CN102708382B - Multi-target tracking method based on variable processing windows and variable coordinate systems - Google Patents

Abstract

A multi-target tracking method based on variable processing windows and variable coordinate systems includes: step one, performing an initialization process; step two, constructing a space-time processing block for the k<th> frame image; step three, solving a position energy density of the space-time processing block constructed in the step two; step four, extracting position parameters of all targets in the k<th> frame image; step five, matching the target with the position parameter in each processing block to obtain a position observed value Z (k+1) of each target; step six, calculating target speed parameters with the Kalman filter algorithm with weighted gain to reduce calculated amount, amending the position observed value of each object, and strengthening accuracy and robustness of the tracking; and step seven, calculating the motion scale of each target in the k<th> frame image. According to the multi-target tracking method, the variable window, variable projection method and Kalman motion estimation are introduced on the basis of continuous wavelet transform and expectation maximization (EM) fitting algorithm, motion parameters are accurately extracted; and calculated amount is reduced; and accurate tracking of a plurality of motion targets is achieved.

Description

A kind of multi-object tracking method based on becoming processing window and change coordinate system

Technical field

The present invention relates to a kind of multi-object tracking method based on becoming processing window and change coordinate system, belong to machine vision and area of pattern recognition.Be specifically related to a kind of image-region in processing window be carried out to the spatio-temporal filtering based on continuous wavelet transform, then filtering result is become to coordinate system projection dimensionality reduction, and then from one dimension energy density curve, extract the kinematic parameter of target, finally realize the method to a plurality of motion target trackings.

Background technology

The basic problem of target following is exactly to estimate in real time, exactly the motion state of target according to observation data.Along with the development of modern navigation, aerospace cause, the research of target following technology has been subject to the great attention of every country.Be no matter at sea with air traffic control or in modern defense system, target following technology has all been brought into play very important effect.

Traditional motion target tracking method is the method based on characteristic matching mostly, such as the method in based target region, method based on profile etc.When clarification of objective information is easy to obtain, the method based on characteristic matching has reasonable effect, and reliability is higher.But if these features of tracked target are not obvious, such as lower in the contrast of target and background, under the scene such as target texture feature is less, and target is less; Or clarification of objective information changes in time at random, such as in the situations such as target size and attitude variation, the above-mentioned method based on characteristic matching does not just have good robustness.

The scholars such as Mujica have designed a kind of space time filter based on continuous wavelet transform, first with this wave filter, continuous some two field pictures are carried out to filtering operation, then filtering result is carried out to speed, position and the motion yardstick that maximum searching just can obtain target.Owing to not needing color and the Texture eigenvalue of target, this strategy can adapt to the not obvious and time dependent scene of target signature of target signature preferably, especially for little target following, has higher tracking accuracy and robustness.But, when a plurality of targets with similar movement feature mutually near time, the method can produce tracing deviation and even there will be trail-and-error.

For the problem in Mujica tracking, L.Hong has proposed a kind of improving one's methods to Mujica tracking.L.Hong thinks, the reason that causes Mujica tracking defect is when two targets are mutually close, the energy density detecting is the stack of a plurality of target energy density, so caused the position of energy density peak with the deviation of target physical location, and then caused and follow the tracks of inaccurate or even follow the tracks of unsuccessfully.For this problem L.Hong, propose should just to energy density, not carry out maximum searching when a plurality of targets are mutually close, and should first two-dimentional position energy density be projected to one dimension, then with EM algorithm, the position energy density of one dimension is carried out to matching, the average that EM algorithm obtains, as the position of target, is finally used the method realize target of data correlation and the coupling between parameter.

The interference problem when method that L.Hong proposes can solve gtoal setting to a certain extent, but also there is following defect:

1. for each target, design separately a processing window, this makes calculated amount follow target number to be linear positive relation, is unfavorable for real-time follow-up;

2. when a certain dimension coordinate value of a plurality of targets is close, this dimension coordinate value that EM matching obtains just has larger deviation, and this is easy to cause data correlation mistake, finally causes following the tracks of unsuccessfully;

3. while extracting the speed of target and direction of motion parameter, need first by wavelet transformation, obtain two-dimension speed energy density curved surface, this can make calculated amount increase sharply.

For above-mentioned three problems, the present invention has introduced respectively change processing window, becomes coordinate system projection and extracts the movement rate of target and the method for direction by Kalman filtering, has greatly reduced calculated amount, has improved accuracy, robustness and the real-time of following the tracks of.

Summary of the invention

1, object: the object of this invention is to provide a kind of multi-object tracking method based on becoming processing window and change coordinate system, it is on the basis of continuous wavelet transform, EM fitting algorithm, to introduce to become window, change projection pattern and Kalman's estimation, accurately extract the kinematic parameter of target, reduce calculated amount, realize to a plurality of moving targets exactly, follow the tracks of robust.

2, technical scheme: a kind of multi-object tracking method based on becoming processing window and change coordinate system of the present invention, the method concrete steps are as follows:

Step 1: initialization process;

Setup parameter k is as frame number index, the number of image frames of setting each space-time processing block is T, determine that the picture frame that wish in space-time processing block is followed the tracks of is τ (2≤τ≤T-1), and in the two field picture of initialization τ-1 position, speed, yardstick, the Kalman Filter Residuals covariance matrix of each target, average, variance and the weight of EM algorithm.

