CN106204485B - Image restoration boundary ringing effect suppressing method based on integral sine - Google Patents
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Abstract
The invention discloses a kind of the image restoration boundary ringing effect suppressing method based on integral sine, first input blurred picture f (x, y), fuzzy core h (x, y) is calculated, then is extended in a mirror-image fashion to original blurred picture, obtain extension image g (x, y)；Then the region of window function w (x, y) is opened up according to the size of extension image g (x, y), and window function is filled using the method that SIN function integrates；Extension image g (x, y) and window function w (x, y) are synthesized again, obtain adding window image g'(x, y)；Finally using Image Restoration Algorithm to adding window image g'(x, y) restored, and the original image size of M × N of intermediate region is cut out, as final restored image.The present invention inhibits the ringing effect in restoring motion blurred image, and not only not excessive extension image increases calculation amount, but also does not ignore the detailed information of image border, improves the Quality of recovery of blurred picture.
Description
Technical Field
The invention belongs to the technical field of motion blur image processing, and particularly relates to an image restoration boundary ringing effect suppression method based on sine integration.
Background
In recent years, motion blur image restoration techniques have become one of the important issues for image restoration techniques. In the process of acquiring image information, the relative motion between a shooting object and a shot object often causes the blurring of the image. Motion-blurred images are ubiquitous in daily life, and some scenes with instant irreproducibility hide or lose valuable instant information. In order to obtain valid information hidden in a blurred image, the blurred image needs to be restored. When the existing motion blurred image restoration method is used for processing a real image, the restored image is often subjected to secondary degradation under the influence of various estimation errors, limitations of image priori knowledge, partial image information loss and other factors, wherein a more obvious degradation phenomenon is a ringing effect. The ringing effect which causes the image restoration is analyzed, and the research on the method for inhibiting the ringing effect is beneficial to improving the performance of the image restoration algorithm, thereby being beneficial to obtaining the restored image with high quality. Therefore, much attention has been paid to how to suppress the ringing effect generated at the image boundary in the image restoration process.
Currently, common methods for suppressing ringing due to image boundary truncation are: a cyclic boundary method, a shift reflection boundary condition method, a gradient-based image block restoration method and an optimal window method. The circular boundary method is to extend the observed image into a new observed image with smooth and differentiable boundary junction in a reflection symmetric mode. The method can weaken the ringing effect, but the method greatly expands the area of the restored image, and particularly for the restoration algorithm with iteration, the calculation amount is multiplied. The de-ringing algorithm based on the shifted reflection boundary condition may also improve the continuity at the boundary, so that the ringing effect at the restored image boundary is significantly reduced. The image block restoration method based on the gradient is to firstly block an observation image, then extend the blocks outwards, and cut overlapping areas for splicing after each block is restored. The three methods have large computation amount and are difficult to realize quickly. The optimal windowing method can also reduce the ringing effect by windowing the observation image, but cannot complete the restoration of the edge detail part of the image after windowing.
Disclosure of Invention
The invention aims to provide an image restoration boundary ringing effect suppression method based on sine integration, and solves the problems that the existing ringing effect suppression method is large in operation amount and cannot consider detail part restoration.
The invention adopts the technical scheme that the image restoration boundary ringing effect suppression method based on the sine integral is characterized by comprising the following steps of:
step 1, inputting a blurred image f (x, y) with the size of M multiplied by N, and calculating a blurred kernel h (x, y);
step 2, extending the original blurred image in a mirror image mode according to the size of the blurred kernel obtained in the step 1 to obtain an extended image g (x, y);
step 3, opening up an area of a window function w (x, y) according to the size of the extension image g (x, y), and filling the window function by using a sine function integration method;
step 4, synthesizing the extended image g (x, y) and the window function w (x, y) to obtain a windowed image g' (x, y);
and 5, restoring the windowed image g' (x, y) by using an image restoration algorithm, and cutting out the size of the original image of the M multiplied by N in the middle area to obtain a final restored image.
The invention is also characterized in that:
step 3, the size of the window function w (x, y) is the same as that of the extension image g (x, y), and the window function w (x, y) is divided into a one-way transition area at the upper, lower, left and right boundaries, a two-way transition area at four corners and a middle area; the pixel value of the middle area is 1, the pixel value of the one-way transition area is calculated according to the formulas (8) and (9),
wherein S isudDenotes the upper and lower boundaries, SlrDenotes the left and right boundaries, Sup、Sdn、Slt、SrtRespectively representing an upper boundary, a lower boundary, a left boundary, and a right boundary.
