CN102073875A - Sparse representation-based background clutter quantification method - Google Patents

Abstract

The invention discloses a sparse representation-based background clutter quantification method, which mainly solves the problem that the conventional cluster scale cannot accord with the physical essence of background clutter relativity well and cannot fully reflect human vision property. The method comprises the following implementation steps of: partitioning a gray background image to be quantified into a plurality of small equal-size units and combining the small units into a background matrix; extracting main characteristics of a target vector and the background matrix so as to obtain a target characteristic vector and a background characteristic matrix; normalizing the target characteristic vector and the background characteristic matrix; and calculating the sparsest representations of the normalized target characteristic vector in the normalized background characteristic matrix, wherein the summation of absolute values of the sparsest representations is taken as the background clutter scale of the entire image. Two major characteristics during human eye search are fully utilized, the consistency between a predicted target detection probability and a subjective practical target detection probability is enhanced, and the method can be used for predicting and evaluating the target acquisition performance of a photoelectric imaging system.

Description

Background clutter quantizing method based on rarefaction representation

Technical field

The invention belongs to technical field of image processing,, can be used for prediction and assessment that the photo electric imaging system target is obtained performance particularly by the background clutter quantizing method of rarefaction representation.

Background technology

It is a key concept in the military missions such as photoelectronic warfare, scouting, early warning and camouflage that the photo electric imaging system target is obtained performance.In recent years, along with the introducing of new material and the progress of manufacturing process, photodetector has reached or near the background limit, contextual factor has become the key factor that restriction photo electric imaging system target is obtained performance.The photo electric imaging system target is obtained and is used rationally background clutter quantization scale accurately, the outfield performance that can make it predict the outcome and embody imaging system more accurately in the performance characterization model.

Background clutter is a kind of visually-perceptible effect, refers to the class object that jamming target is surveyed, and it has two typical characteristics: based on background and target signature; Relative interesting target.Since the last century the eighties, the foreign study person is carrying out a large amount of research aspect the quantification sign of background clutter, multiple background clutter quantificational description yardstick has been proposed, wherein most widely used is statistical variance yardstick SV, as D.E.Schmieder and M.R.Weathersby, " Detection performance in clutter with variable resolution; " IEEE Trans.Aerosp.Electron.Syst.AES-19 (4), 622-630 (1983), with marginal probability yardstick POE, as G.Tidhar, G.Reiter, Z.Avital, Y.Hadar, S.R.Rotmam, V.George, and M.L.Kowalczyk, " Modeling human search and target acquisition performance:IV.Detection probability in the cluttered environment; " Opt.Eng.33,801-808 (1994).Yet statistical variance yardstick SV is based upon on the basis to the photoelectric image statistical treatment, does not consider the human eye vision apperceive characteristic; Marginal probability yardstick POE is reference with the background information only, and having run counter to background clutter is the physical substance of relative target.This feasible clutter yardstick by the two foundation can not reasonably reflect the influence of background to the target acquisition process, is difficult to be used for exactly the prediction and the assessment of photo electric imaging system outfield performance.

Summary of the invention

The objective of the invention is to overcome the deficiency of background clutter quantizing method in the past, propose a kind of background clutter yardstick, to improve accuracy performance prediction of imaging system outfield and assessment based on rarefaction representation.

In order to realize such purpose, the present invention by dimensionality reduction technology with target and background information by space field transformation to property field, and utilize the rarefaction representation theory that background clutter is quantized at feature space.Concrete steps are as follows:

(1) with the target image column vectorization of two dimension, obtains object vector x;

(2) background image is divided into N equal-sized junior unit, the size of each junior unit level and vertical direction is two times of target corresponding size;

(3) background junior unit column vectorization that each is two-dimentional, and be combined into background matrix Ψ;

(4) by principal component analysis (PCA) PCA to object vector x and background matrix Ψ dimensionality reduction, obtain target feature vector respectively

With background characteristics matrix Φ;

(5) to target feature vector

Carry out normalized, obtain the normalization target feature vector

$\hat{x}=\tilde{x}/{\left|\right|\tilde{x}\left|\right|}_2$

Wherein || || ₂The l of expression vector ²Norm;

(6) each vector among the background characteristics matrix Φ is carried out the Θ as a result that normalized obtains _i, by subscript sequence number order from small to large, constitute normalization background characteristics matrix Θ,

Θ _i＝Φ _i/||Φ _i|| ₂，i＝1，2，...，N

Wherein, Φ _iAnd Θ _iBe respectively i the column vector of background characteristics matrix Φ and normalization background characteristics matrix Θ, N is the number of column vector among the background characteristics matrix Φ;

(7) calculate the normalization target feature vector

Rarefaction representation in normalization background characteristics matrix Θ obtains similar vectorial s: promptly find the solution satisfied

The minimum l of s ⁰Norm is separated:

Min||s|| ₀Satisfy

(8) get nonzero element absolute value among the similar vectorial s

I=1,2 ..., K, summation, clutter quantization scale as a setting:

Wherein K is the number of nonzero element among the similar vectorial s.