Step 2: be k two field picture structure space-time processing block;

Get k-(τ-1), k-(τ-1)+1 ..., k, k+1 ... k+ (T-τ) two field picture forms the video flowing of k two field picture, according to position and the speed of each target in k-1 two field picture, estimates the position of all targets in k two field picture:

$(x_1^k,y_1^k)=(x_1^{k-1},y_1^{k-1})+(v_{x_1}^{k-1},v_{y_1}^{k-1})$

$(x_2^k,y_2^k)=(x_2^{k-1},y_2^{k-1})+(v_{x_2}^{k-1},v_{y_2}^{k-1})$

$\begin{array}{c}......\\ (x_n^k,y_n^k)=(x_n^{k-1},y_n^{k-1})+(v_{x_n}^{k-1},v_{y_n}^{k-1})\end{array}$

Wherein: the target number of n for following the tracks of

Calculate the absolute value of the difference of the transverse and longitudinal coordinate between target i and target j:

dx _ij＝|x _i-x _j|

dy _ij＝|y _i-y _i|

Search the impact point m with label minimum ₁between distance satisfy condition

$\left\{\begin{array}{c}{\mathrm{dx}}_{m_1{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA00001627361700011.png"\; state="\{\{state\}\}">j</figure-callout>}}_1}<{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00001627361700011.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\\ {\mathrm{dy}}_{m_1{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA00001627361700011.png"\; state="\{\{state\}\}">j</figure-callout>}}_1}<{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00001627361700011.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\end{array}\right.,$ J ₁=1,2 ..., m ₁-1, m ₁all impact point (x of+1...n _j1, y _j1) form one set C ₁, impact point m ₁the central point that is called this set; Reject m ₁after, then from remaining source location, find out the impact point m of minimum label ₂, the width of setting processing window is d ₁, search with impact point m ₂between distance satisfy condition $\left\{\begin{array}{c}{\mathrm{dx}}_{m_2{j}_2}<{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00001627361700011.png"\; state="\{\{state\}\}">d</figure-callout>}}_1/2\\ {\mathrm{dy}}_{m_2{j}_2}<{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00001627361700011.png"\; state="\{\{state\}\}">d</figure-callout>}}_1/2\end{array}\right.,$ J ₂=1,2 ..., m ₂-1, m ₂all impact point (x of+1...n _j2, y _j2) form one set C ₂, impact point m ₂the central point that is called this set; For all impact points, all find one's own set by that analogy.On each two field picture in the video flowing of k two field picture, to gather centered by center position with d ₁for length of side intercepting processing window forms the space-time processing block of k two field picture, like this with regard to the individual space-time processing block of L (1≤L≤n) that has been n target formation.

Step 3: the position energy density of asking the space-time processing block of constructing in step 2;

By the motion yardstick a of target in k-1 two field picture _k-1, speed c _k-1with angle θ _k-1parameter substitution wavelet function ${\mathrm{\&psi;}}_w(\stackrel{\&RightArrow;}{\mathrm{\&xi;}},t)=a^{-\frac{3}{2}}\mathrm{\&psi;}(a^{-1}{c}^{-\frac{1}{3}}{r}^{-\mathrm{\&theta;}}(\stackrel{\&RightArrow;}{\mathrm{\&xi;}}-\stackrel{\&RightArrow;}{b}),a^{-1}{c}^{\frac{2}{3}}(t-\mathrm{\&tau;})),$ Wherein $r^{-\mathrm{\&theta;}}=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right],$

with this wavelet function, all space-time processing blocks of constructing in step 2 are carried out to the position energy density that continuous wavelet transform obtains all space-time processing blocks:

${\mathrm{\&epsiv;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1},\mathrm{\&tau;})}^{\left(1\right)}\left({\stackrel{\&RightArrow;}{b}}_k\right)=\frac{1}{{\left(a_{k-1}^{\mathrm{\&tau;}-1}\right)}^4}{|<{\mathrm{\&psi;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1},\mathrm{\&tau;})}|B_k>|}^2$

In formula, symbol description is as follows:

τ: the position of the two field picture that wish is followed the tracks of in space-time processing block, with the τ in step 1

A _k-1: the motion yardstick of target in k-1 two field picture

C _k-1: the speed of target in k-1 two field picture

θ _k-1: the angle of target in k-1 two field picture

the position coordinates of pixel

B _k: the space-time processing block of k two field picture

wavelet function

in k two field picture

the position energy density of position

use wavelet function

to space-time processing block B _kdo continuous wavelet transform.

Step 4: the location parameter that extracts all targets in k two field picture;

The two-dimensional position energy density obtaining in step 3 is carried out to projection dimensionality reduction, and with Nelder-Mead simplex search algorithm or EM algorithm, extracts the location parameter of target, according to the number of target in each processing block, be divided into following two kinds of situations:

1. if the target number m in image processing block _i=1, do not need projection dimensionality reduction, directly adopt the maximum position of Nelder-Mead simplex search algorithm search two dimension energy density as the location parameter of this target.

2. if the target number m in image processing block _i>=2, first to carry out One Dimensional Projection to two-dimentional position energy density, obtain the energy density of one dimension; Then calculate with the line of other any one target with the satisfy condition target number n of π/8, π/8≤θ≤3 of the angle theta of x axle ₁, and do not meet the target number n of this condition ₂=m _i-n ₁.Selective basis n for projecting direction ₁and n ₂magnitude relationship be divided into again two kinds of situations: a kind of situation is to work as n ₁>=n ₂time, to x Zhou He y axial projection, obtain the position energy density of x direction and the position energy density of y direction respectively, then utilize EM algorithm respectively the position energy density of the position energy density of x direction and y direction to be carried out to matching, obtain x coordinate figure and the y coordinate figure of all targets in this image block; Another kind of situation is to work as n ₁< n ₂time, need to first former rectangular coordinate system be rotated counterclockwise to π/4 and form new coordinate system; Then the x Zhou He y axial projection to new coordinate system by two-dimensional position energy density, then with EM algorithm, the position energy density of the position energy density of x direction under new coordinate system and y direction is carried out to matching, obtain the coordinate figure of target in new coordinate system (x ', y '); Finally by coordinate transform, ask (x ', y ') coordinate under former coordinate system

$\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{cc}\cos (\mathrm{\&pi;}/4)& -\sin (\mathrm{\&pi;}/4)\\ \sin (\mathrm{\&pi;}/4)& \cos (\mathrm{\&pi;}/4)\end{array}\right]\left[\begin{array}{c}{x}^{\&prime;}\\ y^{\&prime;}\end{array}\right].$

Step 5: realize target in each processing block with the coupling of location parameter, obtain the position detection value Z (k+1) of each target;

Take that to have two targets in processing block be example, the transverse and longitudinal coordinate parameters recording is x ₁, x ₂, y ₁, y ₂, have 4 kinds of possible combinations: (x ₁, y ₁), (x ₁, y ₂), (x ₂, y ₁), (x ₂, y ₂), as long as just these 4 location points can be distributed to 2 targets by the method for data correlation.Image block building method described in analytical procedure one is known, and a target may can obtain many groups position detection value of this target simultaneously in a plurality of set, for these targets, gets the mean value of its all observed readings.