The pixel value of the bidirectional transition area is calculated according to the formula (17);
wherein S isqRepresenting four corner regions, Slu、Sld、Srd、SruRespectively representing the upper left corner, the lower right corner and the upper right corner.
The boundary and the angle can be calculated by the above formulas respectively, or one of the boundary and the angle can be calculated first and then the other can be deduced according to the symmetry principle.
In the step 1, the blurred image f (x, y) is converted into the spectrum domain to perform calculation of the blur kernel, and the spectrogram is corrected by using the formula (1):
G′(u，v)＝|log(1+|G(u，v)|)| (1)
in equation (1), G (u, v) represents the result of fourier transform of the original image onto the spectral domain, and G' (u, v) represents the result of correction of G (u, v).
The method for synthesizing the windowed image g' (x, y) in the step 4 comprises the following steps:
g′(x，y)＝g(x，y)×w(x，y) (20)
the image restoration algorithm in the step 5 is preferably a wiener filtering algorithm or an RL restoration algorithm.
The method has the advantages that the ringing effect in the motion blurred image restoration is suppressed, compared with the conventional restoration method, the method does not extend the image to increase the calculation amount, does not ignore the detail information of the image edge, and improves the restoration quality of the blurred image.
Drawings
FIG. 1 is a flow chart of the image restoration boundary ringing effect suppression method based on sinusoidal integration according to the present invention;
FIG. 2a is a blurred image input by the embodiment;
FIG. 2b is another blurred image of the input of the embodiment;
FIG. 3a is a blur kernel estimated over the spectral domain of the blurred image of FIG. 2 a;
FIG. 3b is a blur kernel estimated over the spectral domain of the blurred image of FIG. 2 b;
FIG. 4a is an expanded image of the image to be processed, like FIG. 2a, expanded according to the dimensions of FIG. 3 a;
FIG. 4b is an expanded image of the image to be processed, like FIG. 2b, expanded according to the dimensions of FIG. 3 b;
FIG. 5a is a schematic diagram of the region partition of a window function;
FIG. 5b is a sine function value coordinate curve of the upper, lower, left and right boundaries of the window function;
FIG. 5c is a coordinate curve of values corresponding to each row (column) of the window function boundary region;
FIG. 5d is a plot of the transverse and longitudinal sine function values for four corner portions of the window function;
FIG. 6a is an image resulting from combining the extended image of FIG. 4a with a window function;
FIG. 6b is an image resulting from combining the extended image of FIG. 4b with a window function;
FIG. 7a is a graph of the effect of FIG. 6a recovered using wiener filtering after windowing using sine function integration;
FIG. 7b is the effect of recovering FIG. 6a using the RL restoration algorithm after windowing using the sine function integration method;
FIG. 7c is a graph of the effect of FIG. 6b recovered using wiener filtering after windowing using sine function integration;
FIG. 7d is the effect of recovering FIG. 6b using the RL restoration algorithm after windowing using the sine function integration method;
FIG. 8a is a graph of the effect of FIG. 2a recovered directly using wiener filtering;
FIG. 8b is a graph of the effect of recovering FIG. 2a directly using the RL restoration algorithm;
FIG. 8c is a graph of the effect of FIG. 2b restored directly using wiener filtering;
fig. 8d is a graph of the effect of recovering fig. 2b directly using the RL recovery algorithm.
Detailed Description
The present invention will be described in further detail with reference to the drawings and the following detailed description, but the present invention is not limited to these embodiments.
The invention relates to a method for suppressing ringing effect of an image restoration boundary based on sine integration.A first part estimates a fuzzy core on a frequency spectrum domain, and extends an image to be processed in a mirror symmetry mode according to the size of the estimated fuzzy core so as to achieve the purpose of retaining complete edge information; the second part is to synthesize the window function in the form of sine function integral and restore the image after windowing to achieve the purpose of suppressing the ringing effect in the gradual transition of the image boundary.
