CN104282004B - Self-adaptation equalization method based on extensible segmentation histogram - Google Patents
Self-adaptation equalization method based on extensible segmentation histogram Download PDFInfo
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Abstract
The invention discloses a self-adaptation equalization method based on an extensible segmentation histogram. The self-adaptation equalization method comprises the following steps that firstly, an input original histogram is extended through an extensible histogram segmentation method; secondly, equalization is carried out on the extended histogram, and each equalized sub-histogram has the length same as that of the original histogram; thirdly, weighting mixture is carried out on the equalized sub-histograms obtained in the second step to obtain a final equalized histogram Ht (i). According to the method, an extensible histogram segmentation strategy is adopted, the image gray level obtained after equalization can be distributed to a large dynamic range again, and sufficient enhancement on the image in the dark area is facilitated; the self-adaptation histogram equalization method is adopted, the gray level uniform distribution degree is controlled according to the image gray level attribute in a self-adaptation mode, and accordingly excessive enhancement, insufficient enhancement and an unnatural halo phenomenon of the image can be avoided; according to the whole method, the calculation speed is high, and an image with the obvious enhanced effect is obtained.
Description
Technical Field
The invention relates to a self-adaptive equalization method based on an extensible segmented histogram.
Background
Histogram Equalization (HE) is widely applied to the fields of traffic monitoring, medical image processing and the like due to the characteristics of simple principle, high calculation speed and the like. The HE increases a difference of improving adjacent gray levels by distributing the high dynamic range gray levels to a uniform distribution, thereby realizing contrast enhancement. However, if there are a plurality of peaks in the histogram, over-enhancement, under-enhancement, and unnatural halo phenomena may occur; in order to avoid the above problems, methods such as Adaptive Local Histogram Equalization (ALHE), contrast-limited adaptive histogram equalization (CLAHE) and the like firstly divide an image into a plurality of small windows, and perform histogram equalization in the small windows respectively; but due to the lack of global information, these methods are often excessive or checkerboard. The Histogram Modification Frame (HMF) method treats the image contrast enhancement as an optimization problem of uniform redistribution of the histogram, original histogram maintenance and smooth combination of the histogram, thereby realizing adjustable enhancement of the image contrast; two-dimensional histogram equalization (2 DHE) synchronously considers the gray level distribution of each pixel and adjacent pixels to construct a two-dimensional histogram, and then uniformly redistributes the two-dimensional histogram to realize image contrast enhancement; the AMHE directly modifies the histogram of the original image and adopts a histogram specification method to realize image enhancement; however, these methods all deal with the whole histogram, and over-enhancement and under-enhancement are difficult to avoid, and in a flat area of the image, a halo phenomenon may occur. For this purpose, researchers have proposed many improved methods such as luminance preserving histogram equalization (BBHE), same region subgraph histogram equalization (DSIHE), minimum mean luminance error double histogram equalization (mmbhe), Recursive Mean Separation Histogram Equalization (RMSHE), and luminance preserving dynamic blur histogram equalization (BPDFHE), among others. Furthermore, a gaussian mixture model is introduced to fit the gray distribution, and then the original histograms are separated by the intersection points between the mixture models, and histogram equalization is performed separately. These multi-histogram equalization methods can effectively preserve luminance, but when used for dark image enhancement, can result in under-enhancement; furthermore, since multiple sub-histograms all use the same equalization strategy, these methods are prone to over-enhancement when the image contrast is large.
Disclosure of Invention
The invention provides an adaptive equalization method based on an expandable segmented histogram, and aims to solve the problems that in the process of enhancing a dark image, the dark area of the image is easily under-enhanced, and the bright area of the image is excessively enhanced or seriously degraded in the conventional method.
An equalization method based on an extensible piecewise self-adaptive histogram comprises the following steps:
step 1: expanding the input original histogram by adopting an expandable histogram segmentation method;
first, the original histogram H isoSegmentation into N non-overlapping segmented histograms hk，k∈[1,…，N](ii) a Then all the segmented histograms hkExpanded to the original histogram H respectivelyoHistogram with same gray level interval, keeping segmented histogram hkThe original histogram is unchanged, and other positions are filled with zeros to obtain the expandable segmented histogram(k∈[1,…，N])， <math>
<mrow>
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Step 2: equalizing the expandable segmented histograms, wherein each equalized sub-histogram has the same length as the original histogram;
and step 3: equalizing the sub-histogram obtained in the step 2Weighted mixing is carried out according to the following formula to obtain a final equalized histogram Ht(i)：
Wherein, wk(i) Is the normalized weight of the k-th equalized-spread-segment histogram,weight functionN is the number of histogram segments, i is the gray level, ukAnd σkRespectively the mean and variance of the weight function.
