CN107403439A - Predicting tracing method based on Cam shift - Google Patents

Predicting tracing method based on Cam shift Download PDF

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CN107403439A
CN107403439A CN201710419084.6A CN201710419084A CN107403439A CN 107403439 A CN107403439 A CN 107403439A CN 201710419084 A CN201710419084 A CN 201710419084A CN 107403439 A CN107403439 A CN 107403439A
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CN107403439B (en
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刘振宇
张百颖
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Shenyang University of Technology
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    • G06T7/207—Analysis of motion for motion estimation over a hierarchy of resolutions
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract

Predicting tracing method based on Cam shift, this method proposes the method that Kalman filter is combined with Cam shift algorithms, propose the target predicting and tracking method that a kind of linear prediction is combined with Cam shift algorithms, replace Kalman filter to complete predicted estimate linear prediction method, and predicted estimate result is substituted into Cam shift algorithms and is tracked.In order to complete the position prediction tracking of mobile target well in the case where there is the complex background for the factor interference such as blocking, this method have studied the method that Kalman filter is combined with Cam shift algorithms.Kalman filter can more accurately be completed to move the position prediction of target, combined with Cam shift algorithms and can be very good to complete tracking.On this basis, it is proposed that the target predicting and tracking method that a kind of linear prediction is combined with Cam shift algorithms, i.e., replace Kalman filter to complete predicted estimate linear prediction method, and predicted estimate result is substituted into Cam shift algorithms and is tracked.Experiment shows that this method can both ensure the accuracy followed the trail of during blocking, and and can reduces iteration time, can better meet the requirement of real-time.

Description

Predicting tracing method based on Cam-shift
Technical field：
The present invention relates to a kind of predicting tracing method based on Cam-shift.
Background technology：
The tracking and prediction of mobile target trajectory are the indispensable parts of field of artificial intelligence research, are that machine regards Feel, the key technology of target following detection.Different application backgrounds, there is different trackings：L-K (Lucas＆Kanade) light Stream method and H-S (Horn＆Schunck) optical flow method are not required to consider background information, by assigning velocity to pixel, according to mesh The difference tracking target of mark and background velocity vector, but require brightness constancy between consecutive frame；It is by target following that figure, which cuts algorithm, Problem is mapped in energy function, and Optimization Solution goes out target area, is calculated complicated；The Snake model algorithms that Kass is proposed[3-4]It is Based on the tracking of contour edge feature, its energy utilization is minimum, but profile initialization is complicated；Dong Chun profits et al. are by by grain Son filtering and GVF-Snake combination, the adaptive nonlinear filtering algorithm of proposition, are tracked to motion and Morph Target, It is but less efficient；And Yizong Cheng[6]The Mean-shift algorithms of proposition are that the density gradient based on color characteristic is estimated without ginseng Calculating method, its form is simple, easily operated, but without the function of real-time update search window, mobile target scale change is fast, easily Cause BREAK TRACK；The Cam-shift algorithms that Bradski is proposed on the basis of Mean-shift algorithms, can be automatic The advantages of adjusting the size of search window in real time, and remaining Mean-shift algorithms, but the color characteristic of mobile target Unobvious or when the factor interference such as blocking, can cause tracking to fail.
The content of the invention：
Goal of the invention：The present invention relates to a kind of predicting tracing method based on Cam-shift, the purpose is to solve conventional institute The problem of existing.
Technical scheme：
A kind of predicting tracing method based on Cam-shift, it is characterised in that：This method proposes Kalman filter and Cam- The method that shift algorithms combine, it is proposed that the target predicting and tracking method that a kind of linear prediction is combined with Cam-shift algorithms, Replace Kalman filter to complete predicted estimate linear prediction method, and predicted estimate result is substituted into Cam-shift algorithms In be tracked.
