CN102567994B - Infrared small target detection method based on angular point gaussian characteristic analysis - Google Patents

Abstract

An infrared small target detection method based on an angular point gaussian characteristic analysis comprises, according to Gaussian characteristics of infrared small target images, introducing the thought of angular point detection and drawing each interest point including the small targets; conducting threshold value segmentation on interest point areas by the OTSU method, and obtaining suspected targets; and analyzing the gaussian characteristics of each suspected target, and selecting suspected targets with the high gaussian characteristics as real targets. According to the infrared small target detection method, traditional dim target detection methods based on gray characteristics and scale characteristics are not directly used, instead, the target detection is conducted based on the space distribution characteristics of the small targets; singular points including targets are drawn through an angular point detection, and strong edge interference is effectively restrained; small targets under object background can be effectively detected, and detestability of small objects under complicated background is greatly improved.

Description

The infrared small target detection method of analyzing based on angle point Gaussian characteristics

Technical field

The invention belongs to the target identification technology in infrared search system, particularly a kind of infrared small target detection method of analyzing based on angle point Gaussian characteristics.

Background technology

Along with the development of target identification Detection Techniques, the operating distance of target detection requires more and more far away, and corresponding target is more and more less in the projection of infrared eye plane.Infrared imaging system operating distance can reach tens kilometers of kilometers even up to a hundred at present, and on infrared image, target shows as 3*3 pixel, is commonly referred to as infrared point target.The information of point target compares to general objective and will lack a lot, the noise spot that the temperature distributing disproportionation that adds atmosphere is even, the noise of detector itself etc. presents on image, also have the interference of complex background, these are surveyed all to the identification of Weak target and bring certain difficulty simultaneously.At present target detection can only the singularity in image judge by it conventionally, and it is a lot of to extract the method for isolated singular point, for example wavelet transformation, high-pass filtering, Local Entropy of Image, morphology tophat algorithm, Robinson's filtering etc.

But along with the research of infrared small object field of detecting is more and more extensive, background can relate to complicated atural object, sea clutter etc. conventionally, this signal to noise ratio (S/N ratio) for target detection requires also further to improve.Traditional method is difficult to reach the detection index of high s/n ratio under complex background.

The target detection image discussed is in the present invention the infrared image with Weak target under complex background, and its infrared image can be described as:

$\begin{array}{c}f(x,y)=f_T(x,y)+f_B(x,y)+n(x,y),\\ 1\≤i\≤M,1\≤j\≤N,\end{array}---\left(1\right)$

In formula: f _t(x, y) is Weak target image; f _b(x, y) is complex background image; N (x, y) is noise image; M, N are respectively width and the height of image.

Infrared target signal model is:

$f_T(x,y)=I_T(x,y)=\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{A}_{l}h(i,j,x_t,y_t),---\left(2\right)$

In formula: A _lbe target peak intensity, can think normal value within a short period of time; (x _t, y _t) be target pixel location; N is the number of target in image; H is point spread function (PSF).

For infrared small target, its point spread function can carry out modeling with dimensional Gaussian model.The sample size of the target image of hypotheses creation is m × m, and dimensional Gaussian model is as follows:

$\begin{array}{c}I(x,y)=I_{\max }\exp (-\frac{1}{2}[\frac{{(x-x_0)}^2}{{{\mathrm{\σ}}_x}^2}+\frac{{(y-y_0)}^2}{{{\mathrm{\σ}}_y}^2}\left]\right),\\ 1\≤x,y\≤m\end{array}---\left(3\right)$

In formula: I _maxtarget's center's gray-scale value, i.e. gray scale peak value; σ _xit is horizontal dispersion parameter; σ _yit is vertical dispersion parameter; (x ₀, y ₀) be target's center's coordinate.(x, y) is other pixel coordinates of sample.

Because the psf model of infrared small object is dimensional Gaussian model, therefore can differentiate suspected target region according to the correlativity of suspected target region and point spread function and whether have Weak target.