Step 6: calculate target velocity parameter with the Kalman filtering algorithm of gain weighting, reduce calculated amount, and the position detection value of each target is revised, strengthen accuracy and the robustness of following the tracks of;

Suppose state vector be X (k)=| x _k, y _k, vx _k, vy _k| the state vector in k two field picture according to system equation estimating target first, in order to simplify, to calculate the present invention and adopt uniform rectilinear motion model, that is:

$X\left(k\right)=\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]X(k-1)+\left[\begin{array}{cccc}1/4& 0& 1/2& 0\\ 0& 1/4& 0& 1/2\\ 1/2& 0& 1& 0\\ 0& 1/2& 0& 1\end{array}\right]$

Can obtain thus the position prediction value X (k|k-1) of target in k two field picture, the predicted value obtaining in calculation procedure four is with the distance between observed reading according to following formula, judge the weight ρ gaining in Kalman filtering algorithm:

$\mathrm{\&rho;}=\left\{\begin{array}{cc}1& \mathrm{ifd}\&le;e\\ {\mathrm{\&rho;}}_1& \mathrm{ifd}>\mathrm{<figure-callout\; id="0"\; label="e"\; filenames="HDA00001627361700022.png,HDA00001627361700031.png"\; state="\{\{state\}\}">e</figure-callout>}\end{array}\right.$ 0 < ρ wherein ₁< 1

The kalman gain calculating is multiplied by gain weight as final gain substitution Kalman filtering fundamental equation, obtain final state vector value X (k), thus obtained the speed of target in k two field picture and to step 5 in the position detection value that obtains revise.

Step 7: the motion yardstick that calculates each target in k two field picture;

By the speed c of target in k two field picture _kwith angle θ _ksubstitution wavelet function ${\mathrm{\&psi;}}_w(\stackrel{\&RightArrow;}{\mathrm{\&xi;}},t)=a^{-\frac{3}{2}}\mathrm{\&psi;}(a^{-1}{c}^{-\frac{1}{3}}{r}^{-\mathrm{\&theta;}}(\stackrel{\&RightArrow;}{\mathrm{\&xi;}}-\stackrel{\&RightArrow;}{b}),a^{-1}{c}^{\frac{2}{3}}(t-\mathrm{\&tau;})),$ Wherein $r^{-\mathrm{\&theta;}}=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right],$

with this wavelet function, the space-time processing block of constructing in step 2 is carried out to the Scale energy density that continuous wavelet transform obtains one dimension:

${\mathrm{\&epsiv;}}_{(c_k,{\mathrm{\&theta;}}_k,\mathrm{\&tau;})}^{\left(2\right)}\left(a_k\right)=\frac{1}{{a_{\mathrm{<figure-callout\; id="4"\; label="k"\; filenames="HDA00001627361700022.png"\; state="\{\{state\}\}">k</figure-callout>}}}^4}{|<{\mathrm{\&psi;}}_{(a_k,c_k,{\mathrm{\&theta;}}_k,{\stackrel{\&RightArrow;}{b}}_k,\mathrm{\&tau;})}|B_k>|}^2$

In formula, symbol description is as follows:

τ: the position of the two field picture that wish is followed the tracks of in space-time processing block, with the τ in step 1

A _k: the motion yardstick of target in k two field picture

C _k: the speed of target in k two field picture

θ _k: the angle of target in k two field picture

the position coordinates of pixel

B _k: the space-time processing block of k two field picture

wavelet function

in k two field picture

the Scale energy density of position

use wavelet function

to space-time processing block B _kdo continuous wavelet transform.

For the processing block that only has a target, adopt the maximum position of Nelder-Mead simplex search algorithm search Scale energy density as the motion scale-value of this target; For the processing block that has a plurality of targets, the average obtaining with EM fitting algorithm, as the scale-value of target, then realizes the coupling between dimension measurement and target by the method for data correlation.

So far, in k two field picture, the position of target, kinematic parameter and scale parameter all obtain, and next will continue the target in subsequent frame to follow the tracks of, until follow the tracks of, finish.

3, advantage: a kind of multi-object tracking method based on becoming processing window and change coordinate system of the present invention, its advantage is:

1) with traditional method for tracking target based on characteristic matching, compare, the method is a kind of method that based target kinematic parameter extracts, Weak target and the unconspicuous target of feature are had to good tracking effect, and can adapt to well target sizes and attitude variation.

2) introduce change processing window, reduced the recruitment of the calculated amount brought because of increasing of target numbers.

3) introduce the mode that becomes projection dimensionality reduction, increased a certain dimension coordinate of a plurality of targets in same processing window measurement accuracy when identical.

4) speed of extracting target with wavelet transformation space time filter is compared with direction of motion, and Kalman filtering algorithm calculates speed and the direction of motion of target for the method, has greatly reduced calculated amount, has improved the real-time of target following.

5) be aided with the Kalman filtering algorithm of the weighting that gains, by judgement predicted value, with the error size between observed reading, change gain weight, strengthened accuracy and the robustness of target following.

Accompanying drawing explanation

Fig. 1: be multiple target tracking overall flow figure of the present invention

Fig. 2: do curvilinear motion with two circular targets that emulating image sequence simulation radius is all 5 pixels, have cross one another tracking results in motion process, dotted line is the actual motion track of two targets, the movement locus that solid line obtains for this tracking.Altogether emulation 100 two field pictures

Fig. 3: the position energy density of two targets of the 50th frame in the simulated experiment shown in Fig. 2, horizontal coordinate is two-dimensional position coordinate, vertically coordinate is position energy density values.