The method solves the problems that a certain degree of over-enhancement is generated in a bright area and under-enhancement is generated in a dark area.
Mean value of the weight functionWherein,respectively, a segmented histogram hkThe first and last gray levels of (a);
variance of the weight function In order to avoid a threshold for excessive enhancement of the image,for a segmented histogram hkOf the cover width, i.e.
Ensures the histogram hkIn the equalization process, both symmetrical directions have the same degree of distribution.
The above-mentionedIs composed ofWherein,for a segmented histogram hkGray average value of (1).
The equalization processing selected in the step 2 is adaptive equalization processing,optimization problem proposed in existing histogram equalization methodsIn the method, the regularization parameters alpha, beta and gamma are optimized by adopting the following formula;
γ＝1-α-β
wherein HxFor the expanded histogram of the input image, HtFor the target histogram of the input image, HuA histogram of the desired equilibrium distribution; h is a histogram obtained after self-adaptive equalization processing, | | | | | represents the Euclidean norm, and D is a dual-diagonal difference matrix;
expanded histogram H for input imagexAnd the histogram H of the expanded input imagexMaximum gray level I ofmaxDistance measure, i is the expanded histogram H of the input imagexL is the number of gray levels, niExpanded histogram H for input imagexFrequency of intermediate gray levels I, ImaxIs the maximum gray level and has a variance σ of 0.2Imax；
miFor a pixel x in the input imagejGray value of I (x)j) A number of pixels equal to i; nG (x)j) Is a pixel xjNormalized local variance, and nG (x)j)＝G(xj)/I(xj)，G(xj) Is a pixel xjThe magnitude of the gradient at (a) is,g denotes a corresponding gradient magnitude map of the input image I, wherein, represents the convolution operation, and S is a Sobel operator template.
The above-mentionedDesired equalized distribution histogram HuThe following formula is used for the assignment:
in the formula, i is a gray scale.
After the final equalized histogram is obtained, the final enhanced image can be easily obtained through histogram correction.
Advantageous effects
The invention provides an equalization method based on an extensible segmented adaptive histogram, which comprises the following steps: step 1: expanding the input original histogram by adopting an expandable histogram segmentation method; step 2: carrying out equalization processing on the expanded histogram, wherein each equalized sub-histogram has the same length as the original histogram; and step 3: weighting and mixing the equalized sub-histograms obtained in the step 2 according to the following formula to obtain a final equalized histogram Ht(i) (ii) a By using the method and adopting the extensible histogram segmentation strategy, the equalization can be realizedThe gray scale of the image after the transformation is redistributed to a larger dynamic range, which is beneficial to the full enhancement of the image in a dark area; the gray level uniform distribution degree is adaptively controlled according to the gray level attribute of the image by applying the proposed adaptive histogram equalization method, so that the phenomena of over-enhancement, under-enhancement and unnatural halo of the image can be avoided; the whole method is high in calculation speed, and the image with an obvious enhancement effect is obtained.
Drawings
Fig. 1 is a schematic diagram of a process of processing an image by applying the method of the present invention, where (a) is an input original image, (b) is a conversion of the original image into an HSV spatial image, (c) is a histogram obtained by applying a scalable histogram segmentation method to a V-channel image in (b), (d) is a histogram obtained by performing adaptive equalization on (c), (e) is a histogram obtained by performing weighting on (d), (f) is an enhanced image of a V-channel obtained by using the histogram obtained from (e), and (g) is an obtained final enhanced effect image;
fig. 2 is a comparison diagram of applying the method of the present invention and other histogram equalization methods to perform enhancement processing on the same image, where diagram (a) is an original image, diagram (b) is an RMSHE method, diagram (c) is a BPBFHE method, diagram (d) is an HMF method, diagram (e) is a 2DHE method, diagram (f) is an AEPHE method, diagram (g) is a gray scale mapping function between input and output of each histogram equalization method, the abscissa is an input gray scale, and the ordinate is an output gray scale;
fig. 3 shows the corresponding segment histogram h when N is 3kWeight function W of1Schematic representation of (a).
Detailed Description
The invention will be further described with reference to the following figures and examples.
