CN102393958A - Multi-focus image fusion method based on compressive sensing - Google Patents

Multi-focus image fusion method based on compressive sensing Download PDF

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CN102393958A
CN102393958A CN2011101993643A CN201110199364A CN102393958A CN 102393958 A CN102393958 A CN 102393958A CN 2011101993643 A CN2011101993643 A CN 2011101993643A CN 201110199364 A CN201110199364 A CN 201110199364A CN 102393958 A CN102393958 A CN 102393958A
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王爽
焦李成
杨奕堂
刘芳
杨淑媛
侯彪
钟桦
刘忠伟
杨国辉
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Xidian University
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Abstract

The invention discloses a multi-focus image fusion method based on compressive sensing and relates to the technical field of image processing. By the multi-focus image fusion method, the main problem that a clear image with all focused sceneries is difficult to acquire due to a limited depth of field of an optical lens in the prior art can be solved. The multi-focus image fusion method is implemented by the following steps of: (1) blocking an image; (2) calculating an average gradient of each image sub block to determine a fusion weight value; (3) performing sparse representation on each image sub block and observing each image sub block by adopting a random Gaussian matrix; (4) performing weighted fusion on the fusion weight value of an observed value of each image sub block; and (5) recovering a fused image observed value by adopting an orthogonal matching traceback algorithm and performing wavelet inverse transformation on a recovered result to acquire a fused fully-focused image. By the multi-focus image fusion method based on the compressive sensing, a better image fusion effect can be achieved and higher convergence property is realized; and the method can be applied to fusion of a multi-focus image.

Description

Multi-focus image fusing method based on compressed sensing
Technical field
The invention belongs to technical field of image processing, relate to image fusion technology, specifically a kind of theoretical multi-focus image fusing method of compressed sensing that combined, this method can be used in the multiple focussing image fusion.
Background technology
Image co-registration has vast potential for future development as an emerging scientific research field.It obtains more accurate, comprehensive, the reliable iamge description to Same Scene or target through extracting with comprehensively from the information of a plurality of sensor images, so as to image further analyze, detection, identification or the tracking of understanding and target.From the early 1980s so far; Multi-sensor image merges and has caused worldwide extensive interest and research boom, and it has a wide range of applications in fields such as automatic target identification, computer vision, remote sensing, machine learning, Medical Image Processing and military applications.Through the development in 30 years nearly, the research of image fusion technology reaches a certain scale, and has developed multiple emerging system both at home and abroad, but this does not show that this technology is perfect.From present case, image fusion technology also exists the problem of many theory and technologies aspect to have to be solved.Especially it is to be noted that the research that image fusion technology is carried out at home starts late with respect to international research work, also be in a backward condition.Therefore press for the basic theory of carrying out extensively and profoundly and the research of basic technology.
Along with fast development of information technology, people grow with each passing day to the demand of quantity of information.Under this background; The traditional image fusion method; Such as fusion method based on multi-scale transform; Referring to article " Region based multisensor image fusion using generalized Gaussian distribution ", in Int.Workshop on Nonlinear Sign.and Image Process.Sep.2007 needs the data volume of processing very considerable; This has just caused the immense pressure to signal sampling, transmission and storage, and how alleviating this pressure, effectively to extract the useful information that is carried in the signal again be one of urgent problem in the Signal and Information Processing.The theoretical CS of the compressed sensing that occurred in the world in recent years provides solution route for alleviating these pressure.Compressed sensing can fully extract the useful information in the image under not needing to suppose in advance any prior imformation of image, like this, only the useful information that extracts is merged and can alleviate data computing and storage pressure greatly.At present, scholars have launched applied research widely at numerous areas such as simulation-intelligence sample, synthetic aperture radar image-forming, remotely sensed image, Magnetic resonance imaging, recognition of face, information source codings to compressed sensing.Recent years the domestic research boom that also starts compressed sensing.But with the compressed sensing theory be used on the image co-registration research also seldom.People such as scholar T.Wan take the lead in the theory of compressed sensing the is used for trial of image co-registration; Referring to article " Compressive Image Fusion "; In Proc.IEEE Int.Conf.Image Process, pp.1308-1311,2008. these methods adopt absolute value to get big fusion rule; Not only computation complexity is high, and fusion results exists much noise and striped.
Summary of the invention
The objective of the invention is to overcome the shortcoming of above-mentioned prior art, proposed a kind of multi-focus image fusing method, to reduce data volume, reduce the complexity of calculating, and when reducing complexity, improve the effect of image co-registration based on compressed sensing.