Fig. 4: the x oriented energy density that the two-dimentional energy density dimensionality reduction projection of Fig. 3 is obtained, and EM fitting result.Solid line is the x oriented energy densimetric curve obtaining after the projection of two-dimentional energy density dimensionality reduction, and dotted line is two single Gaussian curves that EM matching obtains, and adding star curve is two results after single Gaussian curve stack, i.e. matched curve.

Fig. 5: the y oriented energy density that the two-dimentional energy density dimensionality reduction projection of Fig. 3 is obtained, and EM fitting result.Solid line is the y oriented energy densimetric curve obtaining after the projection of two-dimentional energy density dimensionality reduction, and dotted line is two single Gaussian curves that EM matching obtains, and adding star curve is two results after single Gaussian curve stack, i.e. matched curve.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Fig. 1 is image sequence processing process overview flow chart of the present invention, and as shown in Figure 1, realization of the present invention comprises the steps:

Step 1: setup parameter k is as frame number index, the number of image frames of setting each space-time processing block is T, determine that the picture frame that wish in space-time processing block is followed the tracks of is τ (2≤τ≤T-1), and in the two field picture of initialization τ-1 position, speed, yardstick, the Kalman Filter Residuals covariance matrix of each target, average, variance and the weight of EM algorithm.

Step 2: be k two field picture structure space-time processing block, specific as follows:

Step 2-1: get k-(τ-1), k-(τ-1)+1, ..., k, k+1 ... k+ (T-τ) two field picture forms the video flowing of k two field picture, if not enough τ frame above, not enough part is supplemented by copying the 1st two field picture, if not enough T-τ frame below, not enough part is supplemented by copying last frame image.

Step 2-2: according to the position of all targets in the position of all targets in k-1 two field picture and velocity estimation k two field picture:

$(x_1^k,y_1^k)=(x_1^{k-1},y_1^{k-1})+(v_{x_1}^{k-1},v_{y_1}^{k-1})$

$(x_2^k,y_2^k)=(x_2^{k-1},y_2^{k-1})+(v_{x_2}^{k-1},v_{y_2}^{k-1})$

$\begin{array}{c}......\\ (x_n^k,y_n^k)=(x_n^{k-1},y_n^{k-1})+(v_{x_n}^{k-1},v_{y_n}^{k-1})\end{array}$

Wherein: the target number of n for following the tracks of

Step 2-3: the absolute value that calculates the difference of the transverse and longitudinal coordinate between target i and target j:

dx _ij＝|x _i-x _j|

dy _ij＝|y _i-y _j|

Step 2-4: the target m that searches label minimum ₁, search and satisfy condition

j ₁=1,2 ..., m ₁-1, m ₁all impact point (x of+1...n _j1, y _j1) form one set C ₁, by target m ₁position as the central point of this set;

Step 2-5: if all targets have all had own affiliated set, forward step: 2-7 to; Otherwise forward step 2-6 to.

Step 2-6: find the target that also there is no to distribute affiliated set, search the target m of label minimum in these targets ₂, search and satisfy condition

j ₂=1,2 ..., m ₂-1, m ₂all impact point (x of+1...n _j2, y _j2) form one set C ₂, by target m ₂position as the central point of this set, forward step 2-5 to;

Step 2-7: on each two field picture in the video flowing of k two field picture, to gather centered by center position with 2d ₁for length of side intercepting processing window, form the space-time processing block of all targets in k two field picture.

Step 3: by the motion yardstick a of target in k-1 two field picture _k-1, speed c _k-1with angle θ _k-1parameter substitution wavelet function ${\mathrm{\&psi;}}_w(\stackrel{\&RightArrow;}{\mathrm{\&xi;}},t)=a^{-\frac{3}{2}}\mathrm{\&psi;}(a^{-1}{c}^{-\frac{1}{3}}{r}^{-\mathrm{\&theta;}}(\stackrel{\&RightArrow;}{\mathrm{\&xi;}}-\stackrel{\&RightArrow;}{b}),a^{-1}{c}^{\frac{2}{3}}(t-\mathrm{\&tau;})),$ Wherein $r^{-\mathrm{\&theta;}}=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right],$

with this wavelet function, all space-time processing blocks of constructing in step 2 are carried out to the position energy density that continuous wavelet transform obtains all space-time processing blocks:

${\mathrm{\&epsiv;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1},\mathrm{\&tau;})}^{\left(1\right)}\left({\stackrel{\&RightArrow;}{b}}_k\right)=\frac{1}{{\left(a_{k-1}^{\mathrm{\&tau;}-1}\right)}^4}{|<{\mathrm{\&psi;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1},\mathrm{\&tau;})}|B_k>|}^2$

Step 4: extract the location parameter of all targets in k two field picture, specific as follows:

Step 4-1: calculate i the target number m in processing block _iif, m _i=1 forwards step 4-2 to; If m _i>=2 forward 4-3 to.

Step 4-2: adopt the maximum position (x, y) of Nelder-Mead simplex search algorithm search two dimension energy density, coordinate (x, y) is exactly the position detection value of this target, forwards step 4-4 to.

Step 4-3: two-dimentional energy density is projected to one dimension becoming under coordinate system, and by the observed reading of EM algorithm calculated target positions.

Step 4-3-1: predict the position (x (k|k-1), y (k|k-1)) of all targets in this processing block, and the line that calculates all target prodiction values is with the angle of x axle:

x(k|k-1)＝x(k-1)+v _x(k-1)

y(k|k-1)＝y(k-1)+v _y(k-1)

$\mathrm{\&theta;}=\arcsin \left(\frac{|y_1\left(k\right|k-1)-y_2\left(k\right|k-1)|}{(y_1\left(k\right|k-1)-y_2{\left(k\right|k-1))}^2+{(x_1\left(k\right|k-1)-x_2\left(k\right|k-1))}^2}\right)$

Calculating with the line of other any one target with the satisfy condition target number n of π/8, π/8≤θ≤3 of the angle theta of x axle ₁, and do not meet the target number n of this condition ₂=m _i-n ₁.If n ₁>=n ₂forward step 4-3-2 to; Otherwise forward 4-3-3 to.