As shown in fig. 1, the method specifically comprises the following steps:
step 1, inputting a blurred image f (x, y), wherein the size of fig. 2a is 258 × 259, and the size of fig. 2b is 451 × 433, as shown in fig. 2a and 2 b; it is fourier transformed onto the spectral domain. In order to make the spectrogram more clear and stable, G' (u, v) is obtained by performing correction using equation (1), and the blur kernel h (x, y) is estimated according to the correction result, as shown in fig. 3a and 3b, the size of the blur kernel is m × n.
G′(u，v)＝|log(1+|G(u，v)|)| (1)
In equation (1), G (u, v) represents the result of fourier transform conversion of the original image onto the spectral domain, and G' (u, v) represents the result of correction of G (u, v). The blur kernel size of fig. 3a is 5 × 11 and the blur kernel size of fig. 3b is 23 × 23.
And 2, on the basis of estimating the fuzzy kernel, extending the original fuzzy image in the modes of expressions (2) and (3) according to the size of the fuzzy kernel, wherein the upper and lower boundaries extend (m-1) rows of pixels respectively, and the left and right boundaries extend (n-1) columns of pixels respectively to obtain an extended image g (x, y), as shown in fig. 4a and 4 b. Wherein: the pixel values of the (m-i) th line of g (x, y) of the extended image are the same as the pixel values of the i-th line of the original blurred image f (x, y) (i ═ 1, 2...., m-1); the pixel value of the (n-j) th column of g (x, y) of the extended image is the same as the j-th column pixel value of the original blurred image f (x, y) (j ═ 1, 2.... n-1).
g(x，m-i)＝f(x，i) (2)
g(n-j，y)＝f(j，y) (3)
Wherein i represents the distance from the upper and lower parts of the extended image to the upper and lower boundaries of the original image; j represents the distance from the left and right portions of the extended image to the left and right boundaries of the original image. The extended image is 266 x 279 for fig. 4a and 495 x 477 for fig. 4 b.
And 3, opening up an area of the window function w (x, y)) according to the size of the extension image g (x, y), and filling the window function by using a sine function integration method.
The size of the window function w (x, y) is the same as that of the extended image g (x, y), and the window function is mainly divided into a unidirectional transition region at upper, lower, left and right boundaries, a bidirectional transition region at four corner portions, and a middle region. As shown in fig. 5 a. The values of the middle w (N: N + N-1, M: M + M-1) regions are all 1. For the values of the integral upper limit of i row (j column) of the one-way transition region and the corresponding magnitude of the sine function value, as shown in fig. 5b, the area of the shaded portion represents the integral result corresponding to the integral upper limit of i row (j column), i.e. the value of the window function here. (the pixel values are shown in figure 5 c). The values of the upper integration limits for the lateral and longitudinal directions of the two-way transition region are shown in fig. 5 d.
For the one-way transition region, taking the upper boundary and the left boundary as an example, the upper boundary region is a gradual transition process from top to bottom, the left region is a gradual transition process from left to right, and the sine function integral is a transition process from 0 to 1, so the form of the sine function integral is selected to fit the partial region of the window function, and the calculation method is as follows:
in the above formula, the upper boundary SupThe area has m-1 lines, i represents the line number of the area, A is the number of m +1 arithmetic progression divided from 0 to pi/2, A (i) is the value of the i +1 item in the arithmetic progression; left boundary region SltThere are n-1 columns, j represents the column number of the region, A is the number of dividing 0 to pi/2 into n +1 arithmetic progression, A (j) is the value of the j +1 th item in the arithmetic progression.
Wherein:
in the formula, nsA row number representing an upper boundary region; n iscRepresenting the number of columns in the left bounding area.
Then, corresponding lower and right boundaries are constructed from the constructed upper and left boundaries.
Of course, the above sequence is not the only one, and the same method can be used to construct one of the upper and lower boundaries and one of the left and right boundaries, and then deduce the other two corresponding boundaries. In this case, the above formulas (4) and (5) can be expressed as:
wherein,
in the formula (8), SudRepresents the upper and lower boundaries corresponding to the 8 and 4 regions in fig. 5a, i represents the row number to which it belongs; in the formula (9), SlrThe left and right borders correspond to the 2 and 6 regions in fig. 5a, and j represents the column number to which the border belongs. In the formula (10), Sud(*i，:)∈SupIs shown as SudIn the case of the upper boundary, the same applies to the rest. SupRepresents an upper boundary, corresponding to region No. 8 in fig. 5 a; sdnRepresents the lower border, corresponding to region No. 4 in fig. 5 a; sltIndicates the left border, corresponding to region No. 2 in fig. 5 a; srtIndicating the right border, corresponding to region No. 6 in fig. 5 a. SudComprising SupAnd Sdn，SlrThe same is true.