The key problem in technology of realizing the object of the invention is to utilize compressed sensing that the incomplete sampling of signal is reduced data volume; Utilize the orthogonal matching pursuit algorithm to reduce the complexity of calculating; Entire process is divided into three parts; The sub-piece of each multiple focussing image after at first multiple focussing image being carried out piecemeal and adopts the random gaussian matrix to rarefaction representation is observed; Adopt fusion method to merge to each image subblock observed reading after the observation again, adopt the total focus image after the orthogonal matching pursuit algorithm carries out reconstruct and obtains merging the observed reading after merging then based on the average gradient weighting.Its concrete steps comprise as follows:
(1) two width of cloth multiple focussing image A and the B to input carries out piecemeal, obtains n size and is 32 * 32 image subblock x iAnd y i(i=1,2 Λ n);
(2) calculate and write down multiple focussing image A and the sub-piece x of each correspondence image of B iAnd y iAverage gradient
Figure BDA0000076278580000021
With
Figure BDA0000076278580000022
(3) to the sub-piece x of each correspondence image of multiple focussing image A and B iAnd y iCarry out wavelet transformation, obtain the image subblock a after the sparse conversion iAnd b i, the small echo that adopts in the experiment is wave filter CDF 9/7 wavelet basis of biorthogonal wavelet, decomposing the number of plies is 3;
(4) with each image subblock a behind the wavelet transformation iAnd b iLine up column vector, observe, obtain the observed reading y of per two the sub-pieces of correspondence image of multiple focussing image A and B with the random gaussian matrix AAnd y B
(5) to the observed reading y of the image subblock of multiple focussing image A and per two correspondences of B AAnd y B, merging as follows, the image subblock observed reading after obtaining merging is y:
(5a) the fusion weights of the image subblock of calculating multiple focussing image A and per two correspondences of B:
w A = 0.5 if ▿ G ‾ A = ▿ G ‾ B = 0 ▿ G ‾ A ▿ G ‾ A + ▿ G ‾ B else
w B＝1-w A
Wherein,
Figure BDA0000076278580000031
Figure BDA0000076278580000032
Be respectively the average gradient of multiple focussing image A and the sub-piece of B correspondence image, w A, w BBe respectively the fusion weights of image A and the sub-piece of B correspondence image.
(5b) observed reading of the image subblock of multiple focussing image A and per two correspondences of B is carried out weighting fusion:
y＝w 1y A+w 2y B
Wherein, y A, y BBe respectively the observed reading of multiple focussing image A and the sub-piece of B two correspondence image, y is its value after merging.
(6) the observed reading y with the sub-piece of fused image adopts orthogonal matching pursuit OMP algorithm to recover the image subblock f after being restored;
(7) the image subblock f after will recovering carries out wavelet inverse transformation, the total focus image F after obtaining merging.
The present invention is owing to adopt image co-registration quality evaluation index average gradient to confirm that image subblock merges weights and combined compressed sensing theoretical, so compare with the traditional image fusion method, has the following advantages:
(A) sampling process does not need to suppose in advance any prior imformation of image;
(B) sub-piece fusion can obtain more excellent fusion weights to multiple focussing image;
(C) data volume of reconstruct is little, saves storage space.
Experiment showed, that the present invention merges problem to multiple focussing image, the visual effect of fusion results is better, and speed of convergence is also very fast.
Description of drawings
Figure l is whole realization flow figure of the present invention;
Fig. 2 is the source images figure of two groups of multiple focussing images;
Fig. 3 is the figure as a result that the burnt Clock image of poly is merged with the present invention and existing two kinds of blending algorithms;
Fig. 4 is the figure as a result that the burnt Pepsi image of poly is merged with the present invention and existing two kinds of blending algorithms.
Embodiment
With reference to Fig. 1, concrete performing step of the present invention is following:
Step 1 is to two width of cloth multiple focussing image A and B piecemeal of importing and average gradient
Figure BDA0000076278580000033
and
Figure BDA0000076278580000034
that calculates each image subblock
Image A and B are respectively that two width of cloth left sides focuses on and right focusedimage, the message complementary sense of the clear part of two width of cloth images, and purpose is to obtain about a width of cloth all total focus image clearly through fusion.Image is carried out piecemeal, help handling, and can reduce computation complexity, it is 32 * 32 image subblock that the present invention is divided into size to two width of cloth multiple focussing image A and B, and calculates the average gradient of each image subblock, by following formula calculating:
▿ G ‾ I = 1 M × N Σ i = 1 M Σ j = 1 N [ Δxf ( i , j ) 2 + Δyf ( i , j ) 2 ] 1 2
Wherein, and Δ xf (x, y); (x is that (i is j) at x for the sub-piece pixel of multiple focussing image I y) to Δ yf; First order difference on the y direction, I=A, B; M * N is the image subblock size, and
Figure BDA0000076278580000042
is the average gradient of the sub-piece of multiple focussing image I.
