CN109903239B - Self-adaptive image defogging method based on weighted total variation - Google Patents
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Abstract
The invention discloses a self-adaptive image defogging method based on weighted total variation, which comprises the following steps: inputting an observation image; estimating an ambient brightness value; establishing an optimization objective function according to the atmospheric imaging model and the regularization constraint thought; initializing a transmittance map and a restoration result image; solving sub-objective functions of the optimized transmittance graph; solving a sub-objective function of the image with the optimized restoration result; judging whether the current iteration number reaches a set value: if not, returning to the step S5; and if so, outputting a recovery result image. The method improves the image contrast and definition of foggy day imaging, and simultaneously inhibits the enhanced noise in the image restoration process.
Description
Technical Field
The invention relates to the field of image enhancement, in particular to a self-adaptive image defogging method based on weighted total variation.
Background
Under the foggy environment, light is interfered by forward and backward scattering of suspended particles such as fog, haze and water vapor in a medium in a transmission process, so that the image is degraded due to low contrast, dark color, fuzzy texture and the like, the image is fuzzy, the original color of the surface of the object is covered, and the detail information of the object at the distant view is lost. The image quality in the foggy day is seriously reduced, the integral information quantity of the image is greatly reduced, and the subsequent application of computer vision systems such as traffic monitoring, target tracking and the like is influenced. For fog-free image restoration in foggy days, the prior art generally starts from an atmospheric imaging model I (x) = t (x) · J (x) + (1-t (x)) a reflecting an image degradation process (wherein x represents a pixel coordinate index, I (x) is an observed image, t (x) is a transmittance map reflecting scattering effects of suspended particles, J (x) is a restoration result image to be solved, and a is an environmental brightness value), and different priori knowledge such as dark channel prior [1 ] is provided]Reproducibility of image blocks [2]Unknown in the peer modelIs estimated from the transmittance map t (x) and the ambient brightness value A, and is then mathematically operated on the model
To obtain a restoration result image.
The prior art estimates the transmittance map t (x) by means of proposing a priori knowledge, and obtains a restored image J (x) directly through the equation operation of a model on the basis of the transmittance map t (x). However, in the prior art, direct equation operation is adopted, and different processing on noise in an observed image is not considered, so that the prior art can enhance the noise existing in a distant view region of the image while restoring, noise which is not obvious in visual effect due to haze superposition on the observed image is obviously visible on a restoration result, and image quality is influenced.
Reference documents:
[1]He K,Jian S,Tang X.Single image haze removal using dark channel prior[C]//IEEE Conference on Computer Vision&Pattern Recognition.2009.
[2]Michaeli T,Irani M.Blind Deblurring Using Internal Patch Recurrence[C]//European Conference on Computer Vision.Springer International Publishing,2014.
disclosure of Invention
The invention mainly aims to overcome the defects and shortcomings of the prior art and provide a self-adaptive image defogging method based on weighted total variation.
The purpose of the invention is realized by the following technical scheme:
a self-adaptive image defogging method based on weighted total variation comprises the following steps:
s1, inputting an observation image;
s2, estimating an environment brightness value;
s3, establishing an optimization objective function according to the atmospheric imaging model and the regularization constraint thought;
s4, initializing a transmissivity graph and a restoration result image;
s5, solving a sub-objective function of the optimized transmittance graph;
s6, solving a sub-objective function of the image with the optimized restoration result;
s7, judging whether the current iteration number reaches a set value: if not, returning to the step S5; and if so, outputting a recovery result image.
