CN115660994A - Image enhancement method based on regional least square estimation - Google Patents
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Abstract
An image enhancement method based on regional least square estimation belongs to the technical field of image processing. The invention solves the problem of poor quality of the enhanced image obtained by the existing method. The method comprises a region boundary brightness calculation method based on segmented brightness linear mapping and a non-boundary pixel brightness calculation method based on a region least square method, wherein the region boundary brightness calculation method based on the segmented brightness linear mapping determines the overall brightness distribution of the enhanced image, and the non-boundary pixel brightness calculation method based on the region least square method calculates the brightness of non-boundary pixels so as to keep the detail characteristics of the enhanced image consistent with the original image. The algorithm designed by the invention can enhance the brightness distribution of the image, improve the overall visualization effect of the image, effectively maintain the local details of the enhanced image and improve the quality of the enhanced image. The method can be applied to the field of image processing.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image enhancement method based on regional least square estimation.
Background
The image enhancement is realized by enhancing the characteristics of contrast, local detail texture and the like in the image, so that the problem of poor image visual effect caused by poor ambient light and equipment defects in the acquisition and transmission processes of the image is solved, and the image quality of the digital image is improved. Early image enhancement algorithms included: histogram equalization algorithm, adaptive filtering algorithm and contrast enhancement algorithm. The three algorithms can improve the image quality to a certain extent, but the local details, the definition and the overall brightness distribution of the enhanced image are improved in a limited range, so that the quality of the enhanced image obtained by the existing method is still poor and needs to be further improved.
Disclosure of Invention
The invention aims to solve the problem of poor quality of an enhanced image obtained by the existing method, and provides an image enhancement method based on regional least square estimation, which can improve the overall contrast effect of the enhanced image on the premise of ensuring the local detail characteristics of the original image.
The technical scheme adopted by the invention for solving the technical problems is as follows:
an image enhancement method based on regional least squares estimation specifically comprises the following steps:
dividing an image plane to be enhanced into N8 x 8 areas to obtain N image blocks;
step two, calculating low illumination segmentation points of the image to be enhanced
And high luminance segmentation points
Step three, utilizing the low illumination segmentation points calculated in the step two
And high luminance segmentation points
For eachCarrying out piecewise brightness linear mapping on each boundary pixel in the image blocks respectively to obtain enhanced brightness values corresponding to each boundary pixel in each image block;
and fourthly, calculating an enhanced brightness value corresponding to each non-boundary pixel in each image block according to the enhanced brightness value corresponding to each boundary pixel in each image block.
The beneficial effects of the invention are:
the method comprises a region boundary brightness calculation method based on segmented brightness linear mapping and a non-boundary pixel brightness calculation method based on a region least square method, wherein the region boundary brightness calculation method based on the segmented brightness linear mapping determines the overall brightness distribution of the enhanced image, and the non-boundary pixel brightness calculation method based on the region least square method calculates the brightness of non-boundary pixels so as to keep the detail characteristics of the enhanced image consistent with the original image.
Experimental results show that the algorithm designed by the invention can enhance the brightness distribution of the image, improve the overall visualization effect of the image, effectively maintain the local details of the enhanced image and improve the quality of the enhanced image.
Drawings
FIG. 1 is a schematic illustration of boundary pixel and non-boundary pixel numbering;
FIG. 2 is an image kodim;
FIG. 3 is a diagram illustrating a piecewise luminance linear mapping function corresponding to an image kodim;
FIG. 4 is an enhanced image corresponding to image kodim;
FIG. 5 is an original image road;
FIG. 6 is a diagram illustrating a piecewise luminance linear mapping function corresponding to an original image road;
FIG. 7 is an enhanced image corresponding to image road;
FIG. 8 is an image pedestal;
FIG. 9 is a diagram illustrating a piecewise-luminance linear mapping function corresponding to an image seed;
fig. 10 is an enhanced image corresponding to the image pedestal.
