CN107240096A - A kind of infrared and visual image fusion quality evaluating method - Google Patents
A kind of infrared and visual image fusion quality evaluating method Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/0002—Inspection of images, e.g. flaw detection
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/11—Region-based segmentation
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/136—Segmentation; Edge detection involving thresholding
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/194—Segmentation; Edge detection involving foreground-background segmentation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10048—Infrared image
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10052—Images from lightfield camera
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- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30168—Image quality inspection
Abstract
The invention discloses a kind of infrared and visual image fusion quality evaluating method, it the described method comprises the following steps:Obtain infrared source images, visible light source image and fused images;Its global minutia index is calculated using the gradient amplitude comentropy of fused images;Infrared source images are divided into by target area and background area using the marking area extraction method of frequency domain, and division result is mapped to fused images;The marginal texture similarity between infrared image target area and fused images target area and the contrast between fused images target and background are calculated respectively, and their summations are obtained into fused images localized target characteristic index;Finally by the global minutia index of fused images and local target signature index weighted sum, infrared and visual image fusion quality evaluation index is obtained.The present invention can both evaluate the global minutia and local target signature of fused images, can also evaluate the global feature of fused images, taken into account the versatility during actual evaluation and particularity requirement, had higher uniformity with subjective assessment.
Description
Technical field
The present invention relates to image fusion quality assessment field, more particularly to a kind of infrared commented with visual image fusion quality
Valency method.
Background technology
Infrared is the important branch of image co-registration with visual image fusion, is also the emphasis of current image co-registration research.
Infrared sensor is imaged by heat radiation, is conducive to protruding the target area in scene, but it is thin to characterize scene well
Save feature;Visible light sensor passes through object catoptric imaging, using the teaching of the invention it is possible to provide the detailed information of scene where target.Therefore, it is infrared
Not only there is the target signature of good infrared image with visual image fusion, and visible images can also be retained well
Detailed information.Relative to the image fusion technology quickly grown, fused image quality evaluation development is relatively slow.Image co-registration
Quality evaluation can not only compare fusion method performance quality, be also used as instructing the improved foundation of fusion method.Therefore, it is red
It is most important to the application of follow-up fused images with visual image fusion quality evaluating method outside.
Found by the retrieval to prior art, Chinese patent literature CN103049893A, publication date 2013.04.17,
A kind of method and device of image fusion quality assessment is disclosed, is comprised the following steps:Step 1) obtain each source images and described
The fused images of source images;Step 2) each source images using fuzzy clustering method split to obtain segmentation figure picture, and will be each
Segmentation figure picture merges into a total segmentation figure;Step 3) the vision variance notable figures of each source images is obtained, according to vision variance
Notable figure calculates weights figure, and calculates source images and each region of fused images according to vision variance notable figure and total segmentation figure
Notable coefficient;Step 4) according to total segmentation figure, weights figure and notable coefficient, calculate fused images and source images on regional
Weighting structures similarity;Step 5) the weighting structures similarity in all regions, which is summed, obtains the evaluation of the fused image quality
Index.
Chinese patent literature CN104008543A, publication date 2014.08.27, disclose a kind of image co-registration quality and comment
Valency method, comprises the following steps:Step 1) obtain source images:It is required that the source images time is upper synchronously, spatially cover the same area;
Step 2) image preprocessing step:Using quadratic polynomial registration, arest neighbors interpolation method resampling;Step 3) image co-registration:It is right
Source images use the fusion method that multiscale analysis and composition Shift Method are combined, and obtain the fusion figure under different fusion methods
Picture;Step 4) fusion mass evaluation:The cross entropy and structural similarity between fused images and source images are calculated, cross entropy is set up
With structural similarity weighted function model, the fusion mass calculated under preset weights evaluates total value.