The present invention has following advantage:

1) the present invention is owing to adopt the PCA method dimension-reduction treatment of target and background information to be simulated first stage--the feature selecting stage of human eye vision in the search procedure, and simulate second stage--the Syndicating search stage of human eye vision in the search procedure by obtaining the rarefaction representation of target feature vector in the background characteristics matrix, meet the apperceive characteristic of human eye vision in the target acquisition process;

2) the present invention has been owing to not only considered background characteristics in background clutter quantizes, and is also that the relativity influence of target signature is included, meets the physical essence of background clutter.

Based on above 2 points, the physical mechanism that background information influences the target acquisition process in background clutter quantizing method of the present invention and the field trial more conforms to.Experimental result shows: compare with clutter quantization method commonly used in the past, background clutter quantizing method of the present invention is more consistent with the acquisition probability that observer's actual tests obtains to the prediction of acquisition probability, and the prediction of target being obtained performance is more accurate.

Description of drawings:

Fig. 1 is the synoptic diagram of implementation procedure of the present invention;

Low background clutter image, target image and similar vector distribution figure that Fig. 2 uses for the present invention;

Middle background clutter image, target image and similar vector distribution figure that Fig. 3 uses for the present invention;

High background clutter image, target image and similar vector distribution figure that Fig. 4 uses for the present invention;

Fig. 5 is for being experimental data with the Search_2 image data base, the matched curve between each background clutter quantization scale and the observer's realistic objective detection probability.

Embodiment

With reference to Fig. 1, the background clutter quantizing method performing step that the present invention is based on rarefaction representation is as follows:

Step 1 with the unit of classifying as, by initial column sequence number order from small to large, is formed object vector with the pixel value of target image

x＝{t _1，1，t _2，1，t _3，1，...，t _C，1，t _1，2，...，t _C，D} ^T

T wherein _{I, j}The expression position (i, the target pixel value of j) locating, C and D are represented the line number and the columns of target image respectively, T represents vector is carried out matrix transpose operation.

Step 2 is divided into N equal-sized junior unit with background image to be quantified, and the horizontal direction of each junior unit and the size of vertical direction are the twice of target corresponding size.

The size of N determined by the big or small M=C * D of the big or small A * B of background image to be quantified and each junior unit, promptly Wherein, A and B represent the line number and the columns of background image respectively,

The maximum integer that is less than or equal to x is got in expression.

Step 3, the column vector that each background junior unit column vectorization is successively obtained

I=1,2 ..., N, combination background matrix

Ψ＝{A ₁，A ₂，...，A _N}

Step 4 is carried out dimension-reduction treatment with principal component analysis (PCA) PCA to object vector x and background matrix Ψ, and concrete steps are as follows:

(4a) will deduct the X as a result that place row element average obtains with each element among the background matrix Ψ _Ij, with subscript (i j) is preface, constitutes background differential matrix X,

$X_{\mathrm{ij}}={\mathrm{\Ψ}}_{\mathrm{ij}}-\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\Ψ}}_{\mathrm{ij}}/N,i=\mathrm{1,2},...,M,j=\mathrm{1,2},...,N$

Wherein, Ψ _IjAnd X _IjBe respectively background matrix Ψ and background differential matrix X and be positioned at that (M and N are respectively line number and the columns of background matrix Ψ for i, the value of j) locating;

(4b) take advantage of its transposed matrix X with the background differential matrix X right side ^T, obtain covariance matrix A:

A＝X ^TX；

(4c) covariance matrix A is carried out characteristic value decomposition, obtain its nonzero eigenvalue λ _kAnd corresponding proper vector v _k, k=1,2 ..., t, wherein t is total number of covariance matrix A nonzero eigenvalue, λ ₁〉=λ ₂〉=Λ 〉=λ _t＞0, the proper vector mutually orthogonal;