The step of this method, is as follows：
(1), Cam-shift algorithm principles are analyzed：
Cam-shift algorithms are the innovatory algorithms proposed on the basis of Mean-shift algorithms, and this method is to sequential chart As each frame of sequence all does Mean-shift algorithm process, the result of present frame is as next frame Mean-shift algorithms The initial value of search window, computing is iterated successively, complete tracking；
(2), the research of Cam-shift innovatory algorithms：
(2.1) Kalman is combined with Cam-shift algorithms：
(2.1.1) Kalman filter：
Kalman filter is the prediction estimation method to mobile realization of goal by minimum mean square error criterion, and it is logical The relation for crossing state equation and observational equation is modeled to build a discrete linearly system, the state equation of system It is respectively with observational equation：
X (k)=AX (k-1)+BU (k)+W (k) (7)
Z (k)=HX (k)+V (k) (8)
Wherein, the state vector of etching system, may be defined as when X (k) is K：
X (k)=[x (k) y (k) v (k) u (k)]T (9)
X (k) and y (k) represents that target's center represents target's center respectively in x, the coordinate components of y-axis, v (k), u (k) respectively In x, the speed of y-axis；U (k) is the system control amount at K moment, and A, B are systematic parameter；W (k) is process noise.
The observation vector of etching system, may be defined as when Z (k) is K：
Z (k)=[xz(k) yz(k)]T (10)
xzAnd y (k)z(k) it is observing matrix to represent target's center respectively in x, the coordinate value of y-axis, H, and V (k) makes an uproar for observation Sound.
xzAnd y (k)z(k) target's center is represented respectively in x, the coordinate value of y-axis,
Kalman filter algorithm is：
Wherein, X (k | k-1) is the prediction result of NextState, and X (k-1 | k-1) is the optimal estimation of system current state, U (k) is the controlled quentity controlled variable of system mode.P (k | k-1) is X (k | k-1) error covariance, and P (k-1 | k-1) is X (k-1 | k-1) Error covariance, X (k | k) is optimal estimation value, and K (k) is kalman gain, and I is unit matrix, and Q, R are motion artifacts phase Close matrix；The prediction that (11) carry out k+1 states is returned to after completing said process, circulation successively can complete complete process；
In this method, equation is accelerated according to random when the state equation and observational equation of Kalman systems are built, is obtained Arrive：
Thus, Kalman filter modeling is completed；
(2.1.2) Kalman is implemented in combination with process with Cam-shift algorithms：
This method is combined, the overall situation is searched into element turns according to the advantage and disadvantage of Kalman algorithms and Cam-shift algorithms Become Local Search, so as to reduce amount of calculation, improve accuracy rate；
(2.2) linear prediction is combined with Cam-shift algorithms：
(2.2.1) linear prediction：
From physics angle, when the target object motion state equation in description system is linear equation, to setting the goal The primary condition of motion state, you can predict the motion state of any time after the target；And from kinematics angle analysis, Curvilinear motion regards what is be made up of the linear uniform motion of short time as, when mobile object speed and the direction of motion and it is previous when When quarter holding is substantially the same, regard linear uniform motion as；Particularly, when the translational speed of target is gentle, due to each frame Time interval is very short, can regard the object of which movement of every interframe as linear uniform motion；
The calculating process of linear prediction method is：The initial position of known target, according to the current position coordinates of target with Initial position co-ordinates, calculate that the coordinate offset of movement velocity and direction is poor, then poor according to the coordinate offset of gained, calculate The desired locations of next frame, i.e. hypothesis target are (x in the center position coordinates of previous framei-1,yi-1), the center of present frame Coordinate is (xi,yi), then coordinate offset difference is approximately (Δ x, Δ y)=(xi-xi-1,yi-yi-1), due to the mobile mesh of two interframe Mark traveling time is very short, and approximation regards linear uniform motion as, so according to kinematics formula, obtains the phase of target in next frame Hope that position is：(xi+1,yi+1)=(xi+Δx,yi+Δy)；
The realization that (2.2.2) linear prediction is combined with Cam-shift algorithms：
This method is combined linear prediction with Cam-shift algorithms, the target phase that will be obtained according to the thought of linear prediction Center of the position as search window is hoped, is substituted into Cam-shift algorithms, and then restrains real mobile mesh in local iteration Barycenter is marked, new center position coordinates is updated, circulates successively, complete tracing process well；Comprise the following steps that：
(1) tracking target image is converted into hsv color histogram, and generates back projection figure；
(2) position of initial target is determined, rational initial window size is set；
(3) according to Cam-shift algorithm search window centroid positions and window center is moved to window centroid position, led to Cross the condition of convergence and export actual centroid position；
(4) to calculate coordinate offset according to the centroid position tried to achieve and previous frame centroid position poor, and predicts next frame mesh Mark desired locations；
(5) window size, return to step (3) cycle criterion successively are updated, until last frame terminates.
