CN103177455A - Method for realizing KLT (Karhunen Loeve Transform) moving target tracking algorithm based on multicore DSP (Digital Signal Processor) - Google Patents

Method for realizing KLT (Karhunen Loeve Transform) moving target tracking algorithm based on multicore DSP (Digital Signal Processor) Download PDF

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CN103177455A
CN103177455A CN2013100897012A CN201310089701A CN103177455A CN 103177455 A CN103177455 A CN 103177455A CN 2013100897012 A CN2013100897012 A CN 2013100897012A CN 201310089701 A CN201310089701 A CN 201310089701A CN 103177455 A CN103177455 A CN 103177455A
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CN103177455B (en
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钱惟贤
胡楷
杨力
尹章芹
任建乐
顾国华
陈钱
路东明
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Nanjing University of Science and Technology
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Abstract

The invention discloses a method for realizing a KLT (Karhunen Loeve Transform) moving target tracking algorithm based on a multicore DSP (Digital Signal Processor). The method disclosed by the invention comprises the steps of: image smoothing, pyramid graph calculating, image gray value difference calculating, feature point selecting, feature point tracking and feature point consistency checking; and six modules for executing the steps are transplanted into the multicore DSP, wherein one core is allocated to each module, and the processing is carried out in a datastream manner. According to the method, a KLT tracking algorithm is adopted, and the advantage and processing speed of multicore parallel execution of the multicore DSP are used, so that the real-time and accurate tracking of moving targets can be realized.

Description

Implementation method based on the KLT Moving Target Tracking Algorithm of multi-core DSP
Technical field
The invention belongs to infrared target search tracking technique field, particularly a kind of moving object real-time tracking field of specifically belonging to.
Background technology
The detection of moving target, tracking are piths of digital image processing techniques.It has comprised a plurality of subject contents such as pattern-recognition, computer vision, vision signal processing, is also increasing to the application of this technology.Recent years, people continually develop new algorithm in the detection and tracking of moving target, but due on the calculated amount of algorithm and the constraint of the processing speed of hardware platform, make two Key Performance Indicators of motion target tracking: the balance of real-time and accuracy is difficult to grasp.In order to realize the requirement of real-time in Motion Object Tracking System, need to take some measures to improve the calculation process speed of algorithm, the one, be optimized on algorithm, the 2nd, improve on hardware system.
The algorithm of motion target tracking is a lot of at present, follow the tracks of or cry the Lucas optical flow method as particle filter (pf), meanshift tracking and KLT, each own advantage separately of these methods, for particle filter, it can be reasonable in global search to optimum solution, but that it finds the solution speed is relatively slow, because being based on color histogram, it plays calculating, so not too can distinguish the same color thing, meanshift follows the tracks of and is easy to be absorbed in local optimum, but speed is still very fast.It is also good that the KLT method shows aspect tracking, has very strong antijamming capability, especially on real-time computing velocity.1981, Kannde and Lucas have proposed track algorithm (the 1. Jianbo Shi based on unique point, Carlo Tomasi, Good Features to Track, IEEE Conference on Computer Vision and Pattern Recognition, 1994, 6.), Lucas and Tomasi expanded this algorithm afterwards, perfect (2.Tiziano Tommasini, Andrea Fusiello, Emanuele Trucco etc., Making Good Features Track Better, Proc. IEEE Int. Conf. on Computer Vision and Pattern Recognition, 1998 (6): 178 ~ 183.).KLT feature point tracking algorithm is followed the tracks of tracking target material texture-rich " corner point ", therefore has very strong anti-interference, and trackability is good, and practical application has also confirmed these characteristics.Although it is moderate that KLT feature point tracking algorithm calculates, if realize on existing hardware platform with software, also be difficult to reach requirement of real time.The KLT algorithm realizes that on GPU arithmetic speed increases, but be based on the consideration of cost, to use widely and also have certain difficulty (3.Sudipta N Sinba, Janmichael Frahm, Marc Pollefeys, et al.GPU-based video feature tracking and matching:TR 06-012 [R] .University of North Carolina, USA, 2006.).Sudipta N (4.Sudipta N. Sinha, Jan-Michael Frahm etc., GPU-based Video Fearure Tracking and Matching, Department of Computer Science, UNC Chapel Hill, Technical Report TR 06-012,2006,5.) etc. on P-IV 3GHz CPU computing machine, the picture of 1024*768 size is carried out KLT and follows the tracks of, calculate spended time as shown in the table:
Table one. the feature corresponding calculating spended time of counting
Feature count (individual) The time (ms) of average every frame cost
100 500
400 550
750 600
1000 645
The modification of depending merely on as can be seen from the above table on algorithm does not reach requirement, therefore need to be broken through on hardware.