The step S2 specifically includes:
s2-1, carrying out combined R, G, B three-channel minimum value filtering operation on the observed image:
wherein, omega is a neighborhood window taking x as a central pixel, y is an adjacent pixel point of x in the window omega, and c belongs to { R, G, B } and is R, G, B triple channels;
s2-2, to I min (x) Maximum value sorting is carried out, and the pixel coordinates corresponding to the first 10 percent are selected as a candidate pixel set S of a pure environment brightness area 1 (x)；
S2-3, converting the observation image into an HSV space, carrying out maximum value sorting on the V-channel image, and selecting the pixel coordinate corresponding to the top 10% as a candidate pixel set S of a pure environment brightness area 2 (x)；
S2-4, obtaining set S 1 (x) And S 2 (x) Intersection of (a): s (x) = S 1 (x)∩S 2 (x) (ii) a If S (x) is empty set, let S (x) = S 1 (x)；
S2-5, obtaining pixel values of corresponding points on the observation image according to the pixel coordinate set S (x), and obtaining an average value as an environment brightness value A:
wherein n is the number of elements in the set S (x).
In step S3, the objective function is:
min J ‖(I(x)-A)-t(x)(J(x)-A)‖ 2 +R(t(x))+R(J(x))；
wherein the first term is a data fidelity term, R (t (x)) is a regularization constraint term for the transmittance map x (x), and R (J (x)) is a regularization constraint term for the restoration result image J (x);
the method comprises the following specific steps:
(1) Design R (t (x)):
the transmittance graph t (x) reflects the degree of attenuation of the light radiation degree reflected by each pixel point by particle scattering in the process of propagation to the imaging plane; the attenuation degree is related to the distance from the scene point corresponding to the pixel point to the imaging plane, namely the depth of field; the farther a scene point is, the farther the light ray transmission distance reflected by the point is, the more serious the attenuation is disturbed by particles, and the corresponding transmissivity is also smaller; in a natural image, the change of the depth of field has the characteristic of smooth slicing, namely the depth of field can be regarded as a constant in a local area; therefore, the transmittance map t (x) also has a slice-smooth property; the method further considers the spatial position relation and the value relation of the transmittance value of each pixel point and the transmittance value of the neighborhood pixel point, and designs a weighted total variation regularization term:
wherein K is a weight convolution kernel,
in order to perform the convolution operation,
is a gradient operator; the specific expression of the weight convolution kernel K is as follows:
wherein, σ is a scale parameter for controlling the size of the template window, and y is a field pixel point of a central pixel point x in the template window; (x-y) 2 The spatial distance between two pixel points is represented,
the difference of two pixel points in the gradient value is represented;
(2) Design R (J (x)):
aiming at the problem that the noise enhancement exists in the restoration process of a result image J (x) to be restored, the method introduces Relative total variation constraint (Relative TV, RTV):
wherein, omega is a neighborhood window taking x as a central pixel, y is an adjacent pixel point of x in the window omega, and theta h And theta v Respectively representing discrete differential operations in the horizontal and vertical directions, epsilon being a very small positive number preventing the denominator from being 0;
weight function g x,y The method specifically comprises the following steps:
wherein δ is a scale parameter;
the method can separate the texture from the main contour in the image by relative total variation, and skillfully analogizes the weak edge in the noisy area to the main contour and the noise to the texture for separation according to the scale relation of the weak edge of the noisy area and the noise. Further, designing a self-adaptive regularization parameter, adaptively adjusting the regularization parameter according to the transmittance value of the pixel point corresponding to the scene point, performing constraint strength of different degrees on different regions, and protecting image details of a close-range region:
wherein c is a constant coefficient;
thus, the regularization constraint term for the restoration result image J (x) is:
R(J(x))＝λ(x)·RTV(J(x))；
(3) And (2) integrating (1) and (2), wherein the objective function is as follows:
the solving method of the objective function comprises the following steps:
(1) Initialization t (x) and J (x):
J(x)＝0；
(2) Optimizing variable t (x), wherein the solving step is as follows:
A. fixing the variable J (x), and removing constant items irrelevant to the optimization of the variable t (x), the sub-objective function is:
B. based on the split Bregman method, an auxiliary variable d is introduced, and the objective function becomes:
C. the fixed variable t optimizes the variable d, and the objective function is:
wherein d is i The superscript i denotes the current iteration round, t i-1 Represents the i-1 st iterationThe obtained transmittance map t; and (3) rapidly solving by adopting a shringkage operation:
D. the fixed variable d optimizes the variable t, and the objective function is as follows:
fast Fourier transform is adopted to obtain closed solution rapidly:
wherein the content of the first and second substances,
in order to perform the fourier transformation, the method,
is an inverse fourier transform of the signal to be processed,
is a complex conjugate operator;
respectively represents d i As a result of the first order difference in the horizontal and vertical directions,
first order gradient operators respectively representing the horizontal direction and the vertical direction;
E. returning to the step C to carry out loop iteration until the set iteration times are reached;
(3) Optimizing variables J (x), wherein the solving step is as follows:
A. fixing the variable t (x), and removing the constant term irrelevant to the optimization of the variable J (x), the sub-objective function is:
min J(x) ||(I(x)-A)-t(x)(J(x)-A)|| 2 +λ(x)·RTV(J(x))；
B. the RTV (J (x)) is rewritten to:
wherein u is h，y ，W h，y ，u v，y ，W v，y Respectively calculated according to the following formula:
wherein G is σ A gaussian filter with standard deviation σ;
C. substituting the rewritten RTV (J (x)) into the sub-targeting function, and writing the elements therein into a matrix form:
wherein upsilon is I 、v A 、υ t And v J Vector forms representing I (x), A, t (x), and J (x), respectively; λ represents a matrix form of the regularization parameter λ (x); c h And C v As a discrete difference operator theta h And theta v The Toeplitz matrix form of (1); u shape h 、U v 、W h And W v Is u h，y 、w h，y 、u v，y And w v，y In the form of a diagonal matrix;
D. removing and v J After optimizing the independent constant terms, the objective function can be reduced to the solution of the linear equation:
wherein 1 is an identity matrix; according to fixed upsilon t Obtaining v J ：
E. V is to be J Converting the image into a matrix form to obtain an optimized image J (x);
(4) And (5) returning to the step (2), and circularly iterating until the set iteration times is reached.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. aiming at the defect that the prior art obtains a recovery result image J (x) directly through the equation operation of a model to cause noise enhancement, the invention designs a targeted novel regularization constraint optimization term according to the characteristics of a transmissivity image t (x) and the recovery result image J (x) respectively, forms an optimized objective function and carries out corresponding solution, so that the defogging result can effectively smooth and inhibit noise and keep weak edge information of a noise area while improving the image contrast and recovering detail information.
2. The method improves the image contrast and definition of foggy day imaging, and simultaneously inhibits the enhanced noise in the image restoration process. The optimization of the transmittance graph t (x) and the restoration result image J (x) can be realized by designing different regularization constraint terms.
Drawings
FIG. 1 is a flow chart of an adaptive image defogging method based on weighted total variation according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
As shown in fig. 1, an adaptive image defogging method based on weighted total variation includes the following steps:
1. estimated ambient brightness value a:
(1) And (3) carrying out minimum value filtering operation of a joint R, G, B three channels on the observation image:
wherein, Ω is a neighborhood window with x as a central pixel, y is an adjacent pixel point of x in the window Ω, and c belongs to { R, G, B } is R, G, B triple channel.
(2) To I min (x) Maximum value sorting is carried out, and the pixel coordinates corresponding to the top 10 percent are selected as a candidate pixel set S of the pure environment brightness area 1 (x)。
(3) Converting the observation image into HSV space, sorting the maximum value of the V-channel image, and selecting the pixel coordinate corresponding to the top 10% as a candidate pixel set S of a pure environment brightness area 2 (x)。
(4) Find set S 1 (x) And S 2 (x) Intersection of (a): s (x) = S 1 (x)∩S 2 (x) In that respect If S (x) is empty set, let S (x) = S 1 (x)。
(5) Acquiring pixel values of corresponding points on an observation image according to a pixel coordinate set S (x), and solving a mean value as an environment brightness value:
wherein n is the number of elements in the set S (x).
2. Establishing an optimization objective function according to an atmospheric imaging model and a regularization constraint thought:
wherein the first item is a data fidelity item. R (t (x)) is a regularization constraint term for the transmittance map t (x), and R (J (x)) is a regularization constraint term for the restoration result image J (x).