The subimage of getting suspected target region m × m size forms suspected target image I _t(i, j), wherein 1≤i, j≤m; Produce Gauss target sample I (i, j) according to little impact point diffusion model function.Judge the similarity of target image and target sample by the related coefficient of two matrixes, related coefficient is:

$\mathrm{\ρ}=\frac{\mathrm{Cov}(I,I_T)}{\sqrt{D\left(I\right)\·D\left(I_T\right)}},---\left(4\right)$

In formula: Cov (I, I _t) be I, I _tcovariance, D (I) and D (I _t) be respectively I, I _tvariance.

Using similarity as quantizating index, whether this index can to determine suspected target region be Weak target if being carried out to threshold operation.The extraction in suspected target region as can be seen here, and the estimation of suspected target Regional Gaussian target sample template is become to the key addressing this problem.

Summary of the invention

Infrared DIM-small Target Image under disturbing for complex background, the object of the present invention is to provide a kind of infrared small target detection method of analyzing based on angle point Gaussian characteristics, can effectively detect the Weak target under world background and urban background.

The technical solution that realizes the object of the invention is: a kind of infrared small target detection method of analyzing based on angle point Gaussian characteristics, and step is as follows:

The first step, extracts suspected target, by Harris operator, the half-tone information of image is detected, and obtains each angle point, using angle point as point of interest, uses maximum variance between clusters to carry out Threshold segmentation to point of interest region, obtains suspected target;

Second step, analyzes the Gaussian characteristics of each suspected target, estimates its corresponding Gauss's sample template according to suspected target region, taken the logarithm in dimensional Gaussian model equations both sides:

$\ln I(x,y)=\ln I_{\max }-\frac{1}{2}[\frac{{(x-x_0)}^2}{{{\mathrm{\σ}}_x}^2}+\frac{{(y-y_0)}^2}{{{\mathrm{\σ}}_y}^2}]$

Order:

$\left\{\begin{array}{c}Z=\ln I(x,y)\\ C=\ln I_{\max }-\frac{1}{2}(\frac{{x_0}^2}{{{\mathrm{\σ}}_x}^2}+\frac{{y_0}^2}{{{\mathrm{\σ}}_y}^2})\\ A_0=\frac{x_0}{{{\mathrm{\σ}}_x}^2}\\ A_1=\frac{1}{2{{\mathrm{\σ}}_x}^2}\\ B_0=\frac{y_0}{{{\mathrm{\σ}}_y}^2}\\ B_1=\frac{1}{2{{\mathrm{\σ}}_y}^2}\end{array}\right.$

Above formula is write and is done:

Z＝C+A ₀x+A ₁x ²+B ₀y+B ₁y ²

According to maximum likelihood estimate, make evaluated error Q get minimum value;

$Q=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(Z_i-C-A_{0}x-A_1{x}^2-B_{0}y-B_1{y^2}_i)}^2$

Get Q respectively about A, B, the partial derivative of C, and to make it be zero:

$\left\{\begin{array}{c}\frac{\∂Q}{\∂C}=-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)=0\\ \frac{\∂Q}{\∂A_0}=-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)x_i=0\\ \frac{\∂Q}{\∂A_1}=-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2){x_i}^2=0\\ \frac{\∂Q}{\∂B_0}=-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)y_i=0\\ \frac{\∂Q}{\∂B_1}=-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2){y_i}^2=0\end{array}\right.$

As calculated:

$\left[\begin{array}{c}C\\ A_0\\ A_1\\ B_0\\ B_1\end{array}\right]={\left[\begin{array}{ccccc}n& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^3& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^3& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^4& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^3\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^3& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^4\end{array}\right]}^1\×\left[\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^2{Z}_i\end{array}\right]$

Finally by A ₀, A ₁, B ₀, B ₁, the value of C calculates I _max, σ _x, σ _y, x ₀, y ₀estimated value, to determine Gauss's sample template in suspected target region;

The 3rd step, choose the suspected target with strong Gaussian characteristics as real goal, the similarity that goes out the suspected target region Gauss sample template corresponding with it according to Calculation of correlation factor judges whether target is real goal, and the determination methods whether existing for the suspected target region of N × N is:

$T_1=\left\{\begin{array}{cc}\mathrm{true}& |x_0-\frac{N+1}{2}|<1,|y_0-\frac{N+1}{2}|<1\\ \mathrm{false}& \mathrm{else}\end{array}\right.$

$T_2=\left\{\begin{array}{cc}\mathrm{true}& \mathrm{\&rho;}>{\mathrm{\&rho;}}_0\\ \mathrm{false}& \mathrm{else}\end{array}\right.$

In formula: (x ₀, y ₀) the maximum value coordinate of Gauss's sample; ρ ₀for relevance threshold, work as T ₁, T ₂be true time simultaneously, think that suspected target region exists real goal.