Detailed Description
In a first embodiment, an image enhancement method based on regional least squares estimation in this embodiment specifically includes the following steps:
dividing an image plane to be enhanced into N8 x 8 areas to obtain N image blocks;
if the width or height of the image to be enhanced cannot be divided by 8, the width and height of the image after the copying boundary can be divided by 8 by copying the right end boundary and the bottom boundary of the image. Since each image partition has a region size of 8 × 8, each region includes 28 boundary pixels and 36 non-boundary pixels. As shown in fig. 1, is a schematic diagram of an 8 × 8 region and the numbering of boundary pixels and non-boundary pixels;
step two, calculating low illumination segmentation points of the image to be enhanced
And high luminance segmentation points
Step three, utilizing the low illumination segmentation points calculated in the step two
And high luminance segmentation points
Performing piecewise brightness linear mapping on each boundary pixel in each image block to obtain an enhanced brightness value corresponding to each boundary pixel in each image block;
and fourthly, calculating an enhanced brightness value corresponding to each non-boundary pixel in each image block according to the enhanced brightness value corresponding to each boundary pixel in each image block.
The second embodiment is as follows: the present embodiment is different from the first embodiment in that the low illuminance segmentation point
The calculation method comprises the following steps:
wherein, the symbol
Represents a rounding down operation;
wherein b represents a gray scale, H b Representing the gray distribution corresponding to the gray scale b;
D l (T l )＝A l (T l )-M l (T l ) (3)
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: in this embodiment, the high-luminance segment point is different from the first or second embodiment
The calculation method comprises the following steps:
step (1), in the gray scale interval [128,255]Arbitrarily selecting one gray level as high illumination segmentation point T h ；
Step (2), calculating the gray scale interval [ T ] of the image to be enhanced h ,255]Middle number of gray levels M h (T h )，M h (T h ) Is calculated as shown in equation (5):
wherein, the symbol
Represents a ceiling operation;
step (3), calculating the gray level interval [128, T ] of the image to be enhanced according to the gray level histogram h +1]Gray level mean value A of h (T h )，A h (T h ) Is calculated as shown in equation (6):
wherein b represents a gray scale, H b Representing the gray distribution corresponding to the gray scale b;
step (4), calculatingMean value of gray scale A h (T h ) And the median M of the gray scale h (T h ) Difference D of h (T h )，D h (T h ) Is calculated as shown in equation (7):
D h (T h )＝M h (T h )-A h (T h ) (7)
step (5) repeating the processes from the step (1) to the step (4) to enable the high-illumination segmentation point T h In the gray scale interval [128,255]Internally traversing to find the maximum difference D h (T h ) The corresponding segmentation point is used as the final high-illumination segmentation point
Is calculated as shown in equation (8):
other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment and one of the first to third embodiments is that the specific process of step three is:
low light level segmentation point
And high illumination segmentation point
The corresponding gray scale value is shown as the formula (9):
wherein ,
is composed of
The corresponding gray-scale value of the gray-scale value,
is composed of
The corresponding value of the gray-scale value,
is composed of
The corresponding cumulative probability distribution is then calculated,
is composed of
Corresponding cumulative probability distributions;
performing piecewise linear brightness mapping on each boundary pixel in each image block to obtain an enhanced brightness value corresponding to each boundary pixel in each image block;
the piecewise linear luminance mapping expression is shown in equation (10):
wherein I represents the luminance value of the boundary pixel,
representing the enhanced luminance values corresponding to the boundary pixels.