(1) Design R (t (x)):
the transmittance map t (x) reflects the degree of attenuation of the light radiance reflected by each pixel point by particle scattering in the propagation process of reaching the imaging plane. The attenuation degree is related to the distance from the scene point corresponding to the pixel point to the imaging plane, i.e. the depth of field. The farther a scene point is, the farther the light reflected at that point travels, the more severely attenuated by the particle interference and the corresponding transmission will be. In a natural image, the depth of field changes have the characteristic of smooth slicing, i.e., the depth of field can be regarded as a constant in a local area. Therefore, the transmittance map t (x) also has a slice-smooth characteristic. The method further considers the spatial position relation and the value relation of the transmittance value of each pixel point and the transmittance value of the neighborhood pixel point, and designs a weighted total variation regularization term:
wherein K is a weight convolution kernel,
in order to perform the convolution operation,
is a gradient operator; the specific expression of the weight convolution kernel K is as follows:
wherein, σ is a scale parameter for controlling the size of the template window, and y is a field pixel point of the central pixel point x in the template window. (x-y) 2 The space between two pixel points is representedThe distance between the first and second electrodes is less than the predetermined distance,
the difference of the two pixel points in the gradient value is represented.
(2) Design R (J (x)):
aiming at the problem that the noise enhancement exists in the restoration process of a result image J (x) to be restored, the method introduces Relative total variation constraint (Relative TV, RTV):
wherein, omega is a neighborhood window taking x as a central pixel, y is an adjacent pixel point of x in the window omega, and theta h And theta v Representing discrete differential operations in the horizontal and vertical directions, respectively, epsilon is a very small positive number that prevents the denominator from being 0. Weight function g x，y The method specifically comprises the following steps:
wherein δ is a scale parameter.
The method can separate the texture from the main contour in the image by relative total variation, and skillfully analogizes the weak edge in the noisy area to the main contour and the noise to the texture for separation according to the scale relation of the weak edge of the noisy area and the noise. Further, designing a self-adaptive regularization parameter, adaptively adjusting the regularization parameter according to the transmittance value of the pixel point corresponding to the scene point, performing constraint strength of different degrees on different regions, and protecting image details of a close-range region:
wherein c is a constant coefficient. Thus, the regularization constraint term for the restoration result image J (x) is:
R(J(x))＝λ(x)·RTV(J(x))
(3) By integrating (1) and (2), the novel self-adaptive image defogging objective function based on the weighted total variation provided by the method is as follows:
3. the solving method of the objective function comprises the following steps:
for two variables t (x) and J (x) in the objective function, an alternating minimization method is employed herein to optimize one variable by fixing the other variable. Therefore, the solution of the novel adaptive image defogging objective function based on the weighted total variation proposed by the method can be converted into the alternative iterative solution of two sub-optimization problems aiming at t (x) and J (x):
(1) Initialization t (x) and J (x):
J(x)＝0
(2) Optimizing variable t (x), wherein the solving step is as follows:
(1) fixing the variable J (x), and removing constant items irrelevant to the optimization of the variable t (x), the sub-objective function is:
(2) based on the split Bregman approach, an auxiliary variable d is introduced and the objective function becomes:
here, the pixel coordinate index x is omitted for simplicity of expression.
(3) The fixed variable t optimizes the variable d, and the objective function is:
wherein d is i The superscript i denotes the current iteration round, t i-1 The transmission diagram t obtained in the i-1 th iteration is shown. And (3) rapidly solving by adopting a shringkage operation:
(4) the fixed variable d optimizes the variable t, and the objective function is:
fast Fourier transform is adopted to obtain closed solution rapidly:
wherein the content of the first and second substances,
in order to perform the fourier transformation, the method,
for the purpose of the inverse fourier transformation,
is a complex conjugate operator.
Respectively represents d i As a result of the first order difference in the horizontal and vertical directions,
representing the first order gradient operators in the horizontal and vertical directions, respectively.