(4d) with covariance matrix A nonzero eigenvalue summation 90% as threshold value, W subduplicate formation diagonal matrix D reciprocal of nonzero eigenvalue before getting:

$D=\left[\begin{array}{ccc}1/\sqrt{{\mathrm{\&lambda;}}_1}& & \\ & \mathrm{<figure-callout\; id="1"\; label="O"\; filenames="HDA0000042845270000041.png"\; state="\{\{state\}\}">O</figure-callout>}& \\ & & 1/\sqrt{{\mathrm{\&lambda;}}_W}\end{array}\right],$ Satisfy $\underset{k=1}{\overset{W}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_k/\underset{k=1}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_k\&ap;0.9$

Simultaneously, get this W nonzero eigenvalue characteristic of correspondence vector v _k, k=1,2 ..., W, composition characteristic matrix: v={v ₁, v ₂..., v _W;

(4e) with background differential matrix X premultiplication eigenmatrix v, premultiplication diagonal matrix D obtains albefaction matrix R again ^{M * W}:

R＝X*v*D

Wherein, the line number M of albefaction matrix R is far longer than its columns W;

(4f), obtain the background characteristics matrix with the transposed matrix premultiplication background differential matrix X of albefaction matrix R:

Φ＝R ^TX；

(4g) will be with the d as a result of corresponding row element average among each element subtracting background matrix Ψ of object vector x _i,, constitute target difference vector d={d according to subscript sequence number order from small to large ₁, d ₂..., d _M} ^T,

$d_i=x_i-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&Psi;}}_{\mathrm{ij}}/N,i=\mathrm{1,2},...,M,j=\mathrm{1,2},...,N;$

X wherein _iBe i the element of object vector x, Ψ _Ij(M and N are respectively line number and the columns of background matrix Ψ for i, the value of j) locating for background matrix Ψ is positioned at;

(4h) the transposed matrix premultiplication target difference vector d with albefaction matrix R obtains target feature vector:

$\tilde{x}=R^{T}d.$

Except adopting described principal component analysis (PCA) PCA, also available following method is carried out dimensionality reduction to this step to the method for object vector and background matrix dimensionality reduction:

1) multi-dimentional scale method MDS (I.Borg, and P.Groenen, " Modern Multidimensional Scaling:theory and applications, " 2nd ed., Springer-Verlag New York, 2005);

2) independent component analysis method ICA (A. And E.Oja, " A Fast Fixed-Point Algorithm for Independent Component Analysis, " Neural Computation, vol.9, No.7, pp:1,483-1,492, Oct.1997.);

3) nonnegative matrix factorization method NMF (D.D.Lee and H.S.Seung. " Algorithms for non-negative matrix factorization, " In Advances in Neural Information Processing systems, 2001.);

4) local linear embedding inlay technique LLE (T.R.Sam and K.S.Lawrence, " Nonlinear Dimensionality Reduction by Locally Linear Embedding, " SCIENCE, Vol.290No.22, Dec.2000.);

5) laplacian eigenmaps method LE (M.Belkin and P.Niyogi, " Laplacian Eigenmaps for Dimensionality Reduction and Data Representation; " Neural Computation 15, pp:1373-1396,2003.).

Step 5 is to target feature vector

Carry out normalized and obtain the normalization target feature vector

$\hat{x}=\tilde{x}/{\left|\right|\tilde{x}\left|\right|}_2$

Wherein || || ₂The l of expression vector ₂Norm.

Step 6 is carried out the Θ as a result that normalized obtains with each vector among the background characteristics matrix Φ _i, by subscript sequence number order from small to large, form normalization background characteristics matrix Θ,

Θ _i＝Φ _i/||Φ _i|| ₂，i＝1，2，...，N

Wherein, Φ _iAnd Θ _iBe respectively i the column vector of background characteristics matrix Φ and normalization background characteristics matrix Θ, N is the number of column vector among the background characteristics matrix Φ.

