CN102779332A - Nonlinear-fitting infrared non-uniform correction method based on time-domain Kalman filtering correction - Google Patents

Abstract

The invention provides a nonlinear-fitting infrared non-uniform correction method based on time-domain Kalman filtering correction. The technical proposal is as follows: firstly, assuming that a response change curve of each array unit of an infrared focal plane detector is continuous on time, and using a high-order multi-parameter nonlinear polynomial to fit and describe the response change curve; secondly, acquiring a response output value of each array unit at four different temperature points, using a nonlinear equation solution method to determine a plurality of parameters in each array unit response expression; thirdly, using time-domain Kalmn filtering to carry out time-shift correction on each parameter in the response expression for solving a problem that the detector response shifts with the time, and acquiring an analysis expression of the response curves of the detector array unit; and finally, using the analysis expression to calculate the response output of each array unit of the detector under any time and any temperature conditions. The nonlinear-fitting infrared non-uniform correction method realizes the correction of inconsistent response of the detector and solves non-uniformity problem of the infrared image.

Description

The infrared nonuniformity correction method of the nonlinear fitting of time domain Kalman filtering correction

Technical field

The invention belongs to the Infrared images pre-processing technical field, relate to a kind of method of infrared image being carried out nonuniformity correction.

Background technology

The infrared image nonuniformity correction is a research direction in the image processing field.The fundamental purpose of infrared image nonuniformity correction is to utilize image processing means; Solve because fault in material, the stability of circuit and the restriction of integrated technique level; The inconsistent problem of the detector that causes output response makes the image after the correction be convenient to subsequent treatment.At present, the main method of infrared image nonuniformity correction can be divided into two types: based on the Temperature Scaling correction method of reference source with based on the adaptively correcting method of scene.The ultimate principle and the technical characterstic of these two class methods are following:

One, based on the Temperature Scaling bearing calibration of reference source

Temperature Scaling bearing calibration based on reference source mainly comprises single-point Temperature Scaling method, 2 Temperature Scaling methods and multi-point temp scaling method etc.The design philosophy of these class methods is: utilize reference source to infrared focal plane array even irradiance to be provided, the response output of each detector cells is measured, calculate correction parameter that there emerged a detector cells thus.

Two, based on the adaptively correcting method of scene

Self-adapting correction method based on scene mainly comprises time domain high-pass filtering method, neural network correction method, constant statistic law, linear filtering correction method and scene matching method etc.This type algorithm basic principle is that the data of gain coefficient and side-play amount are not to take from reference source, but all or part of estimation that comes from scene.

Heterogeneity is the build-in attribute of infrared focal plane detector, and in the ideal case, when the infrared focal plane array detector received even incident radiation, the signal value output of its each pixel should be in full accord; But in fact under the combined influence of the semiconductor material inhomogeneous (unevenness of impurity concentration, crystal defect, inner structure etc.) of making device, device duty, production process and extraneous input etc.; Its output amplitude is also inequality; So-called infrared image heterogeneity that Here it is (Non-Uniformity, NU).For the detector of simple scan mode, there is not the heterogeneity problem; Heterogeneity in the detector of linear array scanning mode is present in the linear array direction; And the heterogeneity of infrared focal plane detector is present on the whole focal plane; More be large-scale device, the heterogeneity problem is just more outstanding.This heterogeneity can cause the temperature resolution of system to descend, and the quality of target image is had a strong impact on, thereby limited its application aspect high-sensitivity detection.

Existing method for correcting image exists not enough when solving infrared image heterogeneity problem, mainly shows the following aspects:

Temperature Scaling bearing calibration based on reference source: correction parameter is changeless; And in fact, along with the variation of device working temperature and environment temperature, the duty of device can change; If also adopt the correction parameter that originally calculated to proofread and correct, will make the calibration result variation; Adaptively correcting method based on scene: be convenient to handle the infrared image that has moving target, and calculated amount is big, processing in real time needs advanced multiprocessor mechanism.

In sum, design is suitable for the engineering technology problem that the wide nonuniformity correction method of image range Project Realization, suitable is a urgent need solution to infrared image heterogeneity problem.Do not find the open research data of relevant this problem at present as yet.