Although above two technology can evaluate fused image quality, they are in infrared and visual image fusion matter
Amount evaluation is performed poor, and is analyzed its reason and is:
1. above two technology is by calculating the similarity evaluation fused image quality between source images and fused images,
Both technologies have ignored the minutia of fused images in itself;
2. one of infrared main purpose with visual image fusion is the target signature for retaining infrared source images, but above-mentioned
The target signature that two kinds of technologies are not directed to fused images is evaluated;
3. a kind of method and device (Chinese patent literature CN103049893A) of image fusion quality assessment uses mould
Clustering method segmentation infrared image is pasted, but the image that disturbs complex background of the dividing method and low signal-to-noise ratio (SNR) images can not be correct
Segmentation, influences follow-up evaluation result;
4. a kind of Quality Measures for Image Fusion (Chinese patent literature CN104008543A) and a kind of image co-registration
The method and device (Chinese patent literature CN103049893A) of quality evaluation calculates fused images using structural similarity
Similarity between source images, fused image quality is evaluated with this.But when two images are more obscured, respectively using both
The image fusion quality assessment result that technology is obtained has poor uniformity with subjective assessment.
Therefore, the global minutia of fused images and local target signature, and and subjective assessment can be reflected by seeking one kind
Infrared and visual image fusion quality evaluating method with higher uniformity, to evaluating infrared and visual image fusion matter
The quality of amount is vital.
The content of the invention
The present invention is directed to deficiencies of the prior art, it is proposed that one kind is infrared to be commented with visual image fusion quality
Valency method.
The present invention uses following technical scheme to solve above-mentioned technical problem:
A kind of infrared and visual image fusion quality evaluating method, is comprised the steps of:
Step 1:Obtain infrared source images A, visible light source image B and fused images F;
Step 2:Calculate the global minutia index of fused images;
Step 3:Calculate the localized target characteristic index of fused images;
Step 4:The global minutia index of fused images and local target signature index are weighted summation, obtained
Fused image quality evaluation index.
It is used as a kind of infrared and the further prioritization scheme of visual image fusion quality evaluating method, step 2 of the invention
Described in calculate the global minutia indexs of fused images, its detailed process is:
Step 2.1:Calculate fused images F gradient magnitude
For fused images F, its horizontal gradient is calculatedAnd vertical gradient
Here, it regard sum of the two as gradient:
Step 2.2:Fused images gradient amplitude comentropy is calculated, and as the global minutia index of fused images
Rglobal。
Wherein, piThe probability that gray value occurs for i pixel in fused images gradient map is represented, L is gray scale of image etc.
Level.
It is used as a kind of infrared and the further prioritization scheme of visual image fusion quality evaluating method, step 3 of the invention
Described in calculate the localized target characteristic indexs of fused images, its detailed process is:
Step 3.1:The region division of infrared source images and fused images
Infrared source images are divided into by target area and background area using the marking area extracting method based on frequency domain,
Marking area extracting method step based on frequency domain is as follows:
The notable feature of infrared source images is extracted using Gaussian band-pass filter, Gaussian band-pass filter is defined as follows:
Wherein, σ1,σ2(σ1> σ2) be Gaussian filter standard variance.
In order to obtain all frequency values of low-frequency range, σ as much as possible1It is set to infinity;In order to remove the high frequency of image
Noise and texture information, are selected first with the discrete Gauss value of small Gaussian kernel filter fits.
The saliency map S of image is calculated using following formula:
S (x, y)=| Aμ-Awhc(x,y)|
In formula, AμFor infrared radiation source gradation of image average value;Awhc(x, y) is image of the infrared source images after gaussian filtering;
| | it is L1Norm.
The target and background of infrared source images is split using region-growing method, comprised the following steps that:1) notable
The maximum point of selection gray value is used as seed point in degree figure;2) centered on seed point, it is considered to its 4 neighborhood territory pixel point, if full
Sufficient growing strategy, is merged.Difference using neighborhood territory pixel point and cut zone gray average is as similarity measure, difference
Minimum neighborhood similitude is merged into cut zone;3) when similarity measure is more than segmentation threshold, then stop growing.