An equalization method based on an extensible piecewise self-adaptive histogram comprises the following steps:
step 1: expanding the input original histogram by adopting an expandable histogram segmentation method;
first, the original histogram H isoSegmentation into N non-overlapping segmented histograms hk，k∈[1,N](ii) a Then all the segmented histograms hkExpanded to the original histogram H respectivelyoHistogram with same gray level interval, keeping segmented histogram hkThe original histogram is unchanged, and other positions are filled with zeros to obtain the expanded sectional histogram(k∈[1,N])， <math>
<mrow>
<msubsup>
<mi>H</mi>
<mi>k</mi>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<mo>[</mo>
<mn>0</mn>
<mo>,</mo>
<mo>.</mo>
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<msub>
<mi>h</mi>
<mi>k</mi>
</msub>
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<mo>.</mo>
<mo>,</mo>
<mn>0</mn>
<mo>]</mo>
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<mo>(</mo>
<mi>k</mi>
<mo>∈</mo>
<mo>[</mo>
<mn>1</mn>
<mo>,</mo>
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<mo>,</mo>
<mi>N</mi>
<mo>]</mo>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
</math>
Step 2: carrying out equalization processing on the expanded segmented histograms, wherein each equalized sub-histogram has the same length as the original histogram;
optimization problem proposed in existing histogram equalization methodsIn the method, the regularization parameters alpha, beta and gamma are optimized by adopting the following formula;
γ＝1-α-β
wherein HxFor the expanded histogram of the input image, HtFor the target histogram of the input image, HuA histogram of the desired equilibrium distribution; h is a histogram obtained after self-adaptive equalization processing, | | | | | represents the Euclidean norm, and D is a dual-diagonal difference matrix;
expanded histogram H for input imagexAnd the histogram H of the expanded input imagexMaximum gray level I ofmaxDistance measure, i is the expanded histogram H of the input imagexL is the number of gray levels, niExpanded histogram H for input imagexFrequency of intermediate gray levels I, ImaxIs the maximum gray level and has a variance σ of 0.2Imax；
miFor a pixel x in the input imagejGray value of I (x)j) A number of pixels equal to i; nG (x)j) Is a pixel xjNormalized local variance, and nG (x)j)＝G(xj)/I(xj)，G(xj) Is a pixel xjThe magnitude of the gradient at (a) is,wherein, represents the convolution operation, and S is a Sobel operator template.
Histogram H of the desired equalized distributionuThe following formula is used for the assignment:
in the formula, i is a gray scale.
After the final equalized histogram is obtained, the final enhanced image can be easily obtained through histogram correction.
And step 3: weighting and mixing the equalized sub-histograms obtained in the step 2 according to the following formula to obtain a final equalized histogram Ht(i)：
Wherein, wk(i) Is the normalized weight of the k-th equalized-spread-segment histogram,weight functionk＝[1,…,N]N is the number of histogram segments, i is the gray level, ukAnd σkRespectively the mean and variance of the weight function.
Mean value of the weight functionWherein,respectively, a segmented histogram hkThe first and last gray levels of (a);
variance of the weight function In order to avoid a threshold for excessive enhancement of the image,for a segmented histogram hkOf the cover width, i.e.
Ensures the histogram hkIn the equalization process, both symmetrical directions have the same degree of distribution.
The above-mentionedIs composed ofWherein,for a segmented histogram hkGray average value of (1).
As shown in fig. 1, a schematic diagram of a process for processing an image by applying the method of the present invention is shown, wherein the process is as follows:
1) inputting an original image I, and calculating a luminance channel histogram of the original image, as shown in (a) and (b);
2) dividing the histogram into N segmented histograms and expanding the N segmented histograms to obtain an expandable segmented histogramAs shown in FIG. (c);
3) segment histogram for each extensionThe histogram obtained by applying the proposed adaptive histogram equalization method is shown in graph (d);
(a) using formulasComputing each extended segment histogramWhen N is equal to 3, the corresponding segment histogram hkWeight function W of1As shown in fig. 3;
(b) calculating alpha (k), beta (k) and gamma (k) by using a formula for optimizing regularization parameters alpha, beta and gamma;
(c) using a formula <math>
<mrow>
<msup>
<mi>H</mi>
<mi>u</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>i</mi>
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<mfenced open='{' close=''>
<mtable>
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</math> Revised uniformly distributed histogram Hu；
(d) Using formulasSolving an object histogramThe final equalized histogram is calculated, and as shown in fig. e, the final output image is obtained by histogram correction, as shown in fig. f and g.
In order to verify the effectiveness of the method, different histogram equalization processing methods and the method of the invention are selected to perform equalization processing on the same original image to obtain an image enhancement effect contrast diagram as shown in a diagram (b) -a diagram (f) in fig. 2, and from the contrast diagram, it can be seen that the gray level mapping function between input and output obtained correspondingly by the diagram (f) is obviously superior to other methods.
