claimed in claim 1, wherein the step (2) is specifically: obtaining spectral image threshold T by using Otsu method1(ii) a Using the formula T2＝EG+gCalculating T2In which EGThe mean value of the spectral image G representing the defocus blur image,grepresents the variance of the defocused blurred image g; using T1And T2The weighted average of (a) obtains the final threshold T, T being 0.9T1+0.1T2(ii) a And (3) performing binary segmentation on the frequency spectrum image according to a threshold value T, setting the pixel value larger than the threshold value T as 1, and setting the pixel value smaller than the threshold value T as 0 to obtain a binary defocused frequency spectrum image.
3. The method for estimating a defocus point spread function based on a one-dimensional spectrum curve as claimed in claim 1, wherein the step (5) is specifically: according to the constructed one-dimensional spectrum curve, d is 2,3, …, Rmax-1 calculation t1d＝Pd-Pd-1、t2d＝Pd+1-PdSeek toFind t1d<0、t2dThe point of more than 0 is the minimum value point of the spectrum curve; in practice, due to the existence of micro-oscillation of the curve, in order to eliminate the influence of local minimum interference, the minimum judgment condition is changed to t1d<σ，t2d> 0, where σ is a relatively small number 10-2Ensuring the minimum value as the minimum point between lobes, and using the minimum value satisfying the conditionnReplacing the estimated value of the zero point of the frequency spectrum curve, and further replacing the nth zero point estimation with the nth dark ring radius r of the two-dimensional spectrogramn。
4. The method for estimating an astigmatic focal point spread function according to claim 3, wherein in step (6), the mathematical relationship between the dark ring radius and the defocus radius is: using the formula R ═ ZnL0/2πrnCalculating the defocus radius R, where ZnRepresenting the nth zero of the bessel function of the first kind.
5. The method for estimating an astigmatism point spread function based on a one-dimensional spectrum curve as claimed in claim 1, wherein in the step (7), the reconstructed point spread function is specifically: reconstructing the scatter focus point diffusion function according to the mathematical expression of the scatter focus point diffusion function, namely estimating the scatter focus point diffusion function, wherein the mathematical expression of the scatter focus point diffusion function is as follows:
where R represents the defocus radius.
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