Summary of the invention

The purpose of this invention is to provide a kind of infrared image nonuniformity correction method, solve the inconsistent image deterioration problem that causes of infrared focal plane detector output response.

Technical scheme is to suppose that at first the response change curve of each array element of infrared focal plane detector is continuous in time, adopts the non-linear polynomial expression of high-order multiparameter to carry out match and description to it; Gather the response output valve of four each array elements of different temperature points then, utilize the nonlinear equation method for solving to confirm a plurality of parameters in each array element response expression formula; The 3rd step utilized time domain Kalman filtering to float correction to responding when each parameter is carried out in the expression formula in order to solve explorer response drifting problem in time, obtained the analytic representation of detector array elements response curve; Utilize this analytic representation to calculate each array element response output of detector under the random time arbitrary temp condition at last, thereby realize, solve infrared image heterogeneity problem the inconsistent correction of explorer response.

Technical scheme of the present invention may further comprise the steps:

The first step: parameter estimation

Between 10 ℃ to 70 ℃ of infrared eye routine work temperature, select four not calibrated different temperature points T arbitrarily ₁, T ₂, T ₃, T ₄Infrared image, f _{I, j}(T ₁), f _{I, j}(T ₂), f _{I, j}(T ₃), f _{I, j}(T ₄) be respectively this four width of cloth infrared image gray values of pixel points, subscript i wherein, j remarked pixel point row and column, with its substitution formula one respectively, find the solution the explorer response equation:

$\left\{\begin{array}{c}\stackrel{\‾}{F}\left(T_1\right)=A_{i,j}\·{\left(f_{i,j}\left(T_1\right)\right)}^3+B_{i,j}\·{\left(f_{i,j}\left(T_1\right)\right)}^2+C_{i,j}\·\left(f_{i,j}\left(T_1\right)\right)+D_{\mathrm{ij}}\\ \stackrel{\‾}{F}\left(T_2\right)=A_{i,j}\·{\left(f_{i,j}\left(T_2\right)\right)}^3+B_{i,j}\·{\left(f_{i,j}\left(T_2\right)\right)}^2+C_{i,j}\·\left(f_{i,j}\left(T_2\right)\right)+D_{\mathrm{ij}}\\ \stackrel{\‾}{F}\left(T_3\right)=A_{i,j}\·{\left(f_{i,j}\left(T_3\right)\right)}^3+B_{i,j}\·{\left(f_{i,j}\left(T_3\right)\right)}^2+C_{i,j}\·\left(f_{i,j}\left(T_3\right)\right)+D_{\mathrm{ij}}\\ \stackrel{\‾}{F}\left(T_4\right)=A_{i,j}\·{\left(f_{i,j}\left(T_4\right)\right)}^3+B_{i,j}\·{\left(f_{i,j}\left(T_4\right)\right)}^2+C_{i,j}\left(f_{i,j}\left(T_4\right)\right)+D_{\mathrm{ij}}\end{array}\right.$ (formula one)

Wherein,

N=1,2,3,4 is above-mentioned four width of cloth infrared image gray averages, A _{I, j}, B _{I, j}, C _{I, j}, D _{I, j}Be each rank characterising parameter of nonlinear curve to be estimated.Utilize above-mentioned equation, solve A _{I, j}, B _{I, j}, C _{I, j}, D _{I, j}Estimated value, be designated as

Second step: realize proofreading and correct

Arbitrary temp is put the infrared image gray values of pixel points g that T needs correction down _{I, j}(T) the substitution formula two, obtain proofreading and correct back infrared image gray values of pixel points

Computing formula is following:

${\hat{g}}_{i,j}\left(T\right)={\hat{A}}_{i,j}\·{\left(g_{i,j}\left(T\right)\right)}^3+\·{\hat{B}}_{i,j}{\left(g_{i,j}\left(T\right)\right)}^2+{\hat{C}}_{i,j}\·\left(g_{i,j}\left(T\right)\right)+{\hat{D}}_{\mathrm{ij}}$ (formula two)