Step 3.2:Calculate the marginal texture similarity between fused images target area and infrared radiation source image target area
ESSIM(Alocal,Flocal)
In formula,The target area of respectively infrared source images and the target area of fused images;l(Alocal,
Flocal), c (Alocal,Flocal), s (Alocal,Flocal), e (Alocal,Flocal) it is respectively target area AlocalAnd target area
FlocalBrightness ratio compare that component, structure compare component and edge compares component compared with component, contrast;Parameter alpha, β, γ, η difference
For their weight, α=β=γ=η=1 is generally taken;Respectively target area AlocalWith target area Flocal's
Pixel average;Respectively target area AlocalWith target area FlocalPixel variance;For target area
Domain AlocalWith target area FlocalBetween covariance,Respectively target area AlocalWith target area Flocal's
The gray variance of edge image,For the gray scale covariance of two edges of regions images, edge image here is to use
Sobel edge detection methods are obtained;c1,c2,c3,c4For constant, it is to there is unstability when avoiding denominator close to 0 to introduce purpose.
Step 3.3:Calculate the contrast between the target and background of fused images
First, the luminance mean value detraction contrast normalization coefficient (abbreviation MSCN coefficients) of fused images is calculated, it calculates public
Formula is as follows:
In formula, constant C is unstable to occur when avoiding image flat region denominator from being intended to zero;
For two dimension
The symmetrical gaussian weighing function of circle, makes K=L=3 here.
Secondly, the weber contrast between target and background is calculated, calculation formula is:Cw=| Lt-Lb|/Lb
Wherein, LtAnd LbThe average value of the MSCN coefficients of pixel respectively in target area and neighbouring background area.
Step 3.4 calculates the localized target characteristic evaluating index of fused images
By the marginal texture similarity ESSIM (A between fused images target area and infrared radiation source image target arealocal,
Flocal) contrast C between the target and background of fused imageswIt is added, the localized target characteristic evaluating for obtaining fused images refers to
Mark Rlocal, i.e.,:
Rlocal=ESSIM (Alocal,Flocal)+CW
The present invention uses above technical scheme compared with prior art, with following technique effect:
1. the present invention had both considered infrared and visual image fusion global minutia, it is contemplated that fused images
Target signature, embodies and infrared merges purpose with visual image fusion;
2. the present invention using the marking area extracting method based on frequency domain by infrared source images be divided into target area and
Background area, for thering is the image of complex background interference and low signal-to-noise ratio (SNR) images correctly to split;
3. the present invention calculates the MSCN coefficients of fused images first, the contrast gain for simulating human vision was covered
Journey, finally calculates weber contrast between target and background, can effectively realize the visitor of fused images target and context-aware contrast
See and evaluate;
4. the present invention is using between marginal texture Similarity Measure fused images target area and infrared radiation source image target area
Correlation, to a certain extent, can effective evaluation more fuzzy infrared and visual image fusion quality.
5. being verified by emulation experiment, infrared and visual image fusion quality evaluating method of the invention has higher
Subjective consistency, can preferably reflect infrared and visual image fusion quality.
Brief description of the drawings
Fig. 1 is a kind of infrared flow chart with visual image fusion quality evaluating method that the present invention is provided;
Fig. 2 is the fused images and its gradient amplitude figure and gradient amplitude histogram that the present invention is provided;
Fig. 3 is the infrared source images that the present invention is provided and the segmentation figure picture of fused images;
Fig. 4 is the first group of source images and fused images that the present invention is provided;
Fig. 5 is the second group of source images and fused images that the present invention is provided;
Fig. 6 is the 3rd group of source images and the fused images that the present invention is provided;
Fig. 7 is the 4th group of source images and the fused images that the present invention is provided.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, below in conjunction with accompanying drawing, the present invention is entered
Row is described in detail.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to limit this hair
It is bright.
With reference to Fig. 1, the invention discloses a kind of infrared and visual image fusion quality evaluating method, following step is included
Suddenly:
Step 1:Obtain infrared source images A, visible light source image B and fused images F;
Step 2:Calculate the global minutia index R of fused imagesglobal;
The gradient information of image is the higher content of human eye sensitivity's degree in image, can be as characterizing image detail
A kind of feature of information.