Following table has provided the KLT algorithm in each platform working time:
Table two KLT algorithm is at each platform working time (ms)
Universal cpu OpenCV GPU DSP
Hardware platform E7400 2.80GHz E7400 2.80GHz NVidia Geforece 7900GTX TMS320C6678
Algorithm execution time 82.87 78.13 40 35.1
Summary of the invention
The object of the present invention is to provide a kind of employing KLT track algorithm, use advantage that the multi-core parallel concurrent of multi-core DSP carries out and its processing speed can realize moving target in real time, accurate implementation method based on the KLT Moving Target Tracking Algorithm of multi-core DSP of following the tracks of.
The technical solution that realizes the object of the invention is:
A kind of implementation method of the KLT Moving Target Tracking Algorithm based on multi-core DSP, step is as follows:
Step 1: utilize the video acquisition plate with network interface and SRIO interface that the video image that CCD obtains is transferred in multi-core DSP by the SRIO interface;
Step 2: the video image of input is carried out smooth operation, and namely input picture being carried out standard deviation is 0.7, and template window is
Figure 2013100897012100002DEST_PATH_IMAGE002
Gaussian filtering is realized the level and smooth of image, improves signal to noise ratio (S/N ratio) and the signal to noise ratio of target;
Step 3: will be the pyramid diagram picture through level and smooth image transitions, then the pyramid diagram of every one-level be looked like to ask unique point, and computed image gray difference value;
Step 4: the Characteristic of Image point is chosen, and namely gray level image is carried out the second order differentiate, obtains
Figure 2013100897012100002DEST_PATH_IMAGE004
Figure 2013100897012100002DEST_PATH_IMAGE006
Matrix, wherein
Figure 652691DEST_PATH_IMAGE006
Matrix is , wherein
Figure 2013100897012100002DEST_PATH_IMAGE010
The expression gray level image,
Figure 2013100897012100002DEST_PATH_IMAGE012
Be single order in certain neighborhood
Figure 2013100897012100002DEST_PATH_IMAGE014
Directional derivative,
Figure 2013100897012100002DEST_PATH_IMAGE016
Single order for correspondence
Figure 2013100897012100002DEST_PATH_IMAGE018
Directional derivative is then according to formula
Figure 2013100897012100002DEST_PATH_IMAGE020
Obtain this second-order matrix two eigenwerts (
Figure 2013100897012100002DEST_PATH_IMAGE022
, ) size judges whether can be used as unique point;
Concrete criterion is as follows:
(1) if
Figure 507515DEST_PATH_IMAGE022
,
Figure 598836DEST_PATH_IMAGE024
All hour, this zone is approximately the flat region;
(2) if ,
Figure 808418DEST_PATH_IMAGE024
When differing larger, illustrate that this zone is fringe region;
(3) if
Figure 2013100897012100002DEST_PATH_IMAGE026
The time, illustrate that this point is the validity feature point, wherein,
Figure 2013100897012100002DEST_PATH_IMAGE028
Be the threshold value of oneself setting;
Step 5: utilize
Figure 2013100897012100002DEST_PATH_IMAGE030
The whole image of window gradient matrix traversal is chosen the window of texture-rich, namely chooses local irregularities in image and the window that has regular characteristic on macroscopic view, and the validity feature point the chosen size according to its eigenwert is sorted;
Step 6, the calculating of picture point side-play amount, any at image
Figure 2013100897012100002DEST_PATH_IMAGE032
The time chart picture frame
Figure 2013100897012100002DEST_PATH_IMAGE034
With The time chart picture frame
Figure 2013100897012100002DEST_PATH_IMAGE038
In the position satisfy Wherein
Figure 568563DEST_PATH_IMAGE014
,
Figure 835597DEST_PATH_IMAGE018
, be the coordinate of the pixel of image,
Figure 2013100897012100002DEST_PATH_IMAGE042
Be a bit of moment,
Figure 2013100897012100002DEST_PATH_IMAGE044
, For the horizontal ordinate of pixel and the displacement of ordinate, namely exist
Figure 408398DEST_PATH_IMAGE038
In each pixel, can by The pixel translation of middle respective window
Figure 2013100897012100002DEST_PATH_IMAGE048
Obtain, purpose is obtained the pixel translational movement exactly
Figure 2013100897012100002DEST_PATH_IMAGE050
Step 7: carry out consistency check with Affine arithmetic for following the tracks of successful unique point;
step 8, above-mentioned algorithm is resolved into several parts, respectively the level and smooth of image, calculate pyramid diagram, computed image gray difference value, unique point is selected, feature point tracking, six modules of unique point consistency check, these six modules are transplanted in multi-core DSP, core of each module assignment wherein, maintenance data stream mode is processed, being task moves according to the transmission of data, a task promotes the another one task run, specifically the data handled well of first core pass to second core, the data of successively previous core being handled well pass to next core, the communication of intermodule realizes by message passing mechanism.