The present invention compared with prior art, its remarkable advantage: (1) not direct traditional detection method of small target based on gray feature and scale feature of use, but according to the spatial characteristics of Weak target, carry out the detection of target; (2), by the detection of angle point, extracted the singular point including target, and effectively suppressed the interference at strong edge; (3) behind near target area extraction singular point, judge target by the intensity profile characteristic in evaluating objects region and the similarity degree of Gaussian characteristics, can effectively detect the Weak target under surface feature background, greatly improve the detectability of Weak target under complex background.

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Brief description of the drawings

Fig. 1 is the infrared image that contains Weak target and corresponding angle point image.

Fig. 2 is the image in angle point region and corresponding suspected target region.

Fig. 3 is the present invention and the background class Weak target detection algorithm image after treatment cut apart based on maximum entropy.

Embodiment

The present invention is based on the infrared small target detection method that angle point Gaussian characteristics is analyzed, step is as follows:

The first step, extracts suspected target, by Harris operator, the half-tone information of image is detected, and obtains each angle point, using angle point as point of interest, uses maximum variance between clusters to carry out Threshold segmentation to point of interest region, obtains suspected target.Harris operator is directly to utilize the half-tone information of image to detect, and is widely used in the fields such as the identification of target detection, target and target following, and it utilizes the gray scale average rate of change in window to represent the angle point amount of window center.If window w produces the rate of gray level of a micro-displacement (x, y) on image in arbitrary pixel:

$\left\{\begin{array}{c}{E}_{x,y}=\underset{u,v}{\mathrm{\&Sigma;}}{w}_{u,v}{[I_{x+u,y+v}-I_{u,v}]}^2\\ =\underset{u,v}{\mathrm{\&Sigma;}}{w}_{u,v}{[x{I}_x+y{I}_y+O(x^2,y^2)]}^2\\ I_x=\frac{\&PartialD;I}{\&PartialD;x}=I\&CircleTimes;[-\mathrm{1,0,1}]\\ I_y=\frac{\&PartialD;I}{\&PartialD;y}=I\&CircleTimes;{[-\mathrm{1,0,1}]}^T\end{array}\right.---\left(5\right)$

In formula: I is input picture; U, v is the size of window w; O (x ², y ²) be higher order indefinite small.Saving dimensionless has:

The local autocorrelation matrix of this pixel of matrix M, is defined as:

$M=W\&CircleTimes;\left[\begin{array}{cc}{I_x}^2& I_x{I}_y\\ I_x{I}_y& {I_y}^2\end{array}\right]---\left(6\right)$

Wherein: W=exp ((x ²+ y ²))

Harris and Stephen propose to form angle point response function CRF with this determinant of a matrix det (M) and mark trace (M):

CRF＝det(M)-k(trace(M)) ² （7）

Wherein: k is by getting 0.04.

Harris angle point amount is almost nil in the response of gradation of image flat site; Be negative value in the fringe region response of image; Very large in the response of the point of crossing place of image border.By the calculating of angle point amount, can determine interested regional location in image, these positions comprise: the end points of the flex point of profile and image middle conductor in Weak target, image.Infrared image and angle point image corresponding to Fig. 1 (b) of Fig. 1 (a) for containing Weak target.