Step 4-3-2: under former coordinate system, two-dimentional energy density is carried out to projection dimensionality reduction, and the position energy density of the position energy density of the x direction obtaining and y direction is carried out to the observed reading that EM matching obtains target location.Specific as follows:

Under former coordinate system, two-dimentional energy density is done to skew integration:

$\mathrm{\&epsiv;}{x}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1})}\left(x\right)=\underset{y}{\&Integral;}{\mathrm{\&epsiv;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1})}(x,y)\mathrm{dy}$

$\mathrm{\&epsiv;}{y}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1})}\left(y\right)=\underset{y}{\&Integral;}{\mathrm{\&epsiv;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1})}(x,y)\mathrm{dx}$

The position energy density of the position energy density of x direction and y direction is carried out to the observed reading that EM matching obtains target: E step, asks the mathematical expectation of complete data collection:

$Q(\mathrm{\&Theta;},{\mathrm{\&Theta;}}^{\left(t\right)})=E\left[l\left(\mathrm{\&theta;}\right)\right|{\mathrm{\&Theta;}}^{\left(t\right)}]=\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{P}^{\left(t\right)}\left(j\right|x)l\left(\mathrm{\&theta;}\right)$

$=\underset{x\&Element;L}{\mathrm{\&Sigma;}}\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{P}^{\left(t\right)}\left(j\right|x)h\left(x\right)\left[\ln (P_j-\frac{1}{2}\ln \left(2\mathrm{\&pi;}\right)-\ln \left({\mathrm{\&sigma;}}_j\right)-\frac{{(x-u_j)}^2}{{2\mathrm{\&sigma;}}_j^2})\right]$

M step: ask and make Q (Θ, Θ ^(t)) maximum parameter Θ:

$u_j=\frac{\underset{x\&Element;L}{\mathrm{\&Sigma;}}h\left(x\right)P^{\left(t\right)}\left(j\right|x)x}{\underset{x\&Element;L}{\mathrm{\&Sigma;}}h\left(x\right)P^{\left(t\right)}\left(j\right|x)}$

${\mathrm{\&sigma;}}_j^2=\frac{\underset{x\&Element;L}{\mathrm{\&Sigma;}}h\left(x\right)P^{\left(t\right)}\left(j\right|x){(x-u_j)}^2}{\underset{x\&Element;L}{\mathrm{\&Sigma;}}h\left(x\right)P^{\left(t\right)}\left(j\right|x)}$

$P_j=\frac{\underset{x\&Element;L}{\mathrm{\&Sigma;}}h\left(x\right)P^{\left(t\right)}\left(j\right|x)}{\underset{x\&Element;L}{\mathrm{\&Sigma;}}h\left(x\right)}$

Wherein: $P^{\left(t\right)}\left(j\right|x)=\frac{P^{\left(t\right)}\left(x\right|j)P_j^{\left(t\right)}}{\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{P}^{\left(t\right)}\left(x\right|j)P_j^{\left(t\right)}}$

E step and M step replace calculating until meet the condition of iteration stopping, the u that last iteration obtains _jbe the position detection value Z (k) recording, forward step 5 to.

Step 4-3-3: first former coordinate system is rotated counterclockwise to π/4 and then under new coordinate system, two-dimentional energy density is done to skew integration:

${\mathrm{\&epsiv;x}}_{\left(a_{k-1}{c}_{k-1}{\mathrm{\&theta;}}_{k-1}\right)}^{\&prime;}\left(x^{\&prime;}\right)=\underset{y}{\&Integral;}{\mathrm{\&epsiv;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1})}(x^{\&prime;},y^{\&prime;}){\mathrm{dy}}^{\&prime;}$

${\mathrm{\&epsiv;y}}_{\left(a_{k-1}{c}_{k-1}{\mathrm{\&theta;}}_{k-1}\right)}^{\&prime;}\left(y^{\&prime;}\right)=\underset{x}{\&Integral;}{\mathrm{\&epsiv;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1})}(x^{\&prime;},y^{\&prime;}){\mathrm{dx}}^{\&prime;}$

With the EM algorithmic formula in step 4-3-2, the position energy density of the position energy density of x ' direction and x ' direction is carried out to matching, obtain position detection value Z ' in new coordinate system (k).Then calculate the position detection value Z (k) in the coordinate system before rotation:

$Z\left(k\right)=\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{cc}\cos (\mathrm{\&pi;}/4)& -\sin (\mathrm{\&pi;}/4)\\ \sin (\mathrm{\&pi;}/4)& \cos (\mathrm{\&pi;}/4)\end{array}\right]\left[\begin{array}{c}{x}^{\&prime;}\\ y^{\&prime;}\end{array}\right].$

Forward step 5 to.

Step 5: by the coupling of overall arest neighbors data correlation (GNN) method realize target and observed reading, specific as follows.

Step 5-1: supposing has m in i processing window _iindividual target, can obtain m _i* m _iindividual observed reading, calculates respectively the predicted value (x of v observed reading and u target _u(k|k-1), y _u(k|k-1) distance)

$d_{\mathrm{uv}}(u=\mathrm{1,2}...m_i,v=\mathrm{1,2}...m_i^2).$

Step 5-2: set a thresholding G, d satisfies condition _uvall d of < G _uvform the set C that likely follows u object matching _u, search for respectively each set C _uminimum value

if all have v for all l _u≠ v _l(l ≠ u), by v _uindividual observed reading is mated to u target; Otherwise execution step 4-5-3 mates again to u target and l target.

Step 5-3: search set C _usub-minimum with set C _isub-minimum

if

by v ' _uindividual observed reading is distributed to u target, by v _lindividual observed reading is distributed to l target; Otherwise, by v _uindividual observed reading is distributed to u target, by v ' _iindividual observed reading is distributed to l target.

Step 5-4: if all processing blocks have all been realized the extraction and associated coupling of observed reading, perform step six, otherwise forward step 4-1 to.