It is as follows that step is implemented in Cam-shift algorithm principle analytical procedures：
(1) foundation of color model：
Hsv color space H components are selected to establish color histogram as clarification of objective is tracked, so can be than complete RGB and HSV models amount of calculation reduces a lot；The conversion formula of RGB and HSV models is as follows：
V=max (R, G, B) (1)
S=(V-min (R, G, B))/V (2)
(2) back projection map generalization：
The H component information histograms of generation are converted into the probability distribution image of color, i.e., it is pixel value is general for 255 point Rate is correspondingly arranged as 1, the probability for the point that pixel value is 0 is arranged into 0, the color probability projected image so obtained is former face The reverse projection image of Color Histogram；
(3) barycenter is found using Mean-shift algorithms：
Search window is initialized, if I (x, y) is the corresponding pixel points of pixel (x, y) back projection figure, is searched by calculating The zeroth order square and first moment of rope window obtain the barycenter of search window, and the center of search window moved on into centroid position, and according to Zeroth order square M00Update window size；Specific formula is as follows：
The barycenter of search window is：
Updating window size is：
When the distance that window is moved to barycenter is more than preset value, the position of window barycenter is recalculated, until meeting to receive Condition is held back, then carries out the tracing computation of next frame, is circulated successively, completes whole tracing process.
It is as follows that Kalman and Cam-shift algorithms are implemented in combination with process specific method：
(1) first, the initial value of tracking target is set；
(2) variance of next two field picture is calculated, substitution formula obtains dbjective state now, utilizes (2.1.1) Kalman The renewal of formula (7) to (11) prediction covariance and state in filtering, estimates tracking target and occurs in next frame most probable Position and movement velocity；
(3) the above results are imported in Cam-shift algorithms, near the target location of predicted estimate, carried out local Target search and matching, the measured value using the window center position after search as Kalman；
(4) tracking window is updated；
(5) covariance matrix and target state equation of more fresh target, repeat step (2), until terminating.
Advantageous effect：The present invention relates to a kind of predicting tracing method based on Cam-shift, in order to the factor such as block The position prediction tracking of mobile target is completed under the complex background of interference well, this method have studied Kalman filter and Cam- The method that shift algorithms combine.Kalman filter can more accurately be completed to move the position prediction of target, with Cam-shift Algorithm, which combines, can be very good to complete tracking.On this basis, it is proposed that a kind of linear prediction is combined with Cam-shift algorithms Target predicting and tracking method, i.e., Kalman filter is replaced to complete predicted estimate linear prediction method, and by predicted estimate result Substitute into Cam-shift algorithms and be tracked.Experiment shows that this method can both ensure the accuracy followed the trail of during blocking, again Iteration time can be reduced, the requirement of real-time can be better met.
Brief description of the drawings：
Fig. 1 is traditional Cam-shift algorithm keeps tracks result figure；Wherein (a) is traditional Cam-shift algorithms under normal background Tracking result；(b) it is to have Cam-shift algorithm keeps tracks result under circumstance of occlusion；
Fig. 2 is trace flow figure；
Fig. 3 is modified hydrothermal process tracking result figure, wherein the tracking effect that (a) is Kalman to be combined with Cam-shift algorithms Fruit；(b) tracking effect combined for linear prediction with Cam-shift.