The 3rd step: time domain Kalman filtering correction

Infrared eye after the correction is after work a period of time; Focal plane arrays (FPA) output response can occur and produce the phenomenon of fluctuation with the work duration; Float when promptly heterogeneity taking place; The time appearance of floating have a strong impact on the detector operation performance; Therefore need float processing when carrying out to proofreading and correct back infrared image gray values of pixel points

; The explorer response parameter of curve is revised, and the present invention floats problem when utilizing time domain Kalman filtering correcting mode to solve.The concrete realization as follows:

The 1st step: when determining whether to carry out, value floats processing according to image NU (T) (Non-uniformity, non-uniformity), and definite α _kAnd β _kFloat factor values in the time of two, NU (T) value calculating method is shown in formula three:

$\mathrm{NU}\left(T\right)=\frac{\underset{i,j}{\mathrm{\Σ}}|{\hat{g}}_{i,j}\left(T\right)-\stackrel{\‾}{G}\left(T\right)|}{N\stackrel{\‾}{G}\left(T\right)}$ (formula three)

Wherein: <img file= " BDA00001867076300042.GIF " he= " 57 " img-content= " drawing " img-format= " tif " inline= " yes " orientation= " portrait " wi= " 101 " /> is the average of infrared image gray value <img file= " BDA00001867076300043.GIF " he= " 58 " img-content= " drawing " img-format= " tif " inline= " yes " orientation= " portrait " wi= " 133 " />; N is this infrared image number of pixels; < maths num= " 0004 " > <! [CDATA[< math > < mrow > < mover > < mi > G </ mi > < mo > &OverBar; </ mo > </ mover > < mrow > < mo > (</ mo > < mi > T </ mi > < mo >) </ mo > </ mrow > < mo >=</ mo > < mfrac > < mn > 1 </ mn > < mi > N </ mi > </ mfrac > < munder > < mi > &Sigma; </ mi > < mrow > < mi > i </ mi > < mo >; </ mo > < mi > j </ mi > </ mrow > </ munder > < msub > < mover > < mi > g </ mi > < mo > ^ </ mo > </ mover > < mrow > < mi > i </ mi > < mo >, </ mo > < mi > j </ mi > </ mrow > </ msub > < mrow > < mo > (</ mo > < mi > T </ mi > < mo >) </ mo > </ mrow > < mo >. </ mo > </ mrow > </ math >]] </maths>

Float processing in the time of need not carrying out when NU (T)≤3.0 ‰, then technical scheme finishes; As NU (T)＞3.0 ‰, get α _k=α ∈ [0.99,1], β _k=β ∈ [0.99,1], and float processing when carrying out; As NU (T)＞4.0 ‰, then make α _k=α ∈ [0.9,0.99], β _k=β ∈ [0.9,0.99], and float processing when carrying out; If the time floats greatlyyer,, make α promptly as NU (T)＞4.5 ‰ _k=α ∈ [0.8,0.9], β _k=β ∈ [0.8,0.9], and float processing when carrying out.

In time, floats to handle and is meant following the 2nd step to the 4th step:

The 2nd step: state equation and the observation equation of setting up Kalman filtering:

State equation: X _{I, j}(k+1)=Φ _kX _{I, j}(k)+M _k+ W _k(formula four)

Observation equation: Y _{I, j}(k)=H _kX _{I, j}(k)+V _k(formula five)

Wherein, k representes current time, and k+1 representes next constantly, k=0, and 1,2 ..., and k=0 floats the moment T of the infrared image of processing when obtaining carrying out; State vector X _{I, j}(k) be defined as

Represent k nonlinear curve characterising parameter constantly respectively,

${\mathrm{\&Phi;}}_k=\left[\begin{array}{cc}{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00001867076400012.png,HDA00001867076400021.png"\; state="\{\{state\}\}">k</figure-callout>}}& 0\\ 0& {\mathrm{\&beta;}}_k\end{array}\right]$ Be state-transition matrix, drive the noise average and be defined as $M_k=\left[\begin{array}{cc}1-{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00001867076400012.png,HDA00001867076400021.png"\; state="\{\{state\}\}">k</figure-callout>}}& 0\\ 0& 1-{\mathrm{\&beta;}}_k\end{array}\right]{\hat{X}}_{i,j}\left(0\right),$ Wherein

Y _{I, j}(k) represent the infrared image gray values of pixel points that k observes constantly,