Determine in image behind suspected target position according to angle point amount again, need to extract suspected target region.Suppose (x, y) angular coordinate for extracting, in 9 × 9 neighborhoods of (x, y), all pixels carried out to following mode mark:

$\begin{array}{c}S(i,j)=\left\{\begin{array}{cc}1,& |I(i,j)-I_0|\&le;T\\ 0,& \mathrm{else}\end{array}\right.,\\ 1\&le;i,j\&le;9,\end{array}---\left(8\right)$

Wherein: I (i, j) is the gray-scale value of all pixels in 9 × 9 neighborhoods; I ₀for the gray-scale value of this regional center pixel;

T is gray scale segmentation threshold, adopts maximum variance between clusters to set in literary composition, and principle is as follows:

From the gray level feature of image, the gray level of establishing original-gray image is L, the picture that gray level is i

Vegetarian refreshments number is n _i, whole pixels of image are N, have:

$\begin{array}{cc}{p}_i=\frac{n_i}{N}& \underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{p}_i=1\end{array}---\left(9\right)$

Gray level is divided into two classes: c with given threshold t ₀=(0,1 ..., t) and c ₁=(t+1, t+2 ..., L-1).C ₀and c ₁

Probability of occurrence and the average of class are respectively:

$\left.\begin{array}{c}{\mathrm{\&omega;}}_0=\underset{i=0}{\overset{t}{\mathrm{\&Sigma;}}}{p}_i=\mathrm{\&omega;}\left(t\right)\\ {\mathrm{\&omega;}}_1=\underset{i=t+1}{\overset{L-1}{\mathrm{\&Sigma;}}}{p}_i=1-\mathrm{\&omega;}\left(t\right)\end{array}\right\}---\left(10\right)$

$\left.\begin{array}{c}{\mathrm{\&mu;}}_0=\underset{i=0}{\overset{t}{\mathrm{\&Sigma;}}}i{p}_i/{\mathrm{\&omega;}}_0=\mathrm{\&mu;}\left(t\right)/\mathrm{\&omega;}\left(t\right)\\ {\mathrm{\&mu;}}_1=\underset{i=t+1}{\overset{L-1}{\mathrm{\&Sigma;}}}i{p}_i/{\mathrm{\&omega;}}_1=\frac{{\mathrm{\&mu;}}_T\left(t\right)-\mathrm{\&mu;}\left(t\right)}{1-\mathrm{\&omega;}\left(t\right)}\end{array}\right\}---\left(11\right)$

Wherein $\mathrm{\&mu;}\left(t\right)=\underset{i=0}{\overset{t}{\mathrm{\&Sigma;}}}i{p}_i,{\mathrm{\&mu;}}_T\left(t\right)=\underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}i{p}_i$

C ₀and c ₁the variance of class:

$\left.\begin{array}{c}{\mathrm{\&sigma;}}_0^2=\underset{i=0}{\overset{t}{\mathrm{\&Sigma;}}}{(i-{\mathrm{\&mu;}}_0)}^2{p}_i/{\mathrm{\&omega;}}_0\\ {\mathrm{\&sigma;}}_1^2=\underset{i=t+1}{\overset{L-1}{\mathrm{\&Sigma;}}}{(i-{\mathrm{\&mu;}}_1)}^2{p}_i/{\mathrm{\&omega;}}_1\end{array}\right\}---\left(12\right)$

Inter-class variance is: ${\mathrm{\&sigma;}}_{\mathrm{\&omega;}}^2={\mathrm{\&omega;}}_0{\mathrm{\&sigma;}}_0^2+{\mathrm{\&omega;}}_1{\mathrm{\&sigma;}}_1^2;$ Class internal variance is: ${\mathrm{\&sigma;}}_B^2={\mathrm{\&omega;}}_0{\mathrm{\&omega;}}_1{({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_T)}^2;$ Population variance is: introduce the decision rule of equal value about t simultaneously: in the time that η (t) value is maximum, get corresponding t value as optimal threshold.

Then, calculate the centre of gravity place of suspected target according to the segmentation result of suspected target in neighborhood, account form is as follows:

$\left\{\begin{array}{c}{g}_x=\frac{\underset{i-1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j-1}{\overset{9}{\mathrm{\&Sigma;}}}i\&CenterDot;S(i,j)}{\underset{i-1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j-1}{\overset{9}{\mathrm{\&Sigma;}}}S(i,j)}-5\\ g_y=\frac{\underset{i-1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j-1}{\overset{9}{\mathrm{\&Sigma;}}}j\&CenterDot;S(i,j)}{\underset{i-1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j-1}{\overset{9}{\mathrm{\&Sigma;}}}S(i,j)}-5\end{array}\right.---\left(13\right)$

In formula: (g _x, g _y) be barycentric coordinates in neighborhood.