Claims (5)
1. An equalization method based on an extensible piecewise self-adaptive histogram is characterized by comprising the following steps:
step 1: expanding the input original histogram by adopting an expandable histogram segmentation method;
first, the original histogram H isoSegmentation into N non-overlapping segmented histograms hk，k∈[1,N](ii) a Then all the segmented histograms hkExpanded to the original histogram H respectivelyoHistogram with same gray level interval, keeping segmented histogram hkAt the position of the original histogramFilling other positions with zero without changing to obtain the extensible segmented histogram <math>
<mrow>
<msubsup>
<mi>H</mi>
<mi>k</mi>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<mo>[</mo>
<mn>0</mn>
<mo>,</mo>
<mo>.</mo>
<mo>.</mo>
<mo>.</mo>
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<mi>h</mi>
<mi>k</mi>
</msub>
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<mo>,</mo>
<mi>N</mi>
<mo>]</mo>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
</math>
Step 2: equalizing the expandable segmented histograms, wherein each equalized sub-histogram has the same length as the original histogram;
and step 3: equalizing the sub-histogram obtained in the step 2Weighted mixing is carried out according to the following formula to obtain a final equalized histogram Ht(i)：
Wherein, wk(i) Is the normalized weight of the k-th equalized-spread-segment histogram,weight functionk＝[1,…,N]N is the number of histogram segments, i is the gray level, ukAnd σkRespectively the mean and variance of the weight function.
2. The scalable segment-based adaptive histogram equalization method according to claim 1, wherein the mean of the weight functionWherein,respectively, a segmented histogram hkThe first and last gray levels of (a);
variance of the weight function In order to avoid a threshold for excessive enhancement of the image,for a segmented histogram hkOf the cover width, i.e.
3. The scalable segment-based adaptation of claim 2A histogram equalization method, characterized in that said methodIs composed ofWherein,for a segmented histogram hkGray average value of (1).
4. The scalable segmentation-based adaptive histogram equalization method according to any one of claims 1-3, wherein the equalization process selected in step 2 is an adaptive equalization process, and an optimization problem proposed in the existing histogram equalization method is presentedIn the method, the regularization parameters alpha, beta and gamma are optimized by adopting the following formula;
γ＝1-α-β
wherein HxFor the expanded histogram of the input image, HtFor the target histogram of the input image, HuA histogram of the desired equilibrium distribution; h is a histogram obtained after self-adaptive equalization processing, | | | | | represents the Euclidean norm, and D is a dual-diagonal difference matrix;
expanded histogram H for input imagexAnd the histogram H of the expanded input imagexMaximum gray level I ofmaxDistance measure, i is the expanded histogram H of the input imagexL is the number of gray levels, niExpanded histogram H for input imagexFrequency of intermediate gray levels I, ImaxIs the maximum gray level and has a variance σ of 0.2Imax；
miFor a pixel x in the input imagejGray value of I (x)j) A number of pixels equal to i; nG (x)j) Is a pixel xjNormalized local variance, and nG (x)j)＝G(xj)/I(xj)，G(xj) Is a pixel xjThe magnitude of the gradient at (a).
5. The scalable segment-based adaptive histogram equalization method according to claim 4, wherein the histogram H of the desired equalization distributionuThe following formula is used for the assignment:
in the formula, i is a gray scale.
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| CN108830800B (en) * | 2018-05-09 | 2023-02-28 | 南京邮电大学 | Brightness improvement and enhancement method for image in dark scene |
| CN113393389B (en) * | 2021-06-02 | 2022-05-31 | 武汉博宇光电系统有限责任公司 | Image enhancement method without artificial halation |
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| US6850642B1 (en) * | 2000-01-31 | 2005-02-01 | Micron Technology, Inc. | Dynamic histogram equalization for high dynamic range images |
| CN101510305A (en) * | 2008-12-15 | 2009-08-19 | 四川虹微技术有限公司 | Improved self-adapting histogram equilibrium method |
| CN102831592A (en) * | 2012-08-10 | 2012-12-19 | 中国电子科技集团公司第四十一研究所 | Image nonlinearity enhancement method based on histogram subsection transformation |
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| US6850642B1 (en) * | 2000-01-31 | 2005-02-01 | Micron Technology, Inc. | Dynamic histogram equalization for high dynamic range images |
| CN101510305A (en) * | 2008-12-15 | 2009-08-19 | 四川虹微技术有限公司 | Improved self-adapting histogram equilibrium method |
| CN102831592A (en) * | 2012-08-10 | 2012-12-19 | 中国电子科技集团公司第四十一研究所 | Image nonlinearity enhancement method based on histogram subsection transformation |
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