The sub-piece x of each correspondence image of step 2 couple multiple focussing image A and B iAnd y iCarry out wavelet transformation, obtain the image subblock a after the sparse conversion iAnd b i
It is in order to let signal satisfy the precondition of compressed sensing that each image subblock of multiple focussing image A and B is carried out sparse conversion; Promptly if signal be compressible or be sparse at certain transform domain; Just can use one with incoherent higher-dimension signal projection to the lower dimensional space of observing matrix of transform-based with the conversion gained on, just can from these a spot of projections, reconstruct original signal through finding the solution an optimization problem then with high probability.Sparse bi-orthogonal filter CDF 9/7 wavelet transformation that is transformed to that this instance adopts, decomposing the number of plies is 3 layers, but is not limited to wavelet transformation, for example can use the discrete cosine dct transform, Fourier FT conversion etc.
Step 3 is carried out CS observation with the random gaussian matrix to the sub-piece of each correspondence image of multiple focussing image A and B.
The CS observation of image is a linear process, and in order to guarantee accurate reconstruct, system of linear equations exists confirms that the necessary and sufficient condition of separating is that observing matrix and sparse transform-based matrix satisfy limited equidistance character RIP.The random gaussian matrix is uncorrelated with the matrix that most of fixedly orthogonal basiss constitute; This characteristic has determined to select it as observing matrix; Other orthogonal basis is during as sparse transform-based; So can satisfy RIP character. the present invention adopts the random gaussian matrix as observing matrix, and the sub-piece of each correspondence image is carried out CS observation, and concrete operations are following:
(3a) with the image subblock a of the N * N of multiple focussing image A and per two correspondences of B iAnd b iLine up N 2* 1 column vector θ AAnd θ B
(3b) generate M * N at random 2Random gaussian matrix and to its orthogonalization utilizes the random gaussian matrix that column vector is observed, and concrete computing formula is following;
y I＝Φθ I
Wherein, Φ is the random gaussian observing matrix, θ IBe the column vector of image subblock, I=A, B, y IObserved reading for each image subblock.The sampling rate of each image subblock in this instance is
Figure BDA0000076278580000043
controls sampling rate through the value of regulating the random gaussian matrix M.
Obtain the observed reading of each image subblock after each image subblock of multiple focussing image A and B observed, the size of observation vector is M * 1, and that in the experiment each image subblock is observed employing is same observing matrix Φ.
Step 4 merges two width of cloth multiple focussing image A and per two the sub-pieces of correspondence image of the B method with weighting.
The observed reading that each image subblock of multiple focussing image A and B obtains after observing through the random gaussian matrix is still keeping all information of the sub-piece of original image; So confirm the fusion weights of each image subblock observed reading of observation back through the average gradient that calculates the sub-piece of original image; Average gradient is an evaluation index of image co-registration, has reflected the readability of image, the distinct image piece; Average gradient is just big, and the weights of getting in the time of fusion also should be big.
The image subblock of image A and per two correspondences of the B method with weighting is merged, and practical implementation is following:
(4a) the fusion weights of the image subblock of calculating multiple focussing image A and per two correspondences of B:
w A = 0.5 if ▿ G ‾ A = ▿ G ‾ B = 0 ▿ G ‾ A ▿ G ‾ A + ▿ G ‾ B else
w B＝1-w A
Wherein,
Figure BDA0000076278580000052
Figure BDA0000076278580000053
Be respectively the average gradient of multiple focussing image A and the sub-piece of B correspondence image, w A, w BBe respectively the fusion weights of image A and the sub-piece of B correspondence image;
(4b) observed reading of the image subblock of multiple focussing image A and per two correspondences of B is carried out weighting fusion:
y＝w Ay A+w By B
Wherein, y A, y BBe respectively the observed reading of multiple focussing image A and the sub-piece of B two correspondence image, y is its observed reading after merging.
Step 5 adopts the orthogonal matching pursuit algorithm to recover the image subblock after being restored the observed reading of the sub-piece of fused image.