Again, use (x+gx, y+gy) to revise suspected target coordinate, and reuse formula (8) target area is cut apart again, obtain S (i, j).Estimate the size of 9 × 9 neighborhood internal objects according to S (i, j), concrete mode is as follows: taking the centre of neighbourhood as initial point, find the maximal value N that origin is offset relatively in the horizontal direction that in S (i, j), all values is 1 _x; Find the maximal value N that origin is offset relatively in the vertical direction that in S (i, j), all values is 1 _y, get max{N _x, N _yas the size N of target.Finally, in input picture, centered by (x+gx, y+gy), get the neighborhood of N × N size as suspected target region I _t(i, j), wherein 1≤i, j≤N.

Wherein, Fig. 2 (a) is first angle point image, and its corresponding suspected target area data is Fig. 2 (g); Fig. 2 (b) is second angle point image, and its corresponding suspected target area data is Fig. 2 (h); Fig. 2 (c) is the 3rd angle point image, its corresponding suspected target area data be Fig. 2 (i); Fig. 2 (d) is the 4th angle point image, and its corresponding suspected target area data is Fig. 2 (j); Fig. 2 (e) is the 5th angle point image, and its corresponding suspected target area data is Fig. 2 (k); Fig. 2 (f) is the 6th angle point image, and its corresponding suspected target area data is Fig. 2 (l).

Then, carry out Gauss's sample template and estimate to estimate its corresponding Gauss's sample template with target discrimination according to suspected target region, due to Gauss's template of Weak target as the formula (3), formula (3) both members is taken the logarithm:

$\ln I(x,y)=\ln I_{\max }-\frac{1}{2}[\frac{{(x-x_0)}^2}{{{\mathrm{\&sigma;}}_x}^2}+\frac{{(y-y_0)}^2}{{{\mathrm{\&sigma;}}_y}^2}]---\left(14\right)$

Order:

$\left\{\begin{array}{c}Z=\ln I(x,y)\\ C=\ln I_{\max }-\frac{1}{2}(\frac{{x_0}^2}{{{\mathrm{\&sigma;}}_x}^2}+\frac{{y_0}^2}{{{\mathrm{\&sigma;}}_y}^2})\\ A_0=\frac{x_0}{{{\mathrm{\&sigma;}}_x}^2}\\ A_1=\frac{1}{2{{\mathrm{\&sigma;}}_x}^2}\\ B_0=\frac{y_0}{{{\mathrm{\&sigma;}}_y}^2}\\ B_1=\frac{1}{2{{\mathrm{\&sigma;}}_y}^2}\end{array}\right.---\left(15\right)$

Formula (15) can be write and do:

Z＝C+A ₀x+A ₁x ²+B ₀y+B ₁y ² （16）

According to maximum likelihood estimate, make evaluated error Q get minimum value.

$Q=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(Z_i-C-A_{0}x-A_1{x}^2-B_{0}y-B_1{y^2}_i)}^2---\left(17\right)$

Get Q respectively about A, B, the partial derivative of C, and to make it be zero:

$\left\{\begin{array}{c}\frac{\&PartialD;Q}{\&PartialD;C}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)=0\\ \frac{\&PartialD;Q}{\&PartialD;A_0}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)x_i=0\\ \frac{\&PartialD;Q}{\&PartialD;A_1}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2){x_i}^2=0\\ \frac{\&PartialD;Q}{\&PartialD;B_0}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)y_i=0\\ \frac{\&PartialD;Q}{\&PartialD;B_1}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2){y_i}^2=0\end{array}\right.---\left(18\right)$

As calculated:

$\left[\begin{array}{c}C\\ A_0\\ A_1\\ B_0\\ B_1\end{array}\right]={\left[\begin{array}{ccccc}n& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^3& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^3& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^4& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^3\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^3& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^4\end{array}\right]}^1\&times;\left[\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2{Z}_i\end{array}\right]---\left(19\right)$