Step 6: speed and the angle of the Kalman filtering algorithm estimating target of use gain weighting in k two field picture, and position observed reading is revised, specific as follows:

Step 6-1:

Set condition vector is X (k)=[x _k, y _k, vx _k, vy _k] ', be the state vector in k two field picture according to system equation estimating target first:

$X\left(k\right|k-1)=\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]X(k-1)+\left[\begin{array}{cccc}1/4& 0& 1/2& 0\\ 0& 1/4& 0& 1/2\\ 1/2& 0& 1& 0\\ 0& 1/2& 0& 1\end{array}\right]$

Step 6-2: calculate predicted value and follow the distance between observed reading:

$d=\sqrt{(Z_x\left(k\right)-X_x{\left(k\right|k-1))}^2+{(Z_y\left(k\right)-X_y\left(k\right|k-1))}^2}.$

The weight ρ of the gain of computer card Kalman Filtering:

0 < ρ wherein ₁< 1.

Step 6-3: according to the final measured value of following formula computing mode vector:

Error covariance predictive equation: P (k|k-1)=AP (k-1) A '+Q

Wherein $A=\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right],$ $Q=\left[\begin{array}{cccc}1/4& 0& 1/2& 0\\ 0& 1/4& 0& 1/2\\ 1/2& 0& 1& 0\\ 0& 1/2& 0& 1\end{array}\right]$

Kalman gain equation: K=P (k|k-1) H ' (HP (k|k-1) H '+R) ^-1, wherein $H=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]$

State revision equation: X (k)=X (k|k-1)+ρ K (Z (k)-HX (k|k-1))

Error covariance update equation: P (k)=(I-ρ KH) P (k|k-1)

So far obtained position and the speed of all targets in k two field picture.

Step 7: the motion yardstick that calculates all targets in k two field picture.

Step 7-1: by the speed c of target in k two field picture _kwith angle θ _kparameter substitution wavelet function ${\mathrm{\&psi;}}_w(\stackrel{\&RightArrow;}{\mathrm{\&xi;}},t)=a^{-\frac{3}{2}}\mathrm{\&psi;}(a^{-1}{c}^{-\frac{1}{3}}{r}^{-\mathrm{\&theta;}}(\stackrel{\&RightArrow;}{\mathrm{\&xi;}}-\stackrel{\&RightArrow;}{b}),a^{-1}{c}^{\frac{2}{3}}(t-\mathrm{\&tau;})),$ Wherein $r^{-\mathrm{\&theta;}}=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right],$

with this wavelet function, the space-time processing block of constructing in step 2 is carried out to the Scale energy density that continuous wavelet transform obtains one dimension:

${\mathrm{\&epsiv;}}_{(c_k,{\mathrm{\&theta;}}_k,\mathrm{\&tau;})}^{\left(2\right)}\left(a_k\right)=\frac{1}{{a_{\mathrm{<figure-callout\; id="4"\; label="k"\; filenames="HDA00001627361700022.png"\; state="\{\{state\}\}">k</figure-callout>}}}^4}\underset{{\stackrel{\&RightArrow;}{b}}_k\&Element;\mathrm{\&Phi;}}{\mathrm{\&Sigma;}}{|<{\mathrm{\&psi;}}_{(a_k,c_k,{\mathrm{\&theta;}}_k,{\stackrel{\&RightArrow;}{b}}_k,\mathrm{\&tau;})}|B_k>|}^2$

If only have a target in i image block, forward step 7-2 to, otherwise forward step 7-3 to.

Step 7-2: adopt the maximum position of Nelder-Mead simplex search algorithm search Scale energy density, as the motion scale-value of this target.Forward step 7-5 to.

Step 7-3: with EM algorithm, Scale energy density is carried out to matching, the average obtaining is as the measured value of the scale-value of target.

Step 7-4: with overall arest neighbors data correlation (GNN) algorithm by m _iindividual dimension measurement is distributed to m _iindividual target.

Step 7-5: do not finish if follow the tracks of, k is increased to 1 and forward step 2 to.

Embodiment

Embodiment adopts emulating image sequence, and radius is all that two circular targets of 5 pixels are done curvilinear motion, and in motion process, two targets are intersected, altogether emulation 100 frames.

The motion target tracking result of the 45th frame to the 55 frames is as shown in the table:

Frame number	45	46	47	48	49	50	51	52	53	54	55
												Target 1 actual coordinate x1	246.25	246.38	246.55	246.75	247.00	247.24	247.53	247.85	248.20	248.59	249.00
The x1 that tracking obtains	247.00	246.76	246.84	246.76	246.71	247.03	247.21	247.36	247.46	247.98	248.35
												Target 1 actual coordinate y1	214.00	217.49	220.99	224.48	228.00	231.47	235.00	238.44	241.92	245.40	248.88
The y1 that tracking obtains	211.33	215.03	218.88	222.34	226.03	229.52	232.73	236.13	239.76	243.13	246.56
												Target 2 actual coordinate x2	267.38	267.30	267.20	267.06	266.89	266.69	266.46	266.20	265.91	265.59	265.24
The x2 that tracking obtains	266.20	226.19	266.47	266.32	266.14	266.28	266.01	265.74	265.51	265.61	265.22
												Target 2 actual coordinate y2	195.58	199.08	202.57	206.07	209.57	213.06	216.55	220.04	223.53	227.02	230.50
The y2 that tracking obtains	194.25	197.58	201.14	204.60	208.25	211.68	215.00	218.35	221.83	225.09	228.68

Fig. 2 is this embodiment actual path and pursuit path figure, and dotted line is two target actual motion tracks, the movement locus that solid line obtains for this tracking.

Fig. 3 is the position energy density of two targets of the 50th frame, and horizontal coordinate is two-dimensional position coordinate, and vertically coordinate is position energy density values.

Fig. 4 is the x oriented energy density obtaining after the two-dimentional energy density dimensionality reduction projection of Fig. 3, and EM fitting result.Solid line is the x oriented energy densimetric curve obtaining after the projection of two-dimentional energy density dimensionality reduction, and dotted line is two single Gaussian curves that EM matching obtains, and adding star curve is two results after single Gaussian curve stack, i.e. matched curve.