The present invention compared with prior art, its remarkable advantage:
(1) in the feature point tracking step, in order to improve the speed of tracking, guarantee that simultaneously the unique point that traces into has of overall importance, smoothed image is converted to the pyramid diagram picture, ask the gradient of every one-level pyramid diagram picture, the unique point pointwise of then choosing is followed the tracks of step by step again.
(2) used Inline Function when optimized algorithm, Inline Function execution efficient is high, and code length is short, and easy to use, and the built-in function that has called DSP, makes the code operational efficiency high, and elapsed time is short.
(3) utilized eight nuclear superiority of multi-core DSP-TMS320C6678, whole algorithm is divided into several parts, executed in parallel in multinuclear, improved whole efficient respectively, shortened operation time, thereby realize real-time tracking.
(4) the tasks carrying Operation Mode Selection of DSP multinuclear be stream socket, namely task is moved according to the transmission of data, a task promotes another task run.This mode relatively is fit to the higher application of requirement of real-time.
Below in conjunction with accompanying drawing, the present invention is described in further detail.
Description of drawings
Fig. 1 is the schematic flow sheet of implementation method that the present invention is based on the KLT Moving Target Tracking Algorithm of multi-core DSP.
Fig. 2 is system hardware one-piece construction figure of the present invention.
Fig. 3 is the consistency check process flow diagram that the present invention follows the tracks of successful unique point.
Fig. 4 is each core maintenance data stream mode method of operation of the present invention.
Fig. 5 is the cut-away view of the multi-core DSP that uses of the present invention.
Embodiment
In conjunction with Fig. 1, the present invention is based on the implementation method of the KLT motion mark track algorithm of multi-core DSP, step is as follows:
The first step, owing to need to every frame of video being processed, therefore the data volume of processing is larger, algorithm complex is high, traditional processor generally can not satisfy the requirement of speed, that native system adopts is the high high speed digital signal processor eight core TMS320C6678 of a cost performance of the up-to-date release of TI company, introduced its inner structure as Fig. 5, can find out that it has powerful multiply-add operation device and parallel processing structure, this processor is eight core floating type DSP, and its each core maximum operation frequency reaches 1.25GHz.The single instruction cycle can be carried out 32 fixed-point data computings, perhaps carries out 16 floating data computings.Whole chip provides 320GMAC fixed point calculation or 160GFLOP Floating-point Computation ability.
As shown in Figure 2, whole hardware system is divided for four modules such as image capture module, image pretreatment module, Digital Image Processing module, display modules, at first utilize the video acquisition plate that the video image that CCD obtains is transferred in DSP-TMS320C6678 by SRIO, compatibility between two plates and error rate are all considerable, namely transmit image data packet loss seldom almost in the process of transmission, can reach requirement.
Second step carries out smooth operation with the video image of input in DSP inside, namely input picture is carried out standard deviation and is
Figure 2013100897012100002DEST_PATH_IMAGE052
Template window is
Figure 883690DEST_PATH_IMAGE002
Gaussian filtering is realized the level and smooth of image, can not lose the energy of target, can weaken to a great extent again the energy of background, thereby improve signal to noise ratio (S/N ratio) and the signal to noise ratio of target, reaches the effect of Background suppression.