Step 7 is asked the normalization target feature vector Rarefaction representation in normalization background characteristics matrix Θ obtains similar vectorial s: promptly find the solution satisfied

The minimum l of s ⁰Norm is separated:

Min||s|| ₀Satisfy

Solution procedure is as follows:

(7a) ask satisfied

The minimum l of s ¹Norm is separated:

Min||s|| ₁Satisfy

(7b) with formula＜1〉relaxing is:

Min||s|| ₁Satisfy

Wherein, ε is not less than 0 arbitrary constant, when ε=0, and formula＜2〉will deteriorate to formula＜1 〉;

(7c) utilize the LASSO algorithm, with formula＜2〉be converted into:

Satisfy || s|| ₁≤ σ＜3 〉

Wherein, σ is not less than 0 arbitrary constant;

(7d) utilize Lagrangian algorithm, with formula＜3〉be converted into the unconstrained optimization formula:

$s^{*}=\arg \underset{s}{\min }\frac{1}{2}{\left|\right|\hat{x}-\mathrm{\&Theta;s}\left|\right|}_2+\mathrm{\&alpha;}{\left|\right|s\left|\right|}_1---<4>$

Wherein, α is a Lagrange multiplier,

The value of the minimum variations per hour s of expression objective function;

(7e) utilize and to block some algorithm in the newton, with formula＜4 turn to the quadratic programming formula of inequality constrain:

$\mathrm{<figure-callout\; id="1"\; label="min"\; filenames="HDA0000042845270000041.png"\; state="\{\{state\}\}">min</figure-callout>}\frac{1}{2}{\left|\right|\hat{x}-\mathrm{\&Theta;s}\left|\right|}_2+\mathrm{\&alpha;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i---<5>$

-μ _i≤s _i≤μ _i，i＝1，2，...，N.

Wherein, s _iBe i the element of similar vectorial s, μ _iBe constraint s _iThe factor ,-μ _i≤ s _i≤ μ _iBe constraint condition;

(7f) be constraint condition-μ _i≤ s _i≤ μ _iSet up the logarithm barrier function:

Utilize the logarithm barrier function, with formula＜5〉be converted into and ask the centrode function F that defines by weight factor β _β(s, μ, optimum solution α)=0:

(7g) utilize Newton iteration method solving equation＜6 〉, can get iterative formula:

$\left(\begin{array}{c}{s}^{(k+1)}\\ {\mathrm{\&mu;}}^{(k+1)}\\ {\mathrm{\&alpha;}}^{(k+1)}\end{array}\right)=\left(\begin{array}{c}{s}^{\left(k\right)}\\ {\mathrm{\&mu;}}^{\left(k\right)}\\ {\mathrm{\&alpha;}}^{\left(k\right)}\end{array}\right)-{\&dtri;}^2{F_{\mathrm{\&beta;}}}^{-1}(s^{\left(k\right)},{\mathrm{\&mu;}}^{\left(k\right)},{\mathrm{\&alpha;}}^{\left(k\right)})\&CenterDot;{\&dtri;F}_{\mathrm{\&beta;}}(s^{\left(k\right)},{\mathrm{\&mu;}}^{\left(k\right)},{\mathrm{\&alpha;}}^{\left(k\right)})$

Wherein, s ^(k), μ ^(k)And α ^(k)Represent s respectively, μ and the α result after the k time iteration, s ^(k+1), μ ^(k+1)And α ^(k+1)Represent s respectively, μ and the α result after the k+1 time iteration, k is not more than 50 nonnegative integer,

The second derivative of function is asked in expression,

The first order derivative of function is asked in expression;

(7h) initial value of weighting repeated factor β=0.5 and solution vector:

$\left(\begin{array}{c}{s}^{\left(0\right)}\\ {\mathrm{\&mu;}}^{\left(0\right)}\\ {\mathrm{\&alpha;}}^{\left(0\right)}\end{array}\right)=\left(\begin{array}{c}{\mathrm{\&Theta;}}^T\hat{x}\\ 0.95\&CenterDot;\mathrm{sgn}\left({\mathrm{\&Theta;}}^T\hat{x}\right)\&CenterDot;{\mathrm{\&Theta;}}^T\hat{x}+0.1\max (\mathrm{sgn}\left({\mathrm{\&Theta;}}^T\hat{x}\right)\&CenterDot;{\mathrm{\&Theta;}}^T\hat{x})\\ 1\end{array}\right)$

Wherein, max represents the maximal value of amount of orientation element, and sgn represents the positive and negative attribute of vector element:

(7i) bring initial value and weight factor into step (7g) and carry out interative computation, bring formula＜5 into up to the result with adjacent twice iteration the difference of subtracting each other is not more than 10 ^-3, this moment, the value of the s that obtains was formula＜1〉in the minimum l of s ¹Norm is separated, and jumps to step (7k); If, reach maximum iteration time 50, do not obtain optimum solution yet, execution in step (7j);