Fig. 5 is the y oriented energy density obtaining after the two-dimentional energy density dimensionality reduction projection of Fig. 3, and EM fitting result.Solid line is the y oriented energy densimetric curve obtaining after the projection of two-dimentional energy density dimensionality reduction, and dotted line is two single Gaussian curves that EM matching obtains, and adding star curve is two results after single Gaussian curve stack, i.e. matched curve.

The above, be only preferred embodiment of the present invention, is not intended to limit protection scope of the present invention.

Claims (1)

1. based on becoming processing window and a multi-object tracking method that becomes coordinate system, it is characterized in that: the method concrete steps are as follows:

Step 1: initialization process;

Setup parameter k is as frame number index, and image block building method is: the number of image frames of setting each space-time processing block is T, determine that the picture frame that wish in space-time processing block is followed the tracks of is τ, and in the two field picture of initialization τ-1 position, speed, yardstick, the Kalman Filter Residuals covariance matrix of each target, average, variance and the weight of EM algorithm; Wherein, 2≤τ≤T-1;

Step 2: be k two field picture structure space-time processing block;

Get k-(τ-1), k-(τ-1)+1 ..., k, k+1 ... k+ (T-τ) two field picture forms the video flowing of k two field picture, according to position and the speed of each target in k-1 two field picture, estimates the position of all targets in k two field picture:

$(x_1^k,y_1^k)=(x_1^{k-1},y_1^{k-1})+(v_{x_1}^{k-1},v_{y_1}^{k-1})$

$(x_2^k,y_2^k)=(x_2^{k-1},y_2^{k-1})+(v_{x_2}^{k-1},v_{y_2}^{k-1})$

......

$(x_n^k,y_n^k)=(x_n^{k-1},y_n^{k-1})+(v_{x_n}^{k-1},v_{y_n}^{k-1})$

Wherein: the target number of n for following the tracks of,

Calculate the absolute value of the difference of the transverse and longitudinal coordinate between target i and target j:

dx _ij=|x _i-x _j|

dy _ij=|y _i-y _j|

Search the impact point m with label minimum ₁between distance satisfy condition $\left\{\begin{array}{c}{\mathrm{dx}}_{m_2{j}_2}<d_1/2\\ {\mathrm{dy}}_{m_2{j}_2}<d_1/2\end{array}\right.,$ J ₁=1,2 ..., m ₁-1, m ₁all impact point (x of+1...n _j1, y _j1) form one set C ₁, impact point m ₁the central point that is called this set; Reject m ₁after, then from remaining source location, find out the impact point m of minimum label ₂, the width of setting processing window is d ₁, search with impact point m ₂between distance satisfy condition $\left\{\begin{array}{c}{\mathrm{dx}}_{m_2{j}_2}<d_1/2\\ {\mathrm{dy}}_{m_2{j}_2}<d_1/2\end{array}\right.,$ J ₂=1,2 ..., m ₂-1, m ₂all impact point (x of+1...n _j2, y _j2) form one set C ₂, impact point m ₂the central point that is called this set; For all impact points, all find one's own set by that analogy; On each two field picture in the video flowing of k two field picture, to gather centered by center position with d ₁for length of side intercepting processing window forms the space-time processing block of k two field picture, like this with regard to L the space-time processing block that be n target formation; Wherein, 1≤L≤n;

Step 3: the position energy density of asking the space-time processing block of constructing in step 2;

By the motion yardstick a of target in k-1 two field picture _k-1, speed c _k-1with angle θ _k-1parameter substitution wavelet function ${\mathrm{\&psi;}}_w(\stackrel{\&RightArrow;}{\mathrm{\&xi;}},t)=a^{-\frac{3}{2}}\mathrm{\&psi;}(a^{-1}{c}^{-\frac{1}{3}}{r}^{-\mathrm{\&theta;}}(\stackrel{\&RightArrow;}{\mathrm{\&xi;}}-\stackrel{\&RightArrow;}{b}),a^{-1}{c}^{\frac{2}{3}}(t-\mathrm{\&tau;})),$ Wherein $r^{-\mathrm{\&theta;}}=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right],$ $\stackrel{\&RightArrow;}{b}=(b_x,b_y),$ With this wavelet function, all space-time processing blocks of constructing in step 2 are carried out to the position energy density that continuous wavelet transform obtains all space-time processing blocks:

${\mathrm{\&epsiv;}}_{(a_{k-1},c_{k-1,{\mathrm{\&theta;}}_{k-1},\mathrm{\&tau;}})}^{\left(1\right)}\left({\stackrel{\&RightArrow;}{b}}_k\right)=\frac{1}{{\left(a_{k-1}^{\mathrm{\&tau;}-1}\right)}^4}{|<{\mathrm{\&psi;}}_{(a_{k-1},c_{k-1},{\mathrm{\&theta;}}_{k-1},\mathrm{\&tau;})}{|B}_k>|}^2$

In formula, symbol description is as follows:

τ: the position of the two field picture that wish is followed the tracks of in space-time processing block, with the τ in step 1

A _k-1: the motion yardstick of target in k-1 two field picture

C _k-1: the speed of target in k-1 two field picture

θ _k-1: the angle of target in k-1 two field picture

the position coordinates of pixel

B _k: the space-time processing block of k two field picture

wavelet function

in k two field picture

the position energy density of position

use wavelet function to space-time processing block B _kdo continuous wavelet transform;

Step 4: the location parameter that extracts all targets in k two field picture;

The two-dimensional position energy density obtaining in step 3 is carried out to projection dimensionality reduction, and with Nelder – Mead simplex search algorithm or EM algorithm, extracts the location parameter of target, according to the number of target in each processing block, be divided into following two kinds of situations:

1. if the target number m in image processing block _i=1, do not need projection dimensionality reduction, directly adopt the maximum position of Nelder – Mead simplex search algorithm search two dimension energy density as the location parameter of this target;