For the bidirectional transition region, taking the upper left corner as an example, for the upper left corner region, a bidirectional transition process is performed, that is, the upper left corner transitions from left to right to the upper boundary region and from top to bottom to the left boundary region, so we adopt the form of double sine function integration to fit the window function of the region. Due to the fact that
The integral upper limit value of each line of the upper boundary region can be obtained as shown in the following formula:
α＝arccos(1-Sup(i，：)) (13)
the integral upper limit value of each column of the left boundary region can be obtained by the same method and is arccos (1-S)lt(：，j))。
Therefore, the upper left corner region is calculated as follows:
in the above formula SluIndicating the upper left hand corner region, i indicates the row index and j indicates the column index. Where a and b denote the number of rows and columns, respectively, in the top left corner region, then for the jth column of this region, A1 would be 0 to arccos (1-S)lt(j)) is divided into an arithmetic progression with a +2 numbers, A1(i) is the value of the (i + 1) th item in the arithmetic progression, and is shown in formula (15); for row i of region 1, A2 is from 0 to arccos (1-S)up(i,: b) is divided into a b +2 number of arithmetic progression, and A2(j) is the value of the j +1 th item in the arithmetic progression as shown in formula (16).
Then, the other three corner regions are constructed according to the constructed upper left corner region.
Of course, the above sequence is not the only one, and any one of the four corner regions can be constructed first by the same method, and then the other three corner regions can be deduced. In this case, the formula (14) can be expressed as:
in the formula (17), SqFour corner regions are shown, corresponding to regions No. 1, 3, 5, 7 in fig. 5a, where i and j indicate the row and column numbers, respectively, corresponding to each region. In the formula (18), the reaction mixture,
Sq(*i，*j)∈Slu||Sruis shown as SqThe same applies to the case of the upper left corner or the upper right corner. SluRepresents the upper left corner, corresponding to region No. 1 in fig. 5 a; sldRepresents the lower left corner, corresponding to region No. 3 in fig. 5 a; srdRepresents the lower right corner, corresponding to region No. 5 in fig. 5 a; sruRepresenting the upper right corner, corresponding to region No. 7 in fig. 5 a. SqComprising Slu、Sld、SrdAnd Sru。
And 4, synthesizing the extended image g (x, y) and the window function w (x, y) in a mode of formula (20) to obtain a windowed image g' (x, y).
g′(x，y)＝g(x，y)×w(x，y) (20)
As can be seen from fig. 6a and 6b, the edge of the image shows a gradual transition trend.
And 5, restoring the windowing function g' (x, y) by using an image restoration algorithm, wherein the image restoration algorithm can adopt a wiener filtering algorithm or an RL restoration algorithm. And extracting the intermediate original image part from the recovery result S' (x, y) by using an expression (21) to obtain the recovery result S (x, y) of the motion blurred image after the ringing effect is suppressed, namely the final recovery image.
S(1：M，1：N)＝S’(m：M+m-1，n：N+n-1) (21)
Equation (21) represents that pixel information of M to M + M-1 rows, N to N + N-1 columns of S' is assigned to S.
As shown in fig. 7a, 7b, 7c, and 7d, the ringing effect is reduced and the restoration quality of the image is improved due to the stretching and windowing of the image to be processed.
A comparison of several common methods of suppressing ringing effects with the method of the present invention in terms of recovery time is given in tables 1 and 2. The blurred images shown in fig. 2a, 2b were restored using wiener filtering and RL algorithm (20 and 30 iterations), respectively, and ringing was suppressed using the loop boundary algorithm, the optimum window algorithm, and the herein proposed sinusoidal integration method, respectively. The time required for using the different methods is shown in table 1 and table 2, respectively.