Quadrature coupling OMP tracing algorithm is based on the algorithm of greedy iteration; Exchange the reduction of computation complexity for the number of samples that needs more than base tracking BP algorithm. utilize orthogonal matching pursuit OMP algorithm to come solving-optimizing problem reformulation signal, improved the speed of calculating greatly, and be easy to realize. during concrete operations; Be that the image block after merging is recovered one by one; The concrete steps of algorithm are referring to " Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit ", IEEE Transactions on Information Theory, vol.53; No.12, December 2007.
Step 6, multiple focussing image A that the pair of orthogonal matching pursuit algorithm recovers and the image subblock of B carry out wavelet inverse transformation.
Adopt the sparse form of orthogonal matching pursuit algorithm recovered data for the total focus image of process fusion; The sub-piece of each image restored is carried out the total focus image subblock that wavelet inverse transformation obtains merging, the total focus image subblock after merging is combined into the total focus image after piece image just can obtain merging.
Effect of the present invention can specify through emulation experiment:
1. experiment condition
Testing used microcomputer CPU is Intel Core (TM) 2Duo 2.33GHz internal memory 2GB, and programming platform is Matlab7.0.1.The view data that adopts in the experiment is two groups of multiple focussing images of registration, and size is respectively 512 * 512, and 512 * 512, two groups of burnt source images of poly derive from the image co-registration website Http: ∥ www.imagefusion.org/, first group is the Clock image, like Fig. 2 (a) and Fig. 2 (b); Wherein Fig. 2 (a) focuses on the source images on the right for Clock; Fig. 2 (b) focuses on the source images on the left side for Clock, and second group is the Pepsi image, like Fig. 2 (c) and Fig. 2 (d); Wherein Fig. 2 (c) for Pepsi focus on the right source images, Fig. 2 (d) focuses on the source images on the left side for Clock.
2. experiment content
(2a) with method of the present invention and existing two kinds of fusion methods the Clock image is carried out fusion experiment, every group of sampling rate is set to 0.3,0.5 respectively; 0.7, fusion results such as Fig. 3, wherein Fig. 3 (a) is the fusion results figure of the existing method of average; Fig. 3 (b) is article " Compressive Image Fusion "; In Proc.IEEE Int.Conf.Image Process, pp.1308-1311,2008 fusion results figure; Fig. 3 (c) is fusion results figure of the present invention, and the sampling rate of three picture groups is 0.5.
(2b) with method of the present invention and existing two kinds of fusion methods the Pepsi image is carried out fusion experiment, every group of sampling rate is set to 0.3,0.5 respectively; 0.7, fusion results such as Fig. 4, wherein Fig. 4 (a) is the fusion results figure of the existing method of average; Fig. 4 (b) is article " Compressive Image Fusion "; In Proc.IEEE Int.Conf.Image Process, pp.1308-1311,2008 fusion results figure; Fig. 4 (c) is fusion results figure of the present invention, and the sampling rate of three picture groups is equal 0.5.The method of average is identical with method operation of the present invention, and just fusion rule is different, and the fusion weights of the method for average are w A=w B=0.5.
3. experimental result
With fusion method of the present invention and method of weighted mean and article " Compressive Image Fusion "; In Proc.IEEE Int.Conf.Image Process; Pp.1308-1311,2008. method compares on three kinds of picture appraisal indexs, estimates effect of the present invention.Fusion method of the present invention and method of weighted mean and article " Compressive Image Fusion "; In Proc.IEEE Int.Conf.Image Process; Pp.1308-1311, fusion qualitative evaluation index such as the table 1 of 2008. method on two groups of multiple focussing images:
Table 1, multiple focussing image merge the qualitative evaluation index
Mean CS-max-abs Ours is respectively the existing method of average, article " Compressive Image Fusion ", in Proc.IEEE Int.Conf.Image Process, pp.1308-1311,2008. method and method of the present invention in the table 1; R is a sampling rate, and MI is a mutual information, and IE is an information entropy, and Q is the edge conservation degree, and T is the time that image reconstruction needs, and unit is second (s).Wherein:
Mutual information (M I): mutual information has embodied fused images what of information extraction from original image, and mutual information is bigger, and the information of then extracting is many more.
Information entropy (IE): image information entropy is to weigh an abundant important indicator of image information, and what of quantity of information that image carries are the size of entropy reflected, entropy is big more, explains that the quantity of information of carrying is big more.
Edge conservation degree (Q): its essence is and weigh the maintenance degree of fused image to the marginal information in the input picture, the scope of value is 0～1, more near 1, explains that the edge keeps degree good more.