Embodiment：
The present invention provides a kind of predicting tracing method based on Cam-shift,
1st, Cam-shift algorithm principles are analyzed：
Cam-shift algorithms are the innovatory algorithms proposed on the basis of Mean-shift algorithms, and this method is to sequential chart As each frame of sequence all does Mean-shift algorithm process, the result of present frame is as next frame Mean-shift algorithms The initial value of search window, computing is iterated successively, complete tracking.It is as follows to implement step：
(1) foundation of color model
Cam-shift algorithms do feature using color model and carry out target following.RGB color model produces or display color Coloured silk, the substantive characteristics of hsv color model energy reaction color, it can separately be handled colourity, saturation degree, lightness, improve algorithm Stability.Therefore, hsv color space H components are selected to establish color histogram as tracking clarification of objective, can so compare Complete RGB and HSV models amount of calculation reduces a lot.The conversion formula of RGB and HSV models is as follows：
V=max (R, G, B) (1)
S=(V-min (R, G, B))/V (2)
(2) back projection map generalization
The H component information histograms of generation are converted into the probability distribution image of color, i.e., it is pixel value is general for 255 point Rate is correspondingly arranged as 1, the probability for the point that pixel value is 0 is arranged into 0, the color probability projected image so obtained is former face The reverse projection image of Color Histogram.
(3) barycenter is found using Mean-shift algorithms
Search window is initialized, if I (x, y) is the corresponding pixel points of pixel (x, y) back projection figure, is searched by calculating The zeroth order square and first moment of rope window obtain the barycenter of search window, and the center of search window moved on into centroid position, and according to Zeroth order square M00Update window size.Specific formula is as follows[9]：
The barycenter of search window is：
Updating window size is：
When the distance that window is moved to barycenter is more than preset value, the position of window barycenter is recalculated, until meeting to receive Condition is held back, then carries out the tracing computation of next frame, is circulated successively, completes whole tracing process.
Fig. 1 shows the tracking result for moving down moving-target sequence in complex background using Cam-shift algorithms, and a figures are 10th, 20,30,40 frame sequence it is normal it is unobstructed in the case of tracking result, b figures are that the 50th, 60,70,80 frame sequence is having screening Tracking result in the case of gear.It can easily be seen that Cam-shift algorithms can automatically adjust the size of search window in real time, Can accurately track target under glitch-free background, but when run into the factor such as block and influence when, it is easy to because color is special Unobvious are levied, iterative process is numerous and diverse and causes counting loss, and then causes tracking to fail.Therefore, introduce and estimate for this shortcoming The position of the mobile target of gauge prediction, reduces iterations, and then reduce fault rate.
The research of 2Cam-shift innovatory algorithms：
2.1Kalman is combined with Cam-shift algorithms：
2.1.1Kalman filtering:
Kalman filter is the prediction estimation method to mobile realization of goal by minimum mean square error criterion, and it is logical The relation for crossing state equation and observational equation is modeled to build a discrete linearly system.The state equation of system It is respectively with observational equation：
X (k)=AX (k-1)+BU (k)+W (k) (7)
Z (k)=HX (k)+V (k) (8)
Wherein, the state vector of etching system, may be defined as when X (k) is K：
X (k)=[x (k) y (k) v (k) u (k)]T (9)
X (k) and y (k) represents target's center in x, the coordinate components of y-axis respectively；V (k), u (k) represent target's center respectively In x, the speed of y-axis；The controlled quentity controlled variable and observation vector of etching system, x when U (k) Z (k) are respectively KzAnd y (k)z(k) represent respectively Target's center is in x, the coordinate value of y-axis.
Kalman filter algorithm is：
Wherein, X (k | k-1) is the prediction result of NextState, and X (k-1 | k-1) is the optimal estimation of system current state, P (k | k-1) is X (k | k-1) error covariance, and X (k | k) is excellent estimate, and K (k) is kalman gain.Complete said process The prediction that (10) carry out k+1 states is returned afterwards, and circulation successively can complete complete process.
In this method, equation is accelerated according to random when the state equation and observational equation of Kalman systems are built, can Obtain：
Thus, Kalman filter modeling is completed.
2.1.2Kalman it is implemented in combination with process with Cam-shift algorithms
It is the global search based on pixel due to being predicted using Kalman filter algorithm during tracking, it is computationally intensive, when During applied to complex background, global search antijamming capability is weak, is easily lost tracking target.This method according to Kalman algorithms and The advantage and disadvantage of Cam-shift algorithms, are combined, you can the overall situation is searched into element and is transformed into Local Search, is calculated so as to reduce Amount, improve accuracy rate.