TABLE 1 FIG. 2a comparison of recovery times
TABLE 2 FIG. 2b recovery time comparison
From tables 1 and 2, it can be seen that the time used by the loop boundary algorithm is higher than the optimal window and the method of the present invention, especially as the number of iterations increases, the time consumed increases greatly; the time consumed by the method is slightly higher than that of the optimal window algorithm but far lower than that of the cycle boundary algorithm. The main reason is that the proposed method extends the image edge part in order to avoid neglecting the image edge information when the optimal window method is recovered, but does not extend the image with a large area like the cyclic boundary method, so the calculation time is still within the acceptable range.
It can be seen from fig. 8a, 8b, 8c, and 8d that a clearer image can be restored by directly using wiener filtering or RL restoration algorithm, however, due to the influence of the boundary truncation effect, a more obvious ringing effect is generated around the image, and the restoration quality of the image is reduced.
Tables 3 and 4 show a comparison of the quality of recovery of several common methods of suppressing ringing effects with the method of the present invention. The peak signal-to-noise ratio (PSNR), the normalized mean square error (MMSE), and the image quality index (Q) were used in the experiment to measure the restoration quality of the image. The results of direct restoration of the two images shown in fig. 2a and 2b using wiener filtering and RL algorithm, ringing suppression using the loop boundary method, ringing suppression using the optimum window algorithm, and ringing suppression using the sinusoidal integration method proposed by the present invention are shown in table 3 and table 4, respectively.
Table 3 figure 2a restoration quality evaluation of each algorithm
Table 4 figure 2b restoration quality evaluation of each algorithm
As can be seen from tables 3 and 4, the image quality after suppressing ringing is significantly better than the directly restored image; most indexes of image quality after ringing suppression by the sine integration method are superior to those of a cycle boundary method and an optimal window method. The main reason is that the edge information is not ignored in the process of suppressing the ringing effect by using the method, so that the image is closer to the original image.
The foregoing description of the invention is only a few examples, and the invention is not limited to the specific embodiments described above. The foregoing detailed description is exemplary rather than limiting in nature. All such modifications are intended to be included within the scope of this invention as defined in the following claims and their equivalents.
Claims (4)
1. The image restoration boundary ringing effect suppression method based on the sine integral is characterized by comprising the following steps of:
step 1, inputting a blurred image f (x, y) with the size of M multiplied by N, and calculating a blurred kernel h (x, y);
step 2, extending the original blurred image in a mirror image mode according to the size of the blurred kernel obtained in the step 1 to obtain an extended image g (x, y);
step 3, opening up an area of a window function w (x, y) according to the size of the extension image g (x, y), and filling the window function by using a sine function integration method;
step 3, the size of the window function w (x, y) is the same as that of the extension image g (x, y), and the window function w (x, y) is divided into a one-way transition area at the upper, lower, left and right boundaries, a two-way transition area at four corners and a middle area; the pixel value of the middle area is 1, and the pixel value of the one-way transition area is calculated according to the formulas (8) and (9);
wherein S isudDenotes the upper and lower boundaries, SlrRepresenting left and right boundaries; sup、Sdn、Slt、SrtRespectively representing an upper boundary, a lower boundary, a left boundary and a right boundary;
the bidirectional transition region pixel value is calculated according to equation (17):
wherein S isqRepresenting four corner regions, Slu、Sld、Srd、SruRespectively representing the upper left corner, the lower right corner and the upper right corner;
step 4, synthesizing the extended image g (x, y) and the window function w (x, y) to obtain a windowed image g' (x, y);
and 5, restoring the windowed image g' (x, y) by using an image restoration algorithm, and cutting out the size of the original image of the M multiplied by N in the middle area to obtain a final restored image.
2. The method for suppressing image restoration boundary ringing effect based on sinusoidal integration according to claim 1, wherein in step 1, the blurred image f (x, y) is converted into the spectral domain for blur kernel calculation, and the spectrogram is modified by using equation (1):
G′(u，v)＝|log(1+|G(u，v)|)| (1)
in equation (1), G (u, v) represents the result of fourier transform of the original image onto the spectral domain, and G' (u, v) represents the result of correction of G (u, v).
3. The method for suppressing ringing effect on restoration boundary of image based on sinusoidal integration according to claim 1, wherein the synthesis method of the windowed image g' (x, y) in step 4 is:
g′(x，y)＝g(x，y)×w(x，y) (20)。
4. the sinusoidal integration-based image restoration boundary ringing effect suppression method according to claim 1, wherein the image restoration algorithm in step 5 is a wiener filtering algorithm or an RL restoration algorithm.
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