The 3rd step will be the pyramid diagram picture through level and smooth image transitions, then the pyramid diagram of every one-level be looked like to ask unique point, and computed image gray difference value;
In the 4th step, the Characteristic of Image point is chosen, and namely gray level image is carried out the second order differentiate, obtains
Figure 638019DEST_PATH_IMAGE006
Then matrix judges whether can be used as unique point according to two eigenwert sizes of this matrix.The below has provided
Figure 437348DEST_PATH_IMAGE006
The specific definition of matrix.
Suppose
Figure 960733DEST_PATH_IMAGE010
The expression gray level image
Figure 390578DEST_PATH_IMAGE012
Be single order in certain neighborhood
Figure 949647DEST_PATH_IMAGE014
Directional derivative,
Figure 224771DEST_PATH_IMAGE016
Single order for correspondence
Figure 868241DEST_PATH_IMAGE018
Directional derivative,
Figure 265725DEST_PATH_IMAGE006
Matrix expression is as follows
Figure 994646DEST_PATH_IMAGE008
If
Figure 73461DEST_PATH_IMAGE022
,
Figure 571438DEST_PATH_IMAGE024
For
Figure 156134DEST_PATH_IMAGE006
Two eigenwerts of matrix specifically judge as follows:
(1) if ,
Figure 989278DEST_PATH_IMAGE024
All hour, this zone is approximately the flat region.
(2) if ,
Figure 346627DEST_PATH_IMAGE024
When differing larger, illustrate that this zone is fringe region.
(3) if
Figure 784562DEST_PATH_IMAGE026
(wherein
Figure 516763DEST_PATH_IMAGE028
The threshold value of setting is fixed by oneself) time, illustrate that this point is the validity feature point.
In the 5th step, utilize
Figure 989333DEST_PATH_IMAGE030
The whole image of window gradient matrix traversal is chosen the window of texture-rich, and the size of the unique point that chooses according to eigenwert sorted, and forms the list of unique point, is used for when feature point tracking the point of place of lost.
The 6th step, the calculating of picture point side-play amount,
Figure 102783DEST_PATH_IMAGE032
The time chart picture frame
Figure 90330DEST_PATH_IMAGE034
With
Figure 314638DEST_PATH_IMAGE036
The time chart picture frame
Figure 376135DEST_PATH_IMAGE038
In the position satisfy
Figure 660486DEST_PATH_IMAGE040
Namely exist
Figure 886062DEST_PATH_IMAGE038
In each pixel, can by
Figure 914061DEST_PATH_IMAGE034
The pixel translation of middle respective window
Figure 95643DEST_PATH_IMAGE048
Obtain, purpose is obtained exactly Specifically being calculated as follows of side-play amount:
Suppose
Figure 247456DEST_PATH_IMAGE036
Characteristic window constantly is
Figure 2013100897012100002DEST_PATH_IMAGE054
, wherein
Figure 2013100897012100002DEST_PATH_IMAGE056
Be window coordinates,
Figure 125151DEST_PATH_IMAGE032
Characteristic window constantly is
Figure 2013100897012100002DEST_PATH_IMAGE058
Due to reasons such as noises, have , wherein For in the time
Figure 489136DEST_PATH_IMAGE042
The interior noise that produces that changes due to illumination condition.
Will
Figure 849711DEST_PATH_IMAGE062
Square and in whole window upper integral, just obtained the gray scale difference quadratic sum (SSD) of video in window
Figure 2013100897012100002DEST_PATH_IMAGE064
(1)
Wherein,
Figure 2013100897012100002DEST_PATH_IMAGE066
,
Figure 2013100897012100002DEST_PATH_IMAGE068
,
Figure 2013100897012100002DEST_PATH_IMAGE070
Usually can be taken as 1.If emphasize the effect of core texture adopt gauss of distribution function, this patent
Figure 112196DEST_PATH_IMAGE070
Adopt gauss of distribution function.