Specific method is as follows：
(1) first, the initial value of tracking target, such as speed, position etc. are set；
(2) variance of next two field picture is calculated, substitution formula obtains dbjective state now, utilizes Kalman correlation formulas The renewal of covariance and state is predicted, estimates tracking target in the position that next frame most probable occurs and movement velocity；
(3) the above results are imported in Cam-shift algorithms, near the target location of predicted estimate, carried out local Target search and matching, the measured value using the window center position after search as Kalman；
(4) tracking window is updated；
(5) covariance matrix and target state equation of more fresh target, repeat step (2), until terminating.
2.2 linear predictions are combined with Cam-shift algorithms：
2.2.1 linear prediction
It was found from physics, when the target object motion state equation in description system is linear equation, to setting the goal The primary condition of motion state, you can predict the motion state of any time after the target.And from kinematics angle analysis, Curvilinear motion can be regarded as what is be made up of the linear uniform motion of short time, when the speed and the direction of motion of mobile object are with before When one moment kept being substantially the same, linear uniform motion can be regarded as.Particularly, when the translational speed of target is gentle, due to The time interval of each frame is very short, can regard the object of which movement of every interframe as linear uniform motion.
The calculating process of linear prediction method is：The initial position of known target, according to the current position coordinates of target with Initial position co-ordinates, calculate that the coordinate offset of movement velocity and direction is poor, then poor according to the coordinate offset of gained, calculate The desired locations of next frame, i.e. hypothesis target are (x in the center position coordinates of previous framei-1,yi-1), the center of present frame Coordinate is (xi,yi), then coordinate offset difference can be approximately (Δ x, Δ y)=(xi-xi-1,yi-yi-1), due to the movement of two interframe Target traveling time is very short, can approximation regard linear uniform motion as, it is possible to according to kinematics formula, obtain next frame The desired locations of middle target are：(xi+1,yi+1)=(xi+Δx,yi+Δy)。
2.2.2 the realization that linear prediction is combined with Cam-shift algorithms
This method is combined it with Cam-shift algorithms, the target desired locations that will be obtained according to the thought of linear prediction As the center of search window, substitute into Cam-shift algorithms, and then restrain real mobile target matter in local iteration The heart, new center position coordinates are updated, are circulated successively, complete tracing process well.
Trace flow figure is as shown in Figure 2：
3 experimental results and analysis：
This method to Kalman with Cam-shift algorithms by being combined and above-mentioned linear prediction and Cam-shift algorithms With reference to comparative analysis, to verify validity and real-time that above-mentioned linear prediction is combined with Cam-shift algorithms.This method is adopted Experiment, track window are tracked with the people for having the process of blocking under the complex background sequence image (size 360*640) that walks upright Mouth is rectangular window, and home window detects that the position of the first frame movement target determines by background subtraction, chooses the 30th respectively, 60,90,130 frame tracking sequence images are to show explanation.
Fig. 3 is the tracking knot that Kalman is combined with Cam-shift algorithms and linear prediction is combined with Cam-shift algorithms Fruit：
From figure 3, it can be seen that method and linear prediction that Kalman is combined with Cam-shift algorithms are calculated with Cam-shift The method that method combines can update window size in real time automatically, when blocking process, the method and biography of two improvements The Cam-shift methods of system compare, and are influenceed by the factor of blocking smaller, can guarantee that the accuracy of tracking, complete tracking well.