(5) And (4) returning to the step (3) to carry out loop iteration until the set iteration times are reached.
(3) Optimizing variables J (x), wherein the solving step is as follows:
(1) fixing the variable t (x), and removing constant items irrelevant to the optimization of the variable J (x), the sub-objective function is:
(2) for ease of calculation, RTV (J (x)) is rewritten to:
wherein u is h，y ，w h，y ，u v，y ，w v，y Respectively calculated according to the following formula:
wherein G is σ Is a gaussian filter with standard deviation sigma.
(3) Substituting the rewritten RTV (J (x)) into the sub-targeting function, and writing the elements therein in a matrix form:
wherein upsilon is I 、v A 、υ t And v J Represent vector forms of I (x), A, t (x), and J (x), respectively. λ represents the matrix form of the regularization parameter λ (x). C h And C v As a discrete difference operator theta h And theta v In the form of a Toeplitz matrix. U shape h 、U v 、W h And W v Is u h，y 、w h，y 、u v，y And w v，y In the form of a diagonal matrix.
(4) Removing and v J After optimizing the independent constant terms, the objective function can be reduced to the solution of the linear equation:
where 1 is an identity matrix. According to fixed upsilon t Can find v J ：
(5) V is to be J And converting the image into a matrix form to obtain an optimized image J (x).
(4) And (5) returning to the step (2), and circularly iterating until the set iteration times is reached.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (2)
1. A self-adaptive image defogging method based on weighted total variation is characterized by comprising the following steps:
s1, inputting an observation image;
s2, estimating an environment brightness value;
s3, establishing an optimization objective function according to the atmospheric imaging model and the regularization constraint thought;
in step S3, the objective function is:
min J ‖(I(x)-A)-t(x)(J(x)-A)‖ 2 +R(t(x))+R(J(x))；
wherein the first term is a data fidelity term, R (t (x)) is a regularization constraint term for the transmittance map t (x), and R (J (x)) is a regularization constraint term for the restoration result image J (x);
the method comprises the following specific steps:
(1) Design R (t (x)):
the transmittance graph t (x) reflects the degree of attenuation of the light radiance reflected by each pixel point by particle scattering in the process of propagation to an imaging plane; the attenuation degree is related to the distance from the scene point corresponding to the pixel point to the imaging plane, namely the depth of field; the farther a scene point is, the farther the light ray transmission distance reflected by the point is, the more serious the attenuation is disturbed by particles, and the corresponding transmissivity is also smaller; in a natural image, the change of the depth of field has the characteristic of smooth slicing, namely the depth of field can be regarded as a constant in a local area; therefore, the transmittance map t (x) also has a slice-smooth property; designing a weighted total variation regularization term:
wherein K is a weight convolution kernel,
in order to perform the convolution operation,
is a gradient operator; the specific expression of the weight convolution kernel K is as follows:
wherein, sigma is a scale parameter for controlling the size of the template window, and y is a domain image of a central pixel point x in the template windowPrime points; (x-y) 2 The spatial distance between two pixel points is represented,
the difference of two pixel points in the gradient value is represented;
(2) Design R (J (x)):
aiming at the problem that the noise enhancement exists in the restoration process of a result image J (x) to be restored, the method introduces a relative total variation constraint:
wherein, omega is a neighborhood window with x as a central pixel, y is an adjacent pixel point of x in the window omega,
and
respectively representing discrete differential operations in the horizontal and vertical directions, epsilon being a very small positive number preventing the denominator from being 0;
weight function g x,y The method specifically comprises the following steps:
wherein δ is a scale parameter;
designing a self-adaptive regularization parameter, adaptively adjusting the regularization parameter according to the transmittance value of the scene point corresponding to the pixel point, carrying out constraint force of different degrees on different regions, and protecting the image details of a near scene region:
wherein c is a constant coefficient;
thus, the regularization constraint term for the restoration result image J (x) is:
R(J(x))＝λ(x)·RTV(J(x))；
(3) And (2) integrating (1) and (2), wherein the objective function is as follows:
the solving method of the objective function comprises the following steps:
(1) Initialization t (x) and J (x):
J(x)＝0；
(2) Optimizing a variable t (x), wherein the solving step comprises the following steps:
A. fixing the variable J (x), and removing constant items irrelevant to the optimization of the variable t (x), the sub-objective function is:
B. based on the split Bregman approach, an auxiliary variable d is introduced and the objective function becomes:
C. the fixed variable t optimizes the variable d, and the objective function is:
wherein, d i The superscript i denotes the current iteration round, t i-1 Representing the transmissivity graph t obtained by the i-1 th iteration; and (3) rapidly solving by adopting a shringkage operation:
D. the fixed variable d optimizes the variable t, and the objective function is:
fast Fourier transform is adopted to obtain closed solution rapidly:
wherein the content of the first and second substances,
in order to perform the fourier transformation, the method,
for the purpose of the inverse fourier transformation,
is a complex conjugate operator;
respectively represents d i As a result of the first order difference in the horizontal and vertical directions,
first order gradient operators respectively representing the horizontal direction and the vertical direction;
E. returning to the step C to carry out loop iteration until the set iteration times are reached;
(3) Optimizing variables J (x), wherein the solving step is as follows:
A. fixing the variable t (x), and removing constant items irrelevant to the optimization of the variable J (x), the sub-objective function is:
min J(x) ‖(J(x)-A)-t(x)(J(x)-A)‖ 2 +λ(x)·RTV(J(x))；
B. the RTV (J (x)) is rewritten to:
wherein u is h,y ,w h,y ,u v,y ,w v,y Respectively calculated according to the following formula:
wherein G is σ A gaussian filter with standard deviation σ;
C. substituting the rewritten RTV (J (x)) into the sub-targeting function, and writing the elements therein into a matrix form:
wherein upsilon is I 、v A 、v t V and v J Vector forms representing I (x), A, t (x), and J (x), respectively; λ represents a matrix form of the regularization parameter λ (x); c h And C v As discrete difference operators
And
the Toeplitz matrix form of (1); u shape h 、U v 、W h And W v Is u h,y 、w h,y 、u v,y And w v,y In the form of a diagonal matrix;
D. removing and purifying v J After optimizing the independent constant terms, the objective function can be summarized as the solution of the linear equation:
wherein 1 is an identity matrix; according to fixed upsilon t Obtaining v J ：
E. V is to be J Converting the image into a matrix form to obtain an optimized image J (x);
(4) Returning to the step (2), and circularly iterating until the set iteration times is reached;
s4, initializing a transmissivity graph and a restoration result image;
s5, solving a sub-objective function of the optimized transmittance graph;
s6, solving a sub-objective function of the image of the optimized restoration result;
s7, judging whether the current iteration number reaches a set value: if not, returning to the step S5; and if so, outputting a recovery result image.
2. The adaptive image defogging method based on the weighted total variation as recited in claim 1, wherein said step S2 specifically comprises:
s2-1, carrying out combined R, G, B three-channel minimum value filtering operation on the observed image:
wherein, omega is a neighborhood window taking x as a central pixel, y is an adjacent pixel point of x in the window omega, and c belongs to { R, G, B } and is R, G, B triple channels;
s2-2, to I min (x) Maximum value sorting is carried out, and the pixel coordinates corresponding to the first 10 percent are selected as a candidate pixel set S of a pure environment brightness area 1 (x)；
S2-3, converting the observation image into an HSV space, carrying out maximum value sorting on the V-channel image, and selecting the pixel coordinate corresponding to the top 10% as a candidate pixel set S of a pure environment brightness area 2 (x)；
S2-4, finding set S 1 (x) And S 2 (x) Intersection of (a): s (x) = S 1 (x)∩S 2 (x) (ii) a If S (x) is empty set, let S (x) = S 1 (x)；
S2-5, obtaining pixel values of corresponding points on the observation image according to the pixel coordinate set S (x), and obtaining an average value as an environment brightness value A:
wherein n is the number of elements in the set S (x).
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