As shown in fig. 1, each image block includes 28 boundary pixels, and the method according to this embodiment may obtain enhanced luminance values corresponding to the 28 boundary pixels of each image block.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is that the specific process of step four is:
step S1, constructing a function f which is related to 28 boundary weights and has an accumulation form for the kth non-boundary pixel in all N areas k (ω 1 ,ω 2 ,...,ω 28 ) Function f k (ω 1 ,ω 2 ,...,ω 28 ) As shown in formula (11):
f k (ω 1 ,ω 2 ,...,ω 28 )＝∑ i (ω 1 I i,1 +ω 2 I i,2 +···+ω 28 I i,28 -I i (k)) 2 (11)
wherein ,ω1 ,ω 2 ,...,ω 28 Weights for the respective boundary pixels, I i,1 Represents the enhanced brightness value corresponding to the 1 st boundary pixel in the I-th area, I =1,2, …, N, I i (k) Representing the original brightness value of the kth non-boundary pixel in the ith area in the image to be enhanced;
according to the least square criterion, for function f k (ω 1 ,ω 2 ,...,ω 28 ) Arbitrary boundary pixel weight ω j The derivative function of (a) is 0, i.e., equation (12) holds:
wherein j =1,2, …,28;
substituting all the boundary weights into equation (12), and combining equation (11) to obtain a linear equation system regarding the boundary weights shown in equation (13):
solving the formula (13) by a Jacobian iteration method to obtain an optimal solution of any boundary weight, as shown in the formula (14):
wherein the superscript t represents the number of iterations,
representing the weight of the jth border pixel obtained from the t iteration,
representing the weight of the jth boundary pixel obtained in the t-1 th iteration;
the Jacobian iterative method converges when equation (15) is consistently true for all boundary pixels:
s2, calculating an enhanced brightness value of a kth non-boundary pixel in the ith area
And S3, repeating the processes from the step S1 to the step S2, and respectively obtaining the enhanced brightness value corresponding to each non-boundary pixel in each image block.
Other steps and parameters are the same as in one of the first to fourth embodiments.
Results and analysis of the experiments
The invention carries out simulation experiment on the algorithm through a desktop computer. Hardware configuration of desktop: the model of the central processing unit is i5-12400F, the specification of the display card is RTX3060, and the memory capacity is 128G. The operating system of the desktop is Windows 11, and the simulation software platform is Matlab 2020a. The input and output of the algorithm are both gray scale images in jpg format. The simulation results are shown in fig. 2 to 10.
Comparing the original image and the enhanced image reveals that: the algorithm designed by the invention can improve the overall visual impression of the image and enhance the contrast of the image to be effectively improved. The luminance of the pixels in the insufficiently illuminated area is effectively stretched to improve the visibility of the area. In addition, the enhanced image has more outstanding capability of maintaining local details of the original image, and the edges and the outlines of all targets in the enhanced image are clearer. Therefore, the algorithm designed by the invention can effectively improve the image quality and greatly improve the visual effect of the enhanced image.
The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.
Claims (5)
1. An image enhancement method based on regional least squares estimation is characterized by specifically comprising the following steps:
dividing an image plane to be enhanced into N8 x 8 areas to obtain N image blocks;
step two, calculating low illumination segmentation points of the image to be enhanced
And high luminance segmentation points
Step three, utilizing the low illumination segmentation points calculated in the step two
And high luminance segmentation points
Performing piecewise brightness linear mapping on each boundary pixel in each image block to obtain an enhanced brightness value corresponding to each boundary pixel in each image block;
and fourthly, calculating an enhanced brightness value corresponding to each non-boundary pixel in each image block according to the enhanced brightness value corresponding to each boundary pixel in each image block.