This method has again carried out the experiment of 50 secondary trackings under complex background, and the tracking of three kinds of algorithms of com-parison and analysis is correct Rate, can intuitively find out from table 1, linear prediction and the Cam-shift combination algorithms and Kalman that this method proposes with Cam-shift combination algorithms tracking accuracy is more much higher than traditional Cam-shift algorithms.It is unobstructed by tracking continuous 30 frame The sequence image of disturbed condition, the com-parison and analysis iterations and elapsed time of traditional Cam-shift algorithms and innovatory algorithm, As can be seen that the calculation that the algorithm that the linear prediction that this method proposes is combined with Cam-shift is combined with Kalman with Cam-shift Total iterations difference of method is seldom, and half or so is reduced than traditional Cam-shift algorithms；And this method proposition is linear pre- The algorithm single iteration that survey is combined with Cam-shift is averagely time-consuming to differ seldom with traditional Cam-shift algorithms, but due to repeatedly Generation number is the half of traditional Cam-shift algorithms, so total time-consuming is few more many than traditional Cam-shift algorithms.And The forecasting system for the algorithm structure that Kalman is combined with Cam-shift is complicated, and single iteration is averagely time-consuming longer, so total time-consuming The cost time of the algorithm proposed higher than this method, but still less than the elapsed time of traditional Cam-shift algorithms.Therefore, originally The algorithm that method proposes such as can meet to block at the accurate tracking of interference, and and can ensures more preferable real-time.
Track accuracy Total iterations Total time-consuming Single iteration is averagely time-consuming
Traditional Cam-shift algorithms 84% 45 68.5ms 1.52ms
Kalman is combined with Cam-shift 100% 21 41.7ms 1.98ms
Linear prediction is combined with Cam-shift 100% 23 35.4ms 1.54ms
The iterations of 1 three kinds of algorithms of table is compared with elapsed time
Tab.1 Iterative number and time comparison of three algorithms
4 in summary：
Because traditional Cam-shift algorithms have a great influence under complex background in the presence of the factor of being blocked, tracking is not accurate Possibility, this method inspired from the methods that are combined with Cam-shift algorithms of research Kalman, replaced with linear prediction Kalman filter simplifies the composition of Linear Estimation system, it is proposed that a kind of linear prediction is combined pre- with Cam-shift algorithms Survey track algorithm.Tracking test shows that the algorithm can meet to move target successfully tracking during blocking, and and can is reduced The single iteration time, and then tracking efficiency is improved, better meet the requirement of real-time.
This method moves the identification and estimation of target with reference to Kalman filter from Cam-shift Algorithm Analysis, Reduce well with the probability for losing target under complex background, and utilize physics motion relevant knowledge, it is proposed that be linear pre- The method being combined with Cam-shift algorithms is surveyed, improved method both can guarantee that successfully tracking under complex background, and and can subtracts The time is calculated less, and there is more preferable real-time.

Claims (4)

  1. A kind of 1. predicting tracing method based on Cam-shift, it is characterised in that：This method proposes Kalman filter and Cam- The method that shift algorithms combine, it is proposed that the target predicting and tracking method that a kind of linear prediction is combined with Cam-shift algorithms, Replace Kalman filter to complete predicted estimate linear prediction method, and predicted estimate result is substituted into Cam-shift algorithms In be tracked.
  2. 2. the predicting tracing method according to claim 1 based on Cam-shift, it is characterised in that：The step of this method It is as follows：
    (1), Cam-shift algorithm principles are analyzed：
    Cam-shift algorithms are the innovatory algorithms proposed on the basis of Mean-shift algorithms, and this method is to consecutive image sequence Each frame of row all does Mean-shift algorithm process, and the result of present frame is as next frame Mean-shift algorithm search The initial value of window, computing is iterated successively, complete tracking；
    (2), the research of Cam-shift innovatory algorithms：
    (2.1) Kalman is combined with Cam-shift algorithms：
    (2.1.1) Kalman filter：
    Kalman filter is the prediction estimation method to mobile realization of goal by minimum mean square error criterion, and it is to pass through shape The relation of state equation and observational equation is modeled to build a discrete linearly system, the state equation of system and sight Surveying equation is respectively：
    X (k)=AX (k-1)+BU (k)+W (k) (7)
    Z (k)=HX (k)+V (k) (8)
    Wherein, the state vector of etching system, may be defined as when X (k) is K：
    X (k)=[x (k) y (k) v (k) u (k)]T (9)
    X (k) and y (k) represent target's center in x respectively, the coordinate components of y-axis, and v (k), u (k) represent target's center in x respectively, The speed of y-axis；U (k) is the system control amount at K moment, and A, B are systematic parameter；W (k) is process noise；
    The observation vector of etching system, may be defined as when Z (k) is K：
    Z (k)=[xz(k) yz(k)]T (10)