(7j) with final iteration result as initial value, weight factor is updated to original 2 times, iterations makes zero, and turns back to step (7i);

(7k) verify the minimum l of all trial image ¹Norm is separated the sparse property of s, according to document D.Donoho, and " For most large underdetermined systems of linear eauations the minimal l ¹-norm near solution approximates the sparest solution, " preprint, the conclusion that proposes in 2004.: as minimum l ¹When norm is separated s and is had sparse characteristic, itself and minimum l ⁰Norm is separated equivalence, as can be known, and the minimum l that the present invention tried to achieve ¹Norm is separated s and is the normalization target feature vector

Rarefaction representation in normalization background characteristics matrix Θ.

Find the solution minimum l ¹The norm problem, the algorithm of in the present invention, giving, can also carry out in order to following method:

1) gradient reflection method (M.Figueiredo, R.Nowak, and S.Wright, " Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems; " IEEE Journal of Selected Topics in Signal Processing, Vol.1, No.4, pp:586-597,2007.);

2) homotopy method (D.Malioutov, M.Cetin, and A.Willsky, " Homotopy continuation for sparse signal representation; " In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.);

3) iteration collapse threshold method (I.Daubechies, M.Defrise, and C.Mol, " Aniterative thresholding algorithm for linear inverse problems with asparsity constraint; " Communications on Pure and Applied Math, Vol.57, pp:1413-1457,2004.);

4) Nesterov ' s method (A.Beck and M.Teboulle, " A fast iterative shrinkage-thresholding algorithm for linear inverse problems; " SIAMJournal on Imaging Sciences, Vol.2, No.1, pp:183-202,2009.);

5) intersection guiding method (J.Yang and Y.Zhang, " Alternating direction algorithms for l ¹-problems in compressive sensing, " (preprint) arXiv:0912.1185,2009.).

Step 8 is got the absolute value of nonzero element among the similar vectorial s I=1,2 ..., K, summation, as the background clutter quantization scale of entire image:

Wherein, K is the number of nonzero element among the similar vectorial s.

Rationality of the present invention and superiority can further describe by following experiment and comparative analysis:

Experimental verification:

1. experiment condition

To be example verify to the rationality of image background clutter yardstick of the present invention and in the superiority that target is obtained aspect the performance prediction Search_2 image data base that provides with Dutch TNO Human Factors research institute.The Search_2 image data base comprises high-resolution digital natural scene image and the concrete parameter of every width of cloth scene and the test result of observer's actual observation experiment of 44 width of cloth different background complexities, the detailed description of relevant this database can be referring to document A.Toet, P.Bijl, and J.M.Valeton, " Image data set for testing search and detection models; " Opt.Eng.40 (9), 1760-1767 (2001); A.Toet, P.Bijl, F.L.Kooi, and J.M.Valeton, " Ahigh-resolution image data set for testing search and detection models; " Report TM-98-A020, TNO Human Factors Research Institute, (1998) and A.Toet, " Errata in Report TNO-TM 1998A020:A high-resolution image data set for testing search and detection models, " (2001).

2. example explanation

That Fig. 2, Fig. 3 and Fig. 4 have provided respectively that the present invention uses is low, in be low background clutter image and target area image with background image, target image and similar vector distribution figure: Fig. 2 of the different clutter grades of Senior Three kind, wherein Fig. 2 (a) is low background clutter image, Fig. 2 (b) is a target area image, be the part that the white rectangle frame is marked among Fig. 2 (a), the corresponding similar vector distribution figure of Fig. 2 (c) for calculating; Fig. 3 is middle background clutter image and target area image, and wherein Fig. 3 (a) is middle background clutter image, and Fig. 3 (b) is a target area image, i.e. the part that the white rectangle frame is marked among Fig. 3 (a), the corresponding similar vector distribution figure of Fig. 3 (c) for calculating; Fig. 4 is high background clutter image and target area image, and wherein Fig. 4 (a) is high background clutter image, and Fig. 4 (b) is a target area image, i.e. the part that the white rectangle frame is marked among Fig. 4 (a), the corresponding similar vector distribution figure of Fig. 4 (c) for calculating.

From Fig. 2 (c), Fig. 3 (c) and Fig. 4 (c) as seen, image for three kinds of different clutter grades, its target image all has sparse characteristic to the similar vector of background image, thereby has proved the rationality of the calculating normalization target feature vector algorithm of rarefaction representation in normalization background characteristics vector that adopts among the present invention.