For fused images F, its horizontal gradient is calculatedAnd vertical gradient
Using sum of the two as fused images gradient:
Fig. 2 gives fused images and its gradient amplitude figure and gradient amplitude histogram, wherein, Fig. 2 a are to be based on averaging method
(AVE) image co-registration, gradient amplitude figure and gradient amplitude histogram corresponding to it are shown in Fig. 2 b and Fig. 2 c respectively;Fig. 2 d are bases
In laplacian pyramid (LAP) image co-registration, its corresponding gradient amplitude figure and gradient amplitude histogram are shown in Fig. 2 e respectively
With Fig. 2 f.
Analysis chart 2 understands that Fig. 2 d texture-rich, high resolution, picture contrast are obvious, and quality is better than Fig. 2 a.Accordingly
Ground, although the shape of the corresponding histogram of gradients of two width fused images is one narrow unimodal, and top is close to Grad
The direction for being zero, but their width and gray scale dynamic range exist it is significantly different:1) peak type of Fig. 2 f peak type compared with Fig. 2 c is delayed;
2) peak-peak is different, Fig. 2 c peak-peak for 14000, Fig. 2 f peak-peak less than 8000;3) grayscale dynamic range
Difference, Fig. 2 f gray scale dynamic range is wide compared with Fig. 2 c, and its information included is more enriched.
Degree can be enriched with the details of quantitative assessment fused images using histogram of gradients.Histogram is the angle from probability
The feature of image gradient is studied, degree is enriched by calculating fused images gradient information entropy quantitative analysis fused images details.Melt
Close image overall minutia Index Formula as follows:
Wherein, piThe probability that gray value occurs for i pixel in fused images gradient map is represented, L is gray scale of image etc.
Level.
Step 3:Calculate the localized target characteristic index R of fused imageslocal;
Calculate the localized target characteristic index R of fused imageslocalComprise the following steps that:
Step 3.1:The region division of infrared source images and fused images
Infrared source images are divided into by target area and background area, base using the marking area extraction method based on frequency domain
Comprised the following steps that in the marking area extraction method of frequency domain:
The notable feature of infrared source images is extracted using Gaussian band-pass filter, Gaussian band-pass filter is defined as follows:
Wherein, σ1,σ2(σ1> σ2) be Gaussian filter standard variance.In order to obtain all of low-frequency range as much as possible
Frequency values, σ1It is set to infinity;In order to remove the high-frequency noise and texture information of image, select first with small Gaussian kernel wave filter
The discrete Gauss value of fitting.
The saliency map S of image is calculated using following formula:
S (x, y)=| Aμ-Awhc(x,y)|
In formula, AμFor infrared radiation source gradation of image average value;Awhc(x, y) is image of the infrared source images after gaussian filtering;
| | it is L1Norm.
The target and background of infrared source images is split using region-growing method, comprised the following steps that:1) notable
The maximum point of selection gray value is used as seed point in degree figure;2) centered on seed point, it is considered to its 4 neighborhood territory pixel point, if full
Sufficient growing strategy, is being merged.Difference using neighborhood territory pixel point and cut zone gray average is as similarity measure, poor
The minimum neighborhood similitude of value is merged into cut zone;3) when similarity measure is more than segmentation threshold, then stop growing.
Fig. 3 gives infrared source images and the segmentation figure picture of fused images, and wherein Fig. 3 a~Fig. 3 c are respectively infrared radiation source figure
Picture, AVE fused images (fused images obtained through averaging method), LAP fused images are (through melting that laplacian pyramid is obtained
Close image), Fig. 3 d~Fig. 3 f are respectively their own region segmentation figure.
From figure 3, it can be seen that this method is effectively extracted the target area of infrared image, as shown in Fig. 3 d;By target area
The division result in domain is respectively mapped to AVE fused images and LAP fused images, the target area segmentation difference of two width fused images
As shown in Fig. 3 e and Fig. 3 f.From human eye observation it is recognized that while AVE fused images and LAP fused images can detect thermal target,
But the target signature of LAP fusion methods preferably remains the target signature of infrared image, its fusion mass is better than AVE fusion sides
Method.