2. The image enhancement method based on area least squares estimation of claim 1, wherein the low illumination segmentation points
The calculation method comprises the following steps:
step 1, in the gray scale interval [0,127]Arbitrarily selecting one gray level as low-illumination segmentation point T l ；
Step 2, calculating the gray scale interval [0,T ] of the image to be enhanced l ]Middle number of gray levels M l (T l )，M l (T l ) The calculation method of (2) is shown in formula (1):
wherein, the symbol
Indicating a rounding-down operation；
Step 3, calculating the gray level interval [ T ] of the image to be enhanced according to the gray level histogram l +1,127]Gray level mean value A of l (T l )，A l (T l ) The calculation method of (2) is shown as the following formula:
wherein b represents a gray scale, H b Representing the gray distribution corresponding to the gray scale b;
step 4, calculating the mean value A l (T l ) And median M l (T l ) Difference D of l (T l )，D l (T l ) The calculation method of (2) is shown in formula (3):
D l (T l )＝A l (T l )-M l (T l ) (3)
step 5, repeating the processes from step 1 to step 4 to make the low illumination segmentation point T l In the gray scale interval [0,127]Internally traversing to find the maximum difference D l (T l ) The corresponding low-illumination segmentation point is used as the final low-illumination segmentation point
Namely, it is
3. The image enhancement method based on regional least squares estimation of claim 1, wherein the high brightness segmentation points
The calculation method comprises the following steps:
step (1), in the gray scale interval [128,255]Arbitrarily selecting one gray level as high illumination segmentation point T h ；
Step (2), calculating the gray scale interval [ T ] of the image to be enhanced h ,255]Middle number of gray levels M h (T h )，M h (T h ) Is calculated as shown in equation (5):
wherein, the symbol
Represents a ceiling operation;
step (3), calculating the gray level interval [128, T ] of the image to be enhanced according to the gray level histogram h +1]Gray level mean value A of h (T h )，A h (T h ) Is calculated as shown in equation (6):
wherein b represents a gray scale, H b Representing the gray distribution corresponding to the gray scale b;
step (4), calculating the gray average value A h (T h ) And the median M of the gray scale h (T h ) Difference D of h (T h )，D h (T h ) Is calculated as shown in equation (7):
D h (T h )＝M h (T h )-A h (T h ) (7)
step (5) repeating the processes from the step (1) to the step (4) to enable the high-illumination segmentation point T h In the gray scale interval [128,255]Internally traversing to find the maximum difference D h (T h ) The corresponding segmentation point is used as the final high-illumination segmentation point
Is calculated as shown in equation (8):
4. the image enhancement method based on regional least squares estimation according to claim 1, wherein the specific process of the third step is as follows:
low light level segmentation point
And high illumination segmentation point
The corresponding gray scale value is shown as the formula (9):
wherein ,
is composed of
The corresponding gray-scale value of the gray-scale value,
is composed of
The corresponding gray-scale value of the gray-scale value,
is composed of
The corresponding cumulative probability distribution is then calculated,
is composed of
Corresponding cumulative probability distributions;
performing piecewise linear brightness mapping on each boundary pixel in each image block to obtain an enhanced brightness value corresponding to each boundary pixel in each image block;
the piecewise linear luminance mapping expression is shown in equation (10):
wherein I represents the luminance value of the boundary pixel,
representing the enhanced luminance values corresponding to the boundary pixels.
5. The image enhancement method based on regional least squares estimation according to claim 1, wherein the specific process of the fourth step is as follows:
step S1, constructing a function f which is related to 28 boundary weights and has an accumulation form for the kth non-boundary pixel in all N areas k (ω 1 ,ω 2 ,...,ω 28 ) Function f k (ω 1 ,ω 2 ,...,ω 28 ) As shown in formula (11):
f k (ω 1 ,ω 2 ,...,ω 28 )＝∑ i (ω 1 I i,1 +ω 2 I i,2 +···+ω 28 I i,28 -I i (k)) 2 (11)
wherein ,ω1 ,ω 2 ,...,ω 28 Weights for the respective boundary pixels, I i,1 Represents the enhanced brightness value corresponding to the 1 st boundary pixel in the ith area, I =1,2, …, N, I i (k) Representing the original brightness value of the kth non-boundary pixel in the ith area in the image to be enhanced;
according to the least square criterion, for function f k (ω 1 ,ω 2 ,...,ω 28 ) Arbitrary boundary pixel weight ω j The derivative function of (a) is 0, i.e., equation (12) holds:
wherein j =1,2, …,28;
substituting all the boundary weights into equation (12), and combining equation (11) to obtain a linear equation system regarding the boundary weights shown in equation (13):
solving the formula (13) by a Jacobian iteration method to obtain an optimal solution of any boundary weight, as shown in the formula (14):
wherein the superscript t represents the number of iterations,
representing the weight of the jth boundary pixel obtained at the tth iteration,
representing the weight of the jth boundary pixel obtained by the t-1 iteration;
the jacobian iteration method converges when equation (15) holds for all boundary pixels:
s2, calculating an enhanced brightness value of a kth non-boundary pixel in the ith area
And S3, repeating the processes from the step S1 to the step S2, and respectively obtaining the enhanced brightness value corresponding to each non-boundary pixel in each image block.
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