Finally by A ₀, A ₁, B ₀, B ₁, the value of C calculates I _max, σ _x, σ _y, x ₀, y ₀estimated value, to determine Gauss's sample template in suspected target region, the similarity that calculates the suspected target region Gauss sample template corresponding with it according to formula (4) judges whether target is real goal.The visible table 1 of design parameter of the estimation of Gauss's sample template in each suspected target region in Fig. 2, has very strong correlativity for real goal (a), (b), (c) with Gauss's sample template as seen by table 1; Compare and there is larger difference with real goal with the correlativity of Gauss's sample template for non-Corner region (e), (f), but not Corner region (d) compares more approaching with the correlativity of Gauss's sample template with real goal.This is that grey scale change is very smooth comparatively speaking, the horizontal dispersion parameter σ of the Gauss's sample template estimating like this due to (d) though for angle point region _xjust larger with vertical dispersion parameter, just higher with the correlativity in angle point region, approach the level of real goal, whether be real goal, so need extra basis for estimation if therefore only relying on correlativity to be difficult to judge.The suspected target region I extracting for real goal _t(i, j), 1≤i, the center of gravity of j≤N is in the center in this region, and the maximum value of its corresponding Gauss's sample template is positioned at the center of gravity place of target, therefore should meet the maximum value coordinate (x of its corresponding Gauss's sample template for real goal ₀, y ₀) be positioned near the center in suspected target region.Therefore the determination methods, whether existing for the suspected target region of N × N is:

$T_1=\left\{\begin{array}{cc}\mathrm{true}& |x_0-\frac{N+1}{2}|<1,|y_0-\frac{N+1}{2}|<1\\ \mathrm{false}& \mathrm{else}\end{array}\right.---\left(20\right)$

$T_2=\left\{\begin{array}{cc}\mathrm{true}& \mathrm{\&rho;}>{\mathrm{\&rho;}}_0\\ \mathrm{false}& \mathrm{else}\end{array}\right.$

In formula: (x ₀, y ₀) the maximum value coordinate of Gauss's sample; ρ ₀for relevance threshold, get 0.9 according to experiment; Work as T ₁, T ₂be true time simultaneously, think that suspected target region exists real goal.

In order to verify algorithm herein, from infrared video, intercept three width images, Fig. 3 (a) is the first width infrared image; Fig. 3 (b) is the second width infrared image; Fig. 3 (c) is the 3rd width infrared image.Wherein part target is flooded by complicated background substantially, and naked eyes are difficult to differentiate, and this three width image is processed according to algorithm described herein.Fig. 3 (d) is the image after Fig. 3 (a) extracts through angle point; Fig. 3 (e) is the image after Fig. 3 (b) extracts through angle point; Fig. 3 (f) is the image after Fig. 3 (c) extracts through angle point; Fig. 3 (g) is the net result of Fig. 3 (a) through obtaining after this paper algorithm process; Fig. 3 (h) is the net result of Fig. 3 (b) through obtaining after this paper algorithm process; Fig. 3 is (i) the net result of Fig. 3 (c) through obtaining after this paper algorithm process; Fig. 3 (j) uses the result after the background class Weak target detection algorithm of cutting apart based on maximum entropy for Fig. 3 (a); Fig. 3 (k) uses the result after the background class Weak target detection algorithm of cutting apart based on maximum entropy for Fig. 3 (b); Fig. 3 (l) uses the result after the background class Weak target detection algorithm of cutting apart based on maximum entropy for Fig. 3 (c); Fig. 3 (m) is for Fig. 3 (a) is by the target image extracting after wavelet multi-scale analysis; Fig. 3 (n) is for Fig. 3 (b) is by the target image extracting after wavelet multi-scale analysis; Fig. 3 (o) is for Fig. 3 (c) is by the target image extracting after wavelet multi-scale analysis.

After classifying by background complexity based on background class Weak target detection algorithm, background is divided into flat site and complex background two classes, be that two class background areas are set different segmentation thresholds and carried out Target Segmentation, if can find out, Threshold due to flat site is relatively low can extract little target effectively, but for complex background region, because the high segmentation threshold of background complexity is corresponding higher, if being just difficult to passing threshold style, the little target being more or less the same with background gray scale extracts.

Input picture is carried out multiple dimensioned decomposition by detection method of small target based on wavelet multi-scale analysis, by the subimage under different scale is merged, suppress the background component inconsistent with Weak target yardstick, the proportion of outstanding Weak target in fused images, but owing to there being the clutter that part is close with target scale to be detected in the complex background of ground, multiple dimensioned decomposition is difficult to suppress these clutters, therefore in last target image, also has part background component.