Be observing matrix; W _kAnd V _kBe respectively noise, its covariance Q _kAnd R _kBe respectively;

$Q_k=\left[\begin{array}{cc}(1-{\mathrm{\&alpha;}}_k^2){\mathrm{\&sigma;}}_{\mathrm{\&alpha;}0}^2& 0\\ 0& (1-{\mathrm{\&beta;}}_k^2){\mathrm{\&sigma;}}_{\mathrm{\&beta;}0}^2\end{array}\right],$ $R_k={\mathrm{I\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="vk"\; filenames="HDA00001867076400012.png,HDA00001867076400021.png"\; state="\{\{state\}\}">vk</figure-callout>}}^2.$ (formula six)

Get according to practical experience ${\mathrm{\&sigma;}}_{\mathrm{\&alpha;}0}^2\&Element;\left[\mathrm{0.2,0.25}\right],$ ${\mathrm{\&sigma;}}_{\mathrm{\&beta;}0}^2\&Element;\left[\mathrm{0.05,0.1}\right],$ ${\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="vk"\; filenames="HDA00001867076400012.png,HDA00001867076400021.png"\; state="\{\{state\}\}">vk</figure-callout>}}^2\&Element;\left[\mathrm{0.05,0.1}\right].$

The 3rd step: with α _kAnd β _kThe state equation and the observation equation of value substitution Kalman filtering, iteration obtains final Filtering Estimation value

Promptly obtain

Be the revised nonlinear curve characterising parameter of process time domain Kalman filtering.

The 4th step: float correction during realization

In

substitution formula seven;

floated correction when carrying out, obtain the infrared image gray values of pixel points

of floating processing through out-of-date

${\hat{\hat{g}}}_{i,j}\left(T\right)=(1-{\mathrm{\&alpha;}}_k)\&CenterDot;{\hat{\hat{A}}}_{i,j}\left(k\right)\&CenterDot;\stackrel{\&OverBar;}{G}\left(T\right)+(1-{\mathrm{\&beta;}}_k)\&CenterDot;{\hat{\hat{B}}}_{i,j}\left(k\right)$ (formula seven)

Adopt the present invention can obtain following technique effect:

The present invention can reliablely and stablely realize the infrared image Nonuniformity Correction; Obviously improve because the inconsistent image non-uniform noise that causes of each pixel response of detector; Improve system temperature resolution, promote the image pretreatment quality, for follow-up image detection, identification, tracking provide the good data source.Infrared image nonuniformity correction method proposed by the invention has following apparent in view characteristics and advantage:

1. according to experimental result of the present invention and visible with the performance comparison result of other infrared image nonuniformity correction method commonly used: the present invention can overcome non-homogeneous interference of noise effectively; Have simple, accuracy rate is high, strong robustness, be easy to FPGA (Field Programmable Gate Array, field programmable gate array);

2. according to the first step of the present invention and second step, can characterize the nonlinearities change rule of infrared eye output response well, solve traditional bearing calibration and be difficult to handle infrared image correction problem near the filament saturation zone with temperature;

3. according to the 3rd step " time domain Kalman filtering correction " of the present invention; Float correction in the time of can dynamically accomplishing explorer response; Solved the infrared eye after the correction after work a period of time; Array output response produces the problem of fluctuation with the work duration, has greatly improved the scene adaptability of bearing calibration.

Description of drawings

Fig. 1 is a principle flow chart of the present invention;

The The simulation experiment result that Fig. 2 utilizes the present invention to carry out when being 20 ℃ of temperature spots;

The The simulation experiment result that Fig. 3 utilizes the present invention to carry out when being 50 ℃ of temperature spots;

Fig. 4 utilizes the present invention and two-point method to compare result of experiment;

Fig. 5 utilizes the present invention and stable state Kalman filtering method to compare result of experiment.

Embodiment

Below in conjunction with accompanying drawing the present invention is further specified.