Visible from table 1 data: on performance index; The edge conservation degree Q index of method of the present invention is existing higher than the method for average and CS-max-abs method; On mutual information MI index, method of the present invention is higher than the method for average, and more more than CS-max-abs method height; The information entropy IE index and the method for average are suitable, but lower than CS-max-abs method.On the image reconstruction time T, the required time ratio CS-max-abs fusion method of method of the present invention will be lacked a lot.Along with the raising of sampling rate, each item index of fusion results also improves gradually.
Visible from Fig. 3-Fig. 4: the fusion results of fusion method of the present invention on two groups of multiple focussing images is better than the method for average and CS-max-abs fusion method visual effect; The fusion results of CS-max-abs fusion method exists much noise and ribbon grain, and contrast is also lower.CS-max-abs fusion method visual effect is not so good as method of the present invention but on information entropy IE index, is higher than method of the present invention is because in fusion process, produced noise, causes information entropy IE index can not truly reflect the useful information amount of fused images.
The multi-focus image fusing method based on compressed sensing that the above-mentioned the present invention of experiment showed, proposes merges problem to multiple focussing image and can obtain good visual effect, and computation complexity is also lower.

Claims (3)

1. the multi-focus image fusing method based on compressed sensing comprises the steps:
(1) two width of cloth multiple focussing image A and the B to input carries out piecemeal, obtains n size and is 32 * 32 image subblock x iAnd y i, i=1,2 Λ n;
(2) calculate and write down multiple focussing image A and the sub-piece x of each correspondence image of B iAnd y iAverage gradient
Figure FDA0000076278570000011
With
Figure FDA0000076278570000012
(3) to the sub-piece x of each correspondence image of multiple focussing image A and B iAnd y iCarry out wavelet transformation, obtain the image subblock a after the sparse conversion iAnd b i, the small echo that adopts in the experiment is wave filter CDF 9/7 wavelet basis of biorthogonal wavelet, decomposing the number of plies is 3;
(4) with each image subblock a behind the wavelet transformation iAnd b iLine up column vector, column vector is observed, obtain the observed reading y of per two the sub-pieces of correspondence image of multiple focussing image A and B with the random gaussian matrix AAnd y B
(5) to the observed reading y of the image subblock of multiple focussing image A and per two correspondences of B AAnd y B, merging as follows, the image subblock observed reading after obtaining merging is y:
(5a) the fusion weights of the image subblock of calculating multiple focussing image A and per two correspondences of B:
w A = 0.5 if ▿ G ‾ A = ▿ G ‾ B = 0 ▿ G ‾ A ▿ G ‾ A + ▿ G ‾ B else
w B＝1-w A
Wherein,
Figure FDA0000076278570000014
Figure FDA0000076278570000015
Be respectively the average gradient of multiple focussing image A and the sub-piece of B correspondence image, w A, w BBe respectively the fusion weights of image A and the sub-piece of B correspondence image;
(5b) observed reading of the image subblock of multiple focussing image A and per two correspondences of B is carried out weighting fusion:
y＝w Ay A+w By B
Wherein, y A, y BBe respectively the observed reading of multiple focussing image A and the sub-piece of B two correspondence image, y is its value after merging;
(6) the observed reading y with the sub-piece of fused image adopts orthogonal matching pursuit OMP algorithm to recover the image subblock f after being restored;
(7) the image subblock f after will recovering carries out wavelet inverse transformation, the total focus image F after obtaining merging.
2. the multi-focus image fusing method based on compressed sensing according to claim 1, the wherein described calculating of step (2) and record multiple focussing image A and the sub-piece x of each correspondence image of B iAnd y iAverage gradient, calculate by following formula:
▿ G ‾ I = 1 M × N Σ i = 1 M Σ j = 1 N [ Δxf ( i , j ) 2 + Δyf ( i , j ) 2 ] 1 2
Wherein, and Δ xf (x, y); (x is that (i is j) at x for the sub-piece pixel of multiple focussing image I y) to Δ yf; First order difference on the y direction, I=A, B; M * N is the image subblock size, and
Figure FDA0000076278570000022
is the average gradient of the sub-piece of multiple focussing image I.
3. the multi-focus image fusing method based on compressed sensing according to claim 1, wherein step (4) is described observes column vector with the random gaussian matrix, is to carry out through following formula;
y I＝Φθ I
Wherein, Φ is the random gaussian observing matrix, θ IBe the column vector of image subblock, I=A, B, y IObserved reading for each image subblock.
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