The estimated value of Gauss's sample template parameter in each suspected target region and suspected target and Gauss's template related coefficient in table 1 Fig. 2

Table1 Estimated parameters of Gaussian template and correlation coefficient of the images in Fig2

Claims (1)

1. an infrared small target detection method of analyzing based on angle point Gaussian characteristics, is characterized in that step is as follows:

The first step, extracts suspected target, by Harris operator, the half-tone information of image is detected, and obtains each angle point, using angle point as point of interest, uses maximum variance between clusters to carry out Threshold segmentation to point of interest region, obtains suspected target;

Second step, analyzes the Gaussian characteristics of each suspected target, estimates its corresponding Gauss's sample template according to suspected target region, taken the logarithm in dimensional Gaussian model equations both sides:

$\mathrm{InI}(x,y)={\ln I}_{\max }-\frac{1}{2}[\frac{{(x-x_0)}^2}{{{\mathrm{\&sigma;}}_x}^2}+\frac{{(y-y_0)}^2}{{{\mathrm{\&sigma;}}_y}^2}]$

Order:

$\left\{\begin{array}{c}Z=\ln I(x,y)\\ C={\ln I}_{\max }-\frac{1}{2}(\frac{{x_0}^2}{{{\mathrm{\&sigma;}}_x}^2}+\frac{{y_0}^2}{{{\mathrm{\&sigma;}}_y}^2})\\ A_0=\frac{x_0}{{{\mathrm{\&sigma;}}_x}^2}\\ A_1=-\frac{1}{{{2\mathrm{\&sigma;}}_x}^2}\\ B_0=\frac{y_0}{{{\mathrm{\&sigma;}}_y}^2}\\ B_1=-\frac{1}{{{2\mathrm{\&sigma;}}_y}^2}\end{array}\right.$

Above formula is write and is done:

Z＝C+A ₀x+A ₁x ²+B ₀y+B ₁y ²

According to maximum likelihood estimate, make evaluated error Q get minimum value;

$Q=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(Z_i-C-A_{0}x-A_1{x}^2-B_{0}y-B_1{y^2}_i)}^2$

Get Q respectively about A, B, the partial derivative of C, and to make it be zero:

$\left\{\begin{array}{c}\frac{\&PartialD;Q}{\&PartialD;C}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C{-A}_0{x}_i-A_1{x_i}^2{-B}_0{y}_i-B_1{y_i}^2)=0\\ \frac{\&PartialD;Q}{{\&PartialD;A}_0}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)x_i=0\\ \frac{\&PartialD;Q}{{\&PartialD;A}_1}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2){x_i}^2=0\\ \frac{\&PartialD;Q}{{\&PartialD;B}_0}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C{-A}_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2)y_i=0\\ \frac{\&PartialD;Q}{{\&PartialD;B}_1}=-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(Z_i-C-A_0{x}_i-A_1{x_i}^2-B_0{y}_i-B_1{y_i}^2){y_i}^2=0\end{array}\right.$

As calculated:

$\left[\begin{array}{c}C\\ A_0\\ A_1\\ B_0\\ B_1\end{array}\right]={\left[\begin{array}{ccccc}n& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^3& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^3& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^4& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y_i}^2\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^3\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^3& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^4\end{array}\right]}^1\&times;\left[\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{Z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2{Z}_i\end{array}\right]$

Finally by A ₀, A ₁, B ₀, B ₁, the value of C calculates I _max, σ _x, σ _y, x ₀, y ₀estimated value, to determine Gauss's sample template in suspected target region;

The 3rd step, choose the suspected target with strong Gaussian characteristics as real goal, the similarity that goes out the suspected target region Gauss sample template corresponding with it according to Calculation of correlation factor judges whether target is real goal, and the determination methods whether existing for the suspected target region of N × N is:

$T_1=\left\{\begin{array}{cc}\mathrm{true}& |x_0-\frac{N+1}{2}|<1,|y_0-\frac{N+1}{2}|<1\\ \mathrm{false}& \mathrm{else}\end{array}\right.$