When For with
Figure 2013100897012100002DEST_PATH_IMAGE072
When comparing insignificant a small amount of, will Taylor expansion is removed high-order term, obtains
Figure 2013100897012100002DEST_PATH_IMAGE076
(2)
With formula (2) substitution formula (1), and right simultaneously to the both sides of formula (1)
Figure 746494DEST_PATH_IMAGE050
Get 0 after differentiate, can obtain
Figure 2013100897012100002DEST_PATH_IMAGE078
(3)
At this moment The minimal value of getting.Variable being changed to of formula (3)
Figure 2013100897012100002DEST_PATH_IMAGE082
(4)
If order
Figure 2013100897012100002DEST_PATH_IMAGE084
(5)
Figure 2013100897012100002DEST_PATH_IMAGE086
(6)
Formula (4) can be expressed as
(7)
For every two width images, solve an equation (7) can obtain the displacement of characteristic window
In the 7th step, as Fig. 3, need to carry out consistency check with Affine arithmetic for following the tracks of successful unique point.Because the tracking of unique point realizes by multiple image, the information of image tends to distorted, therefore needs consistency check.For the signature tracking from the frame to the frame, carry out consistency check with simple translation transformation not enough often, therefore select affine maps to realize conforming inspection.
the 8th step, requirement due to real-time and accuracy, requirement to hardware platform is very high, especially require high to the processing speed of chip, therefore above-mentioned algorithm is resolved into several parts, respectively the level and smooth of image, calculate pyramid diagram, computed image gray difference value, the unique point consistency check, unique point is selected, six modules of feature point tracking, consider the calculated amount of each part and coupling and the associativity between every part, this algorithm has been resolved into six modules to be transplanted in DSP-TMS320C6678, core of each module assignment wherein, the maintenance data stream method of operation such as Fig. 4, the data that first core is handled well pass to second core, the data of successively previous core being handled well pass to next core.the communication of intermodule realizes by information transmission mechanism, call the DSP Integrated Development Environment SYS/BIOS and IPC instrument are provided, SYS/BIOS mainly completes internuclear task scheduling, IPC realize internuclear synchronously with communicate by letter, receive the sequence image that transmits from the video acquisition plate by UDP, and to the above-mentioned algorithm process of these data applications, utilize the optimization of the powerful fixed and floating hybrid operation ability of C66x and multinuclear streamline, realized the real-time follow-up of moving target, then the result that will process is transferred to upper realization of PC by network interface and shows in real time, with circle the aiming circle that is traced to, use little square and indicate unique point in circle.

Claims (3)

1. implementation method based on the KLT Moving Target Tracking Algorithm of multi-core DSP is characterized in that comprising the following steps:
Step 1: utilize the video acquisition plate with network interface and SRIO interface that the video image that CCD obtains is transferred in multi-core DSP by the SRIO interface;
Step 2: the video image of input is carried out smooth operation, and namely input picture being carried out standard deviation is 0.7, and template window is
Figure 2013100897012100001DEST_PATH_IMAGE002
Gaussian filtering is realized the level and smooth of image, improves signal to noise ratio (S/N ratio) and the signal to noise ratio of target;
Step 3: will be the pyramid diagram picture through level and smooth image transitions, then the pyramid diagram of every one-level be looked like to ask unique point, and computed image gray difference value;
Step 4: the Characteristic of Image point is chosen, and namely gray level image is carried out the second order differentiate, obtains
Figure 2013100897012100001DEST_PATH_IMAGE004
Figure 2013100897012100001DEST_PATH_IMAGE006
Matrix, wherein
Figure 129130DEST_PATH_IMAGE006
Matrix is
Figure 2013100897012100001DEST_PATH_IMAGE008
, wherein The expression gray level image,
Figure 2013100897012100001DEST_PATH_IMAGE012
Be single order in certain neighborhood
Figure 2013100897012100001DEST_PATH_IMAGE014
Directional derivative,
Figure 2013100897012100001DEST_PATH_IMAGE016
Single order for correspondence Directional derivative is then according to formula
Figure 2013100897012100001DEST_PATH_IMAGE020
Obtain this second-order matrix two eigenwerts (
Figure 2013100897012100001DEST_PATH_IMAGE022
,
Figure 2013100897012100001DEST_PATH_IMAGE024
) size judges whether can be used as unique point;
Concrete criterion is as follows:
(1) if ,
Figure 392650DEST_PATH_IMAGE