Step 3.2:Calculate the marginal texture similarity between fused images target area and infrared radiation source image target area
In formula,The target area of respectively infrared source images and the target area of fused images;l(Alocal,
Flocal), c (Alocal,Flocal), s (Alocal,Flocal), e (Alocal,Flocal) be respectively infrared source images target area
AlocalWith fused images target area FlocalBrightness ratio compare component, structure compared with component, contrast and compare component and edge
Compare component;Parameter alpha, beta, gamma, η is respectively their weight, generally takes α=β=γ=η=1;Respectively target
Region AlocalWith target area FlocalPixel average;Respectively target area AlocalWith target area Flocal's
Pixel variance;For target area AlocalWith target area FlocalBetween covariance,Respectively target area
Domain AlocalWith target area FlocalEdge image gray variance,For the gray scale covariance of two edges of regions images,
Here edge image is obtained using Sobel edge detection methods;c1,c2,c3,c4For constant, it is to avoid denominator to introduce purpose
There is unstability during close to 0.
Step 3.3:Calculate the contrast between the target and background of fused images
First, the luminance mean value detraction contrast normalization coefficient (abbreviation MSCN coefficients) of fused images is calculated, it calculates public
Formula is as follows:
In formula, constant C is unstable to occur when avoiding image flat region denominator from being intended to zero;
For two dimension
The symmetrical gaussian weighing function of circle, makes K=L=3 here.
Secondly, the weber contrast between target and background is calculated, calculation formula is:Cw=| Lt-Lb|/Lb.Wherein, LtAnd Lb
The average value of the MSCN coefficients of pixel respectively in target area and neighbouring background area.
Step 3.4:Calculate the localized target characteristic evaluating index R of fused imageslocal
By edges of regions structural similarity ESSIM (Alocal,Flocal) contrast between the target and background of fused images
CwIt is added, obtains the localized target characteristic evaluating index R of fused imageslocal, i.e.,:Rlocal=ESSIM (Alocal,Flocal)+CW。
Step 4:The global minutia index of fused images and local target signature index are weighted summation, obtained
Fused image quality evaluation index, calculation formula is:R=w1Rglobal+w2Rlocal
In formula, w1,w2Respectively global minutia RglobalWith local target signature RlocalWeight, generally take w1=
0.6,w2=0.4.
Evaluation criterion:Evaluation index R values are bigger, represent infrared more excellent with visual image fusion quality;Conversely, representing red
It is poorer with visual image fusion quality outside.
The present invention gives based on the simulation result figure under certain simulated conditions, technical solution of the present invention acquisition is embodied
Beneficial effect.
The present invention is infrared to four groups first to use averaging method (AVE), principal component analytical method with visible light source image
(PCA), Laplacian-pyramid method (LAP) and discrete wavelet (DWT) are merged, and the recycling present invention is a kind of infrared and can
See that light image fusion mass evaluation method is evaluated fused images.
The present invention choose it is wherein representative it is 4 groups infrared be shown with visible light source image and fused images, divide
Not as shown in Fig. 4-Fig. 7, wherein, in figure a, b be respectively in the infrared and visible light source image of rigid registrations, figure c-f respectively should
The fused images obtained with AVE, PCA, LAP, DWT.
Table 1 gives above-mentioned 4 groups infrared and visual image fusion evaluation of estimate.
Table is 1 four groups infrared with visual image fusion quality evaluation value
As can be seen from Table 1:1) in Fig. 4, the optimal quality of LAP fusion methods, next to that DWT fusion methods;2) exist
In Fig. 5, DWT fusion method optimal qualities, next to that LAP fusion methods.Although the fused images details that PCA fusion methods are obtained
Compare abundant, but its localized target characteristic mass is poor, causes the total quality of fused images poor.3) in Fig. 6 and Fig. 7
In, it is that DWT fusion methods are optimal, next to that LAP fusion methods.