    xzAnd y (k)z(k) it is observing matrix to represent target's center respectively in x, the coordinate value of y-axis, H, and V (k) is observation noise；
    xzAnd y (k)z(k) target's center is represented respectively in x, the coordinate value of y-axis,
    Kalman filter algorithm is：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>A</mi> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>B</mi> <mi>U</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>A</mi> <mi>P</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>A</mi> <mi>T</mi> </msup> <mo>+</mo> <mi>Q</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>Z</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <mi>H</mi> <mi>X</mi> <mo>(</mo> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>K</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>P</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>H</mi> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>H</mi> <mi>P</mi> <mo>(</mo> <mrow> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <msup> <mi>H</mi> <mi>T</mi> </msup> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <mi>K</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mi>H</mi> <mo>)</mo> </mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, X (k | k-1) is the prediction result of NextState, and X (k-1 | k-1) is the optimal estimation of system current state, U (k) For the controlled quentity controlled variable of system mode；P (k | k-1) for X (k | k-1) error covariance, P (k-1 | k-1) for X (k-1 | k-1) mistake Poor covariance, and X (k | k) it is optimal estimation value, K (k) is kalman gain, and I is unit matrix, and Q, R are motion artifacts Correlation Moment Battle array；The prediction that (11) carry out k+1 states is returned to after completing said process, circulation successively can complete complete process；
    In this method, equation is accelerated according to random when the state equation and observational equation of Kalman systems are built, is obtained：
    <mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>t</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>t</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>H</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Thus, Kalman filter modeling is completed；
    (2.1.2) Kalman is implemented in combination with process with Cam-shift algorithms：
    This method is combined, the overall situation is searched into element is transformed into according to the advantage and disadvantage of Kalman algorithms and Cam-shift algorithms Local Search, so as to reduce amount of calculation, improve accuracy rate；
    (2.2) linear prediction is combined with Cam-shift algorithms：
    (2.2.1) linear prediction：
    From physics angle, when the target object motion state equation in description system is linear equation, to the motion that sets the goal The primary condition of state, you can predict the motion state of any time after the target；And from kinematics angle analysis, curve Motion regards what is be made up of the linear uniform motion of short time as, when the speed and the direction of motion and previous moment of mobile object are protected Hold when being substantially the same, regard linear uniform motion as；Particularly, when the translational speed of target is gentle, due to the time of each frame Interval is very short, can regard the object of which movement of every interframe as linear uniform motion；
    The calculating process of linear prediction method is：The initial position of known target, according to the current position coordinates of target and initially Position coordinates, calculates that the coordinate offset of movement velocity and direction is poor, then poor according to the coordinate offset of gained, calculates next The desired locations of frame, i.e. hypothesis target are (x in the center position coordinates of previous framei-1,yi-1), the center position coordinates of present frame For (xi,yi), then coordinate offset difference is approximately (Δ x, Δ y)=(xi-xi-1,yi-yi-1), because the mobile target of two interframe is moved The dynamic time is very short, and approximation regards linear uniform motion as, so according to kinematics formula, obtains the expectation position of target in next frame It is set to：(xi+1,yi+1)=(xi+Δx,yi+Δy)；
    The realization that (2.2.2) linear prediction is combined with Cam-shift algorithms：
    Linear prediction is combined according to the thought of linear prediction, obtained target it is expected into position by this method with Cam-shift algorithms The center as search window is put, is substituted into Cam-shift algorithms, and then restrains real mobile target matter in local iteration The heart, new center position coordinates are updated, are circulated successively, complete tracing process well；Comprise the following steps that：
    (1) tracking target image is converted into hsv color histogram, and generates back projection figure；
    (2) position of initial target is determined, rational initial window size is set；
    (3) according to Cam-shift algorithm search window centroid positions and window center is moved to window centroid position, passes through receipts Hold back the actual centroid position of output with conditions；
    (4) to calculate coordinate offset according to the centroid position tried to achieve and previous frame centroid position poor, and predicts the next frame target phase Hope position；
    (5) window size, return to step (3) cycle criterion successively are updated, until last frame terminates.