$T_2=\left\{\begin{array}{cc}\mathrm{true}& \mathrm{\&rho;}>{\mathrm{\&rho;}}_0\\ \mathrm{false}& \mathrm{else}\end{array}\right.$

In formula: (x ₀, y ₀) the maximum value coordinate of Gauss's sample; ρ ₀for relevance threshold, work as T ₁, T ₂be true time simultaneously, think that suspected target region exists real goal;

In the first step:

(1) by Harris operator, the half-tone information of image is detected, utilize the gray scale average rate of change in window to represent the angle point amount of window center, if window w produces the rate of gray level of a micro-displacement (x, y) on image in arbitrary pixel:

$\left\{\begin{array}{c}{E}_{x,y}=\underset{u,v}{\mathrm{\&Sigma;}}{w}_{u,v}{[I_{x+u,y+v}-I_{u,v}]}^2\\ =\underset{u,v}{\mathrm{\&Sigma;}}{w}_{u,v}{[{\mathrm{xI}}_x+{\mathrm{yI}}_y+O(x^2,y^2)]}^2\\ I_x=\frac{\&PartialD;I}{\&PartialD;x}=I\&CircleTimes;[-\mathrm{1,0},1]\\ I_y=\frac{\&PartialD;I}{\&PartialD;y}=I\&CircleTimes;{[-\mathrm{1,0,1}]}^T\\ \end{array}\right.$

In formula: I is input picture; U, v is the size of window w; O (x ², y ²) be higher order indefinite small, saving dimensionless has: the local autocorrelation matrix of the pixel of matrix M window w, is defined as:

$M=W\&CircleTimes;\left[\begin{array}{cc}{I_x}^2& I_x{I}_y\\ I_x{I}_y& {I_y}^2\end{array}\right]$

Wherein: W=exp ((x ²+ y ²))

Form angle point response function CRF with this determinant of a matrix det (M) and mark trace (M):

CRF＝det(M)-k(trace(M)) ²

Wherein: k gets 0.04;

(2) determine in image behind suspected target position according to angle point amount again, suspected target region is extracted, suppose (x, y) angular coordinate for extracting, in 9 × 9 neighborhoods of (x, y), all pixels are carried out to following mode mark:

$\begin{array}{c}S(i,j)=\left\{\begin{array}{cc}1,& |I(i,j)-I_0|\&le;T\\ 0,& \mathrm{else}\end{array}\right.,\\ 1\&le;i,j\&le;9,\end{array}---\left(8\right)$

Wherein: I (i, j) is the gray-scale value that 9 × 9 neighborhood internal coordinates are (i, j) pixel; I ₀for the gray-scale value of this regional center pixel; T is gray scale segmentation threshold, adopts maximum variance between clusters to set T;

(3) according to the centre of gravity place of the segmentation result calculating suspected target of suspected target in neighborhood, account form is as follows:

$\left\{\begin{array}{c}{g}_x=\frac{\underset{i=1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{9}{\mathrm{\&Sigma;}}}i\&CenterDot;S(i,j)}{\underset{i=1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{9}{\mathrm{\&Sigma;}}}S(i,j)}-5\\ g_y=\frac{\underset{i=1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{9}{\mathrm{\&Sigma;}}}j\&CenterDot;S(i,j)}{\underset{i=1}{\overset{9}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{9}{\mathrm{\&Sigma;}}}S(i,j)}-5\end{array}\right.$

In formula: (g _x, g _y) be barycentric coordinates in neighborhood;

(4) use (x+g _x, y+g _y) revise suspected target coordinate, and reuse formula (8) target area is cut apart again, obtain S (i, j), estimate the size of 9 × 9 neighborhood internal objects according to S (i, j), concrete mode is as follows: taking the centre of neighbourhood as initial point, find the maximal value N that origin is offset relatively in the horizontal direction that in S (i, j), all values is 1 _x; Find the maximal value N that origin is offset relatively in the vertical direction that in S (i, j), all values is 1 _y, get max{N _x, N _yas the size N of target; Finally, in input picture with (x+g _x, y+g _y) centered by, get the neighborhood of N × N size as suspected target region I _t(i, j), wherein 1≤i, j≤9.