The result that Fig. 2 to Fig. 5 experimentizes, horizontal ordinate is image frame number, and ordinate is a pictures different heterogeneity characterising parameter.When utilizing the first step of the present invention to carry out parameter estimation in the experiment, select four different temperature points T ₁, T ₂, T ₃, T ₄It is respectively 15 ℃, 25 ℃, 40 ℃, 55 ℃.Infrared image to temperature spot T needs down to proofread and correct is handled, and the value of temperature T is respectively 20 ℃, 50 ℃ and 40 ℃.

Fig. 2 (a) is 20 ℃ of temperature spot infrared image sequence gray scale mean square deviation change curves, and left side figure is result before proofreading and correct, and right figure proofreaies and correct the back result; Fig. 2 (b) is 20 ℃ of temperature spot infrared image sequence non-uniformity change curves, and left side figure is result before proofreading and correct, and right figure proofreaies and correct the back result; Can find out from experimental result; The present invention has tangible calibration result to the heterogeneity of 20 ℃ of temperature spot infrared images; The gradation of image mean square deviation is reduced to about 1.4 after the correction by about 171 before proofreading and correct; The image non-uniformity is by about 9.5 ‰ before proofreading and correct, and is reduced to about 0.14 ‰ after the correction, and the result has all proved validity of the present invention.

Fig. 3 (a) is 50 ℃ of temperature spot infrared image sequence gray scale mean square deviation change curves, and left side figure is result before proofreading and correct, and right figure proofreaies and correct the back result; Fig. 3 (b) is 50 ℃ of temperature spot infrared image sequence non-uniformity change curves, and left side figure is result before proofreading and correct, and right figure proofreaies and correct the back result; Can find out from experimental result; The present invention has tangible calibration result to the heterogeneity of 50 ℃ of temperature spot infrared images; The gradation of image mean square deviation is by the 1.3-2.0 that proofreaies and correct after preceding 384-385 is reduced to correction; The image non-uniformity is by 13.08 ‰-13.10 ‰ before proofreading and correct, and is reduced to 0.6 ‰-0.10 ‰ after the correction, and the result has all proved validity of the present invention.

Fig. 4 is for being directed against 50 ℃ of temperature spot infrared image sequences, and the calibration result comparison diagram of the present invention and two-point calibration correction method, the corresponding curve of the present invention are with "----" expression, and the corresponding curve of two-point calibration correction method is used "---" expression; Fig. 4 (a) is a gray scale mean square deviation change curve, and left side figure is a comparing result before proofreading and correct, and right figure proofreaies and correct the back comparing result; Fig. 4 (b) is the non-uniformity change curve, and left side figure is a comparing result before proofreading and correct, and right figure proofreaies and correct the back comparing result; Can find out from experimental result; Compare with the two-point calibration correction method of in the engineering practice process, extensively using; Calibration result of the present invention obviously is superior to the two-point calibration correction method; Two image non-uniform characterising parameters of gradation of image mean square deviation and non-uniformity are significantly less than two-point calibration method relevant parameters index, particularly under the situation near filament saturation, because the present invention has adopted the nonlinear fitting method to realize the estimation to the explorer response parameter; The problem of dtmf distortion DTMF of having avoided linear fit method to bring has guaranteed the robustness of calibration result.

Fig. 5 is for being directed against 40 ℃ of temperature spot infrared image sequences, and the calibration result comparison diagram of the present invention and the bearing calibration of stable state Kalman filtering, the corresponding curve of the present invention are with "----" expression, and the corresponding curve of stable state Kalman filtering bearing calibration is used "---" expression; Fig. 5 (a) is a gray scale mean square deviation change curve, and left side figure is a comparing result before proofreading and correct, and right figure proofreaies and correct the back comparing result; Fig. 5 (b) is the non-uniformity change curve, and left side figure is a comparing result before proofreading and correct, and right figure proofreaies and correct the back comparing result; Can find out from experimental result; With typically compare based on the infrared nonuniformity correction method-stable state Kalman filtering bearing calibration of scene; Utilize two evaluation indexes of gradation of image mean square deviation and non-uniformity to carry out the Nonuniformity Correction effect assessment; Because the present invention has made full use of the real time imagery characteristic, therefore obviously be superior to the stable state Kalman filtering method in correcting feature.