  3. 3. the predicting tracing method according to claim 1 based on Cam-shift, it is characterised in that：Cam-shift algorithms It is as follows that step is implemented in principle analysis step：
    (1) foundation of color model：
    Select hsv color space H components to establish color histogram as tracking clarification of objective, so can than complete RGB and HSV models amount of calculation reduces a lot；The conversion formula of RGB and HSV models is as follows：
    V=max (R, G, B) (1)
    S=(V-min (R, G, B))/V (2)
    <mrow> <mi>H</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>60</mn> <mrow> <mo>(</mo> <mi>G</mi> <mo>-</mo> <mi>B</mi> <mo>)</mo> </mrow> <mo>/</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>=</mo> <mi>R</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>120</mn> <mo>+</mo> <mn>60</mn> <mrow> <mo>(</mo> <mi>B</mi> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>/</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>=</mo> <mi>G</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>240</mn> <mo>+</mo> <mn>60</mn> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <mi>G</mi> <mo>)</mo> </mrow> <mo>/</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo>=</mo> <mi>B</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    (2) back projection map generalization：
    The H component information histograms of generation are converted into the probability distribution image of color, i.e., by point probability pair that pixel value is 255 1 should be arranged to, the probability for the point that pixel value is 0 is arranged to 0, the color probability projected image so obtained is that native color is straight The reverse projection image of square figure；
    (3) barycenter is found using Mean-shift algorithms：
    Search window is initialized, if I (x, y) is the corresponding pixel points of pixel (x, y) back projection figure, by calculating search window The zeroth order square and first moment of mouth obtain the barycenter of search window, and the center of search window is moved on into centroid position, and according to zeroth order Square M00Update window size；Specific formula is as follows：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>M</mi> <mn>10</mn> </msub> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mi>x</mi> </munder> <munder> <mo>&amp;Sigma;</mo> <mi>y</mi> </munder> <mi>x</mi> <mi>I</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>M</mi> <mn>01</mn> </msub> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mi>x</mi> </munder> <munder> <mo>&amp;Sigma;</mo> <mi>y</mi> </munder> <mi>y</mi> <mi>I</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>M</mi> <mn>00</mn> </msub> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mi>x</mi> </munder> <munder> <mo>&amp;Sigma;</mo> <mi>y</mi> </munder> <mi>I</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    The barycenter of search window is：
    <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>M</mi> <mn>10</mn> </msub> <msub> <mi>M</mi> <mn>00</mn> </msub> </mfrac> <mo>,</mo> <msub> <mi>y</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>M</mi> <mn>01</mn> </msub> <msub> <mi>M</mi> <mn>00</mn> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    Updating window size is：
    <mrow> <mi>s</mi> <mo>=</mo> <mn>2</mn> <msqrt> <mfrac> <msub> <mi>M</mi> <mn>00</mn> </msub> <mn>256</mn> </mfrac> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    When the distance that window is moved to barycenter is more than preset value, the position of window barycenter is recalculated, until meeting convergence bar Part, then the tracing computation of next frame is carried out, circulate successively, complete whole tracing process.
  4. 4. the predicting tracing method according to claim 1 based on Cam-shift, it is characterised in that：
    It is as follows that Kalman and Cam-shift algorithms are implemented in combination with process specific method：
    (1) first, the initial value of tracking target is set；
    (2) variance of next two field picture is calculated, substitution formula obtains dbjective state now, utilizes (2.1.1) Kalman filter In formula (7) to (11) prediction covariance and state renewal, estimate tracking target in the position that next frame most probable occurs Put and movement velocity；
    (3) the above results are imported in Cam-shift algorithms, near the target location of predicted estimate, carries out local target Search and matching, the measured value using the window center position after search as Kalman；
    (4) tracking window is updated；
    (5) covariance matrix and target state equation of more fresh target, repeat step (2), until terminating.
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