Comprehensive to understand, the fused image quality obtained using DWT or LAP fusion methods is preferable.Because:One side
Face, because wavelet analysis method take into account the characteristic of multiresolution, no matter reasonability from algorithm or human eye subjective assessment
In terms of be superior to AVE fusion methods and PCA fusion methods;On the other hand, DWT fusion methods be can be seen that from Fig. 4-Fig. 7
AVE fusion methods and PCA fusion methods are superior to LAP fusion methods.Therefore, the present invention is effective, its result and subjectivity
Evaluation result has preferable uniformity.
It can be seen from Table 1 that:The present invention can both evaluate the infrared global minutia with visible ray fused images and
Localized target feature, can also evaluate the global feature of fused images, take into account versatility during actual evaluation and special
Property require that there is certain directive function to further improving infrared with visible light image fusion method.
Claims (3)
1. a kind of infrared and visual image fusion quality evaluating method, it is characterised in that comprise the steps of:
Step 1) obtain infrared source images A, visible light source image B and fused images F;
Step 2) calculate fused images global minutia index;
Step 3) calculate fused images localized target characteristic index;
Step 4) the global minutia index of fused images and local target signature index are weighted summation, obtain infrared
With visual image fusion quality evaluation index.
2. one kind according to claim 1 is infrared with visual image fusion quality evaluating method, it is characterised in that step
2) detailed process of the global minutia index of the calculating fused images described in is:
Fused images F horizontal gradient is calculated firstAnd vertical gradient
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Fused images gradient amplitude comentropy is calculated again, in this, as the global minutia index R of fused imagesglobal, its table
It is as follows up to formula:
In formula, piThe probability that gray value occurs for i pixel in fused images gradient map is represented, L is the tonal gradation of image.
3. one kind according to claim 1 is infrared with visual image fusion quality evaluating method, it is characterised in that step
3) detailed process of the localized target characteristic index of the calculating fused images described in is:
First, infrared source images are divided into by target area and background area using the marking area extracting method based on frequency domain
Domain, and division result is mapped in fused images;
Secondly, the marginal texture similarity ESSIM between fused images target area and infrared radiation source image target area is calculated
(Alocal,Flocal), expression formula is shown in shown in formula (1):
ESSIM(Alocal,Flocal)=[l (Alocal,Flocal)]α[c(Alocal,Flocal)]β[s(Alocal,Flocal)]γ[e(Alocal,
Flocal)]η (1)
In formula, Alocal,FlocalThe target area of respectively infrared source images and the target area of fused images;l(Alocal,
Flocal), c (Alocal,Flocal), s (Alocal,Flocal), e (Alocal,Flocal) be respectively infrared source images target area Alocal
With fused images target area FlocalBrightness ratio compare that component, structure compare component and edge compares point compared with component, contrast
Amount;Parameter alpha, beta, gamma, η is respectively their weight, generally takes α=β=γ=η=1.
Then, the contrast C between the target and background of fused images is calculatedW, expression formula is shown in shown in formula (2):
Cw=| Lt-Lb|/Lb (2)
In formula, LtAnd LbThe average value of the MSCN coefficients of pixel respectively in target area and neighbouring background area.Wherein, merge
The MSCN coefficient formulas of image is as follows:
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</mrow>
<mo>+</mo>
<mi>C</mi>
</mrow>
</mfrac>
</mrow>
In formula, constant C is unstable to occur when avoiding image flat region denominator from being intended to zero;
ω={ ωkl|
K=-K ..., K;L=-L ..., L } it is the symmetrical gaussian weighing function of two-dimensional circle, K=L=3 is made here.
Finally, by target area marginal texture similarity ESSIM (Alocal,Flocal) contrast C between target and backgroundWAsk
With, obtain obtain fused images localized target characteristic evaluating index Rlocal, i.e. Rlocal=ESSIM (Alocal,Flocal)+CW。
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