Claims (1)

1. the infrared nonuniformity correction method of the nonlinear fitting of time domain Kalman filtering correction is characterized in that, comprises the steps:

The first step: parameter estimation:

Between 10 ℃ to 70 ℃, select four not calibrated different temperature points T arbitrarily ₁, T ₂, T ₃, T ₄Infrared image, f _{I, j}(T ₁), f _{I, j}(T ₂), f _{I, j}(T ₃), f _{I, j}(T ₄) be respectively this four width of cloth infrared image gray values of pixel points, subscript i wherein, j remarked pixel point row and column, with its substitution formula one respectively, find the solution the explorer response equation:

$\left\{\begin{array}{c}\stackrel{\&OverBar;}{F}\left(T_1\right)=A_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_1\right)\right)}^3+B_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_1\right)\right)}^2+C_{i,j}\&CenterDot;\left(f_{i,j}\left(T_1\right)\right)+D_{\mathrm{ij}}\\ \stackrel{\&OverBar;}{F}\left(T_2\right)=A_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_2\right)\right)}^3+B_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_2\right)\right)}^2+C_{i,j}\&CenterDot;\left(f_{i,j}\left(T_2\right)\right)+D_{\mathrm{ij}}\\ \stackrel{\&OverBar;}{F}\left(T_3\right)=A_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_3\right)\right)}^3+B_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_3\right)\right)}^2+C_{i,j}\&CenterDot;\left(f_{i,j}\left(T_3\right)\right)+D_{\mathrm{ij}}\\ \stackrel{\&OverBar;}{F}\left(T_4\right)=A_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_4\right)\right)}^3+B_{i,j}\&CenterDot;{\left(f_{i,j}\left(T_4\right)\right)}^2+C_{i,j}\left(f_{i,j}\left(T_4\right)\right)+D_{\mathrm{ij}}\end{array}\right.$ (formula one)

In the following formula,

N=1,2,3,4 is above-mentioned four width of cloth infrared image gray averages, A _{I, j}, B _{I, j}, C _{I, j}, D _{I, j}Be each rank characterising parameter of nonlinear curve to be estimated; Utilize formula one, solve A _{I, j}, B _{I, j}, C _{I, j}, D _{I, j}Estimated value, be designated as

Second step: realize proofreading and correct:

Arbitrary temp is put the infrared image gray values of pixel points g that T needs correction down _{I, j}(T) the substitution formula two, obtain proofreading and correct back infrared image gray values of pixel points

${\hat{g}}_{i,j}\left(T\right)={\hat{A}}_{i,j}\&CenterDot;{\left(g_{i,j}\left(T\right)\right)}^3+\&CenterDot;{\hat{B}}_{i,j}{\left(g_{i,j}\left(T\right)\right)}^2+{\hat{C}}_{i,j}\&CenterDot;\left(g_{i,j}\left(T\right)\right)+{\hat{D}}_{\mathrm{ij}}$ (formula two)

The 3rd step: time domain Kalman filtering correction:

The 1st step: computed image NU (T):

$\mathrm{NU}\left(T\right)=\frac{\underset{i,j}{\mathrm{\&Sigma;}}|{\hat{g}}_{i,j}\left(T\right)-\stackrel{\&OverBar;}{G}\left(T\right)|}{N\stackrel{\&OverBar;}{G}\left(T\right)}$ (formula three)

Wherein: <img file= " FDA00001867076200017.GIF " he= " 58 " id= " ifm0007 " img-content= " drawing " img-format= " tif " inline= " yes " orientation= " portrait " wi= " 101 " /> is the average of infrared image gray value <img file= " FDA00001867076200018.GIF " he= " 59 " id= " ifm0008 " img-content= " drawing " img-format= " tif " inline= " yes " orientation= " portrait " wi= " 133 " />; N is this infrared image number of pixels; < maths num= " 0004 " > <! [CDATA[< math > < mrow > < mover > < mi > G </ mi > < mo > &OverBar; </ mo > </ mover > < mrow > < mo > (</ mo > < mi > T </ mi > < mo >) </ mo > </ mrow > < mo >=</ mo > < mfrac > < mn > 1 </ mn > < mi > N </ mi > </ mfrac > < munder > < mi > &Sigma; </ mi > < mrow > < mi > i </ mi > < mo >; </ mo > < mi > j </ mi > </ mrow > </ munder > < msub > < mover > < mi > g </ mi > < mo > ^ </ mo > </ mover > < mrow > < mi > i </ mi > < mo >, </ mo > < mi > j </ mi > </ mrow > </ msub > < mrow > < mo > (</ mo > < mi > T </ mi > < mo >) </ mo > </ mrow > < mo >; </ mo > </ mrow > </ math >]] > </maths>