2. if the target number m in image processing block _i>=2, first to carry out One Dimensional Projection to two-dimentional position energy density, obtain the energy density of one dimension; Then calculate with the line of other any one target with the satisfy condition target number n of π/8, π/8≤θ≤3 of the angle theta of x axle ₁, and do not meet the target number n of this condition ₂=m _i-n ₁; Selective basis n for projecting direction ₁and n ₂magnitude relationship be divided into again two kinds of situations: a kind of situation is to work as n ₁>=n ₂time, to x Zhou He y axial projection, obtain the position energy density of x direction and the position energy density of y direction respectively, then utilize EM algorithm respectively the position energy density of the position energy density of x direction and y direction to be carried out to matching, obtain x coordinate figure and the y coordinate figure of all targets in this image block; Another kind of situation is to work as n ₁<n ₂time, need to first former rectangular coordinate system be rotated counterclockwise to π/4 and form new coordinate system, x Zhou He y axial projection by from two-dimensional position energy density to new coordinate system, then with EM algorithm, the position energy density of the position energy density of x direction under new coordinate system and y direction is carried out to matching, obtain the coordinate figure of target in new coordinate system (x ', y '); Finally by coordinate transform, ask (x ', y ') coordinate under former coordinate system

$\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{cc}\cos (\mathrm{\&pi;}/4)& -\sin (\mathrm{\&pi;}/4)\\ \sin (\mathrm{\&pi;}/4)& \cos (\mathrm{\&pi;}/4)\end{array}\right]\left[\begin{array}{c}{x}^{,}\\ y^{,}\end{array}\right];$

Step 5: realize target in each processing block with the coupling of location parameter, obtain the position detection value Z (k+1) of each target;

The transverse and longitudinal coordinate parameters recording is x ₁, x ₂, y ₁, y ₂, have 4 kinds of possible combinations: (x ₁, y ₁), (x ₁, y ₂), (x ₂, y ₁), (x ₂, y ₂), as long as just these 4 location points are distributed to 2 targets by the method for data correlation; Image block building method described in analytical procedure one is known, and a target may can obtain many groups position detection value of this target simultaneously in a plurality of set, for these targets, gets the mean value of its all observed readings;

Step 6: calculate target velocity parameter with the Kalman filtering algorithm of gain weighting, reduce calculated amount, and the position detection value of each target is revised, strengthen accuracy and the robustness of following the tracks of;

Suppose that state vector is X (k)=[x _k, y _k, vx _k, vy _k] ', be the state vector in k two field picture according to system equation estimating target first, adopts uniform rectilinear motion model, that is: in order to simplify to calculate

$X\left(k\right)=\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]X(k-1)+\left[\begin{array}{cccc}1/4& 0& 1/2& 0\\ 0& 1/4& 0& 1/2\\ 1/2& 0& 1& 0\\ 0& 1/2& 0& 1\end{array}\right]$

Obtain thus the position prediction value X (k|k-1) of target in k two field picture, the predicted value obtaining in calculation procedure six is with the distance between observed reading $d=\sqrt{{(Z_x\left(k\right)-X_x\left(k\right|k-1))}^2+{(Z_y\left(k\right)-X_y\left(k\right|k-1))}^2},$ According to following formula judgement Kalman filter

The weight ρ gaining in ripple algorithm:

$\mathrm{\&rho;}=\left\{\begin{array}{cc}1& \mathrm{ifd}\&le;e\\ {\mathrm{\&rho;}}_1& \mathrm{ifd}>e\end{array}\right.$ 0< ρ wherein ₁<1

The kalman gain calculating is multiplied by gain weight as final gain substitution Kalman filtering fundamental equation, obtain final state vector value X (k), thus obtained the speed of target in k two field picture and to step 5 in the position detection value that obtains revise;

Step 7: the motion yardstick that calculates each target in k two field picture;

By the speed c of target in k two field picture _kwith angle θ _ksubstitution wavelet function ${\mathrm{\&psi;}}_w(\stackrel{\&RightArrow;}{\mathrm{\&xi;}},t)=a^{-\frac{3}{2}}\mathrm{\&psi;}(a^{-1}{c}^{-\frac{1}{3}}{r}^{-\mathrm{\&theta;}}(\stackrel{\&RightArrow;}{\mathrm{\&xi;}}-\stackrel{\&RightArrow;}{b}),a^{-1}{c}^{\frac{2}{3}}(t-\mathrm{\&tau;})),$ Wherein $r^{-\mathrm{\&theta;}}=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right],$ $\stackrel{\&RightArrow;}{b}=(b_x,b_y),$ With this wavelet function, the space-time processing block of constructing in step 2 is carried out to the Scale energy density that continuous wavelet transform obtains one dimension:

${\mathrm{\&epsiv;}}_{(c_k,{\mathrm{\&theta;}}_k,\mathrm{\&tau;})}^{\left(2\right)}\left(a_k\right)=\frac{1}{{a_k}^4}\underset{{\stackrel{\&RightArrow;}{b}}_k\&Element;\mathrm{\&Phi;}}{\mathrm{\&Sigma;}}{|<{\mathrm{\&psi;}}_{(a_k,c_k,{\mathrm{\&theta;}}_k,{\stackrel{\&RightArrow;}{b}}_k,\mathrm{\&tau;})}|B_k>|}^2$

In formula, symbol description is as follows:

τ: the position of the two field picture that wish is followed the tracks of in space-time processing block, with the τ in step 1

A _k: the motion yardstick of target in k two field picture

C _k: the speed of target in k two field picture

θ _k: the angle of target in k two field picture

the position coordinates of pixel

B _k: the space-time processing block of k two field picture

wavelet function

in k two field picture

the Scale energy density of position

use wavelet function

to space-time processing block B _kdo continuous wavelet transform;

For the processing block that only has a target, adopt the maximum position of Nelder – Mead simplex search algorithm search Scale energy density as the motion scale-value of this target; For the processing block that has a plurality of targets, the average obtaining with EM fitting algorithm, as the scale-value of target, then realizes the coupling between dimension measurement and target by the method for data correlation;

So far, in k two field picture, the position of target, kinematic parameter and scale parameter all obtain, and next will continue the target in subsequent frame to follow the tracks of, until follow the tracks of, finish.

Images