From Fig. 2 (a) and Fig. 2 (b) as seen, the similarity of background and target is low, and the background clutter of entire image is very low, and the detection of a target is easy to; From Fig. 3 (a) and Fig. 3 (b) as seen, the similarity of background and target is higher, and the background clutter of entire image is higher, and the detection of a target is difficulty; From Fig. 4 (a) and Fig. 4 (b) as seen, compare with front two width of cloth images, the similarity of its background and target is the highest, and the background clutter of entire image is the highest, and the detection of a target is the most difficult.Respectively the background clutter yardstick that Fig. 2 (a), Fig. 3 (a) and Fig. 4 (a) quantize to obtain them is respectively 2.0195,1.3060 and 1.0120 with image background clutter quantization scale of the present invention, this subjective perception with above-described human eye vision is consistent, and visible quantization scale of the present invention can reflect the truth of background clutter.

3. experimental result

The 7th, 15,23,26 and 4 width of cloth images in the Search_2 database when the present invention being experimentized checking, have been removed, this be since the present invention research be that single goal is surveyed, there is the binocular mark in preceding four width of cloth images, exceeded scope of the present invention, and target is too small in the last piece image, belong to Weak target and detect problem, do not belong to research field of the present invention.Thereby in the superiority experiment of checking background clutter quantization scale of the present invention aspect target is obtained performance prediction, final valid data are remaining 39 width of cloth image.

Fig. 5 utilizes result that POE, SV and background clutter yardstick of the present invention quantize to obtain to this 39 width of cloth image and the matched curve between observer's realistic objective detection probability, wherein, Fig. 5 (a), 5 (b) and 5 (c) are respectively the matched curve between POE, SV and background clutter quantization scale of the present invention and the observer's realistic objective detection probability.Fitting formula is:

$\mathrm{PD}=\frac{{(X/X_{50})}^{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HDA0000042845270000041.png"\; state="\{\{state\}\}">E</figure-callout>}}}{1+{(X/X_{50})}^E}$

Wherein, X represents the background clutter yardstick; X ₅₀Be constant with E, can be by obtaining with the match of observer's realistic objective detection probability; PD is observer's realistic objective detection probability that subjective experiment obtains, can be by formula:

PD＝N _c/(N _c+N _f+N _m)

Obtain, wherein N _c, N _fAnd N _mBe respectively the correct detection of every width of cloth image correspondence in the Search_2 database to the number of the number of target, erroneous judgement target with do not detect the number of target.

Table 1 has provided the result of match between the acquisition probability that each background clutter yardstick and actual subjective experiment obtain with the form of data, comprising the X of each background clutter yardstick correspondence ₅₀With the value of E, and performance measure RMSE, CC and SCC are to the target of prediction detection probability and the conforming evaluation result of observer's realistic objective detection probability of each background clutter yardstick.Wherein, X ₅₀With E be curve fitting parameter; RMSE is a root-mean-square error; CC is a Pearson correlation coefficient; SCC is the Spearman rank correlation coefficient.

Table 1: the performance of background clutter yardstick of the present invention, POE and SV relatively

By table 1 as seen, the Pearson correlation coefficient of background clutter quantization scale of the present invention and observer's realistic objective detection probability and Spearman rank correlation coefficient are all greater than other background clutter yardstick, and root-mean-square error is less than other background clutter yardstick, thereby proved that background clutter quantization scale of the present invention obtains superiority aspect the performance prediction in target.

Claims (3)

1. background clutter quantizing method based on rarefaction representation comprises following process:

(1) with the target image column vectorization of two dimension, obtains object vector x;

(2) background image is divided into N equal-sized junior unit, the size of each junior unit level and vertical direction is two times of target corresponding size;

(3) background junior unit column vectorization that each is two-dimentional, and be combined into background matrix Ψ;

(4) by principal component analysis (PCA) PCA to object vector x and background matrix Ψ dimensionality reduction, obtain target feature vector respectively

With background characteristics matrix Φ;

(5) to target feature vector

Carry out normalized, obtain the normalization target feature vector

$\hat{x}=\tilde{x}/{\left|\right|\tilde{x}\left|\right|}_2$

Wherein, || || ₂The l of expression vector ²Norm;

(6) each vector among the background characteristics matrix Φ is carried out the Θ as a result that normalized obtains _i, by subscript sequence number order from small to large, constitute normalization background characteristics matrix Θ,

Θ _i＝Φ _i/||Φ _i|| ₂，i＝1，2，...，N

Wherein, Φ _iAnd Θ _iBe respectively i the column vector of background characteristics matrix Φ and normalization background characteristics matrix Θ, N is the number of column vector among the background characteristics matrix Φ;

(7) calculate the normalization target feature vector

Rarefaction representation in normalization background characteristics matrix Θ obtains similar vectorial s: promptly find the solution satisfied

The minimum l of s ⁰Norm is separated:

Min||s||0 satisfies

(8) get nonzero element absolute value among the similar vectorial s

I=1,2 ..., K, summation, clutter quantization scale as a setting:

Wherein K is the number of nonzero element among the similar vectorial s.

2. background clutter quantizing method according to claim 1, wherein step (4) described by principal component analysis (PCA) PCA to object vector x and background matrix Ψ dimensionality reduction, carry out as follows:

(4a) will deduct the X as a result that place row element average obtains with each element among the background matrix Ψ _Ij, with subscript (i j) is preface, constitutes background differential matrix X,

$X_{\mathrm{ij}}={\mathrm{\&Psi;}}_{\mathrm{ij}}-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&Psi;}}_{\mathrm{ij}}/N,i=\mathrm{1,2},...,M,j=\mathrm{1,2},...,N$

Wherein, Ψ _IjAnd X _IjBe respectively background matrix Ψ and background differential matrix X and be positioned at that (M and N are respectively line number and the columns of background matrix Ψ for i, the value of j) locating;

(4b) take advantage of its transposed matrix X with the background differential matrix X right side ^T, obtain covariance matrix A:

A＝X ^TX

(4c) covariance matrix A is carried out characteristic value decomposition, obtain its nonzero eigenvalue λ _kAnd corresponding proper vector v _k, k=1,2 ..., t, wherein t is total number of covariance matrix A nonzero eigenvalue, λ ₁〉=λ ₂〉=Λ 〉=λ _t＞0, the proper vector mutually orthogonal;

(4d) with covariance matrix A nonzero eigenvalue summation 90% as threshold value, W subduplicate formation diagonal matrix D reciprocal of nonzero eigenvalue before getting:

$D=\left[\begin{array}{ccc}1/\sqrt{{\mathrm{\&lambda;}}_1}& & \\ & O& \\ & & 1/\sqrt{{\mathrm{\&lambda;}}_W}\end{array}\right],$ Satisfy $\underset{k=1}{\overset{W}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_k/\underset{k=1}{\overset{t}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_k\&ap;0.9$

Simultaneously, get this W nonzero eigenvalue characteristic of correspondence vector v _k, k=1,2 ..., W, composition characteristic matrix: v={v ₁, v ₂..., v _W;

(4e) with background differential matrix X premultiplication eigenmatrix v, premultiplication diagonal matrix D obtains albefaction matrix R again ^{M * W}:

R＝X*v*D

Wherein, the line number M of albefaction matrix R is far longer than its columns W;

(4f), obtain the background characteristics matrix with the transposed matrix premultiplication background differential matrix X of albefaction matrix R:

Φ＝R ^TX；

(4g) will be with the d as a result of corresponding row element average among each element subtracting background matrix Ψ of object vector x _i,, constitute target difference vector d={d according to subscript sequence number order from small to large ₁, d ₂..., d _M} ^T,

$d_i=x_i-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&Psi;}}_{\mathrm{ij}}/N,i=\mathrm{1,2},...,M,j=\mathrm{1,2},...,N;$

Wherein, x _iBe i the element of object vector x, Ψ _Ij(M and N are respectively line number and the columns of background matrix Ψ for i, the value of j) locating for background matrix Ψ is positioned at;

(4h) the transposed matrix premultiplication target difference vector d with albefaction matrix R obtains target feature vector:

$\tilde{x}=R^{T}d.$

3. background clutter quantizing method according to claim 1, the wherein described calculating normalization of step (7) target feature vector

Rarefaction representation in normalization background characteristics matrix Θ, calculate as follows:

(7a) ask satisfied

The minimum l of s ¹Norm is separated:

Min||s|| ₁Satisfy

(7b) with formula＜1〉relaxing is:

Min||s|| ₁Satisfy

Wherein, ε is not less than 0 arbitrary constant, when ε=0, and formula＜2〉will deteriorate to formula＜1 〉;

(7c) utilize the LASSO algorithm, with formula＜2〉be converted into:

Satisfy || s|| ₁≤ σ＜3 〉

Wherein, σ is not less than 0 arbitrary constant;

(7d) utilize Lagrangian algorithm, with formula＜3〉be converted into the unconstrained optimization formula:

$s^{*}=\arg \underset{s}{\min }\frac{1}{2}{\left|\right|\hat{x}-\mathrm{\&Theta;s}\left|\right|}_2+\mathrm{\&alpha;}{\left|\right|s\left|\right|}_1---<4>$

Wherein, α is a Lagrange multiplier,

The value of the minimum variations per hour s of expression objective function;

(7e) utilize and to block some algorithm in the newton, with formula＜4 turn to the quadratic programming formula of inequality constrain:

$\min \frac{1}{2}{\left|\right|\hat{x}-\mathrm{\&Theta;s}\left|\right|}_2+\mathrm{\&alpha;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i---<5>$

-μ _i≤s _i≤μ _i，i＝1，2，...，N.

Wherein, s _iBe i the element of similar vectorial s, μ _iBe constraint s _iThe factor ,-μ _i≤ s _i≤ μ _iBe constraint condition;

(7f) be constraint condition-μ _i≤ s _i≤ μ _iSet up the logarithm barrier function:

Utilize the logarithm barrier function, with formula＜5〉be converted into and ask the centrode function F that defines by weight factor β _β(s, μ, optimum solution α)=0:

(7g) utilize Newton iteration method solving equation＜6 〉, can get iterative formula:

$\left(\begin{array}{c}{s}^{(k+1)}\\ {\mathrm{\&mu;}}^{(k+1)}\\ {\mathrm{\&alpha;}}^{(k+1)}\end{array}\right)=\left(\begin{array}{c}{s}^{\left(k\right)}\\ {\mathrm{\&mu;}}^{\left(k\right)}\\ {\mathrm{\&alpha;}}^{\left(k\right)}\end{array}\right)-{\&dtri;}^2{F_{\mathrm{\&beta;}}}^{-1}(s^{\left(k\right)},{\mathrm{\&mu;}}^{\left(k\right)},{\mathrm{\&alpha;}}^{\left(k\right)})\&CenterDot;{\&dtri;F}_{\mathrm{\&beta;}}(s^{\left(k\right)},{\mathrm{\&mu;}}^{\left(k\right)},{\mathrm{\&alpha;}}^{\left(k\right)})$

Wherein, s ^(k), μ ^(k)And α ^(k)Represent s respectively, μ and the α result after the k time iteration, s ^(k+1), μ ^(k+1)And α ^(k+1)Represent s respectively, μ and the α result after the k+1 time iteration, k is not more than 50 nonnegative integer,

The second derivative of function is asked in expression, The first order derivative of function is asked in expression;

(7h) initial value of weighting repeated factor β=0.5 and solution vector:

$\left(\begin{array}{c}{s}^{\left(0\right)}\\ {\mathrm{\&mu;}}^{\left(0\right)}\\ {\mathrm{\&alpha;}}^{\left(0\right)}\end{array}\right)=\left(\begin{array}{c}{\mathrm{\&Theta;}}^T\hat{x}\\ 0.95\&CenterDot;\mathrm{sgn}\left({\mathrm{\&Theta;}}^T\hat{x}\right)\&CenterDot;{\mathrm{\&Theta;}}^T\hat{x}+0.1\max (\mathrm{sgn}\left({\mathrm{\&Theta;}}^T\hat{x}\right)\&CenterDot;{\mathrm{\&Theta;}}^T\hat{x})\\ 1\end{array}\right)$

Wherein, max represents the maximal value of amount of orientation element, and sgn represents the positive and negative attribute of vector element:

(7i) bring initial value and weight factor into step (7g) and carry out interative computation, bring formula＜5 into up to the result with adjacent twice iteration the difference of subtracting each other is not more than 10 ^-3, this moment, the value of the s that obtains was formula＜1〉in the minimum l of s ¹Norm is separated, and jumps to step (7k); If, reach maximum iteration time 50, do not obtain optimum solution yet, execution in step (7j);

(7j) with final iteration result as initial value, weight factor is updated to original 2 times, iterations makes zero, and turns back to step (7i);

(7k) verify the minimum l of all trial image ¹Norm is separated the sparse property of s, and with s as the normalization target feature vector

Rarefaction representation in normalization background characteristics matrix Θ.

Images