Float processing in the time of need not carrying out when NU (T)≤3.0 ‰, then technical scheme finishes; As NU (T)＞3.0 ‰, get α _k=α ∈ [0.99,1], β _k=β ∈ [0.99,1], and float processing when carrying out; As NU (T)＞4.0 ‰, then make α _k=α ∈ [0.9,0.99], β _k=β ∈ [0.9,0.99], and float processing when carrying out; If the time floats greatlyyer,, make α promptly as NU (T)＞4.5 ‰ _k=α ∈ [0.8,0.9], β _k=β ∈ [0.8,0.9], and float processing when carrying out;

In time, floats to handle and is meant following the 2nd step to the 4th step:

The 2nd step: state equation and the observation equation of setting up Kalman filtering:

State equation: X _{I, j}(k+1)=Φ _kX _{I, j}(k)+M _k+ W _k(formula four)

Observation equation: Y _{I, j}(k)=H _kX _{I, j}(k)+V _k(formula five)

Wherein, k representes current time, and k+1 representes next constantly, k=0, and 1,2 ..., and k=0 floats the moment T of the infrared image of processing when obtaining carrying out; State vector X _{I, j}(k) be defined as

Represent k nonlinear curve characterising parameter constantly respectively,

${\mathrm{\&Phi;}}_k=\left[\begin{array}{cc}{\mathrm{\&alpha;}}_k& 0\\ 0& {\mathrm{\&beta;}}_k\end{array}\right]$ Be state-transition matrix, drive the noise average and be defined as $M_k=\left[\begin{array}{cc}1-{\mathrm{\&alpha;}}_k& 0\\ 0& 1-{\mathrm{\&beta;}}_k\end{array}\right]{\hat{X}}_{i,j}\left(0\right),$ Wherein

Y _{I, j}(k) represent the infrared image gray values of pixel points that k observes constantly,

Be observing matrix; W _kAnd V _kBe respectively noise, its covariance Q _kAnd R _kBe respectively;

$Q_k=\left[\begin{array}{cc}(1-{\mathrm{\&alpha;}}_k^2){\mathrm{\&sigma;}}_{\mathrm{\&alpha;}0}^2& 0\\ 0& (1-{\mathrm{\&beta;}}_k^2){\mathrm{\&sigma;}}_{\mathrm{\&beta;}0}^2\end{array}\right],$ $R_k={\mathrm{I\&sigma;}}_{\mathrm{vk}}^2;$ (formula six)

In the following formula, get ${\mathrm{\&sigma;}}_{\mathrm{\&alpha;}0}^2\&Element;\left[\mathrm{0.2,0.25}\right],$ ${\mathrm{\&sigma;}}_{\mathrm{\&beta;}0}^2\&Element;\left[\mathrm{0.05,0.1}\right],$ ${\mathrm{\&sigma;}}_{\mathrm{vk}}^2\&Element;\left[\mathrm{0.05,0.1}\right];$

The 3rd step: with α _kAnd β _kThe state equation and the observation equation of value substitution Kalman filtering, iteration obtains final Filtering Estimation value

Promptly obtain

Be the revised nonlinear curve characterising parameter of process time domain Kalman filtering;

The 4th step: float correction during realization:

In substitution formula seven; floated correction when carrying out, obtain the infrared image gray values of pixel points of floating processing through out-of-date

${\hat{\hat{g}}}_{i,j}\left(T\right)=(1-{\mathrm{\&alpha;}}_k)\&CenterDot;{\hat{\hat{A}}}_{i,j}\left(k\right)\&CenterDot;\stackrel{\&OverBar;}{G}\left(T\right)+(1-{\mathrm{\&beta;}}_k)\&CenterDot;{\hat{\hat{B}}}_{i,j}\left(k\right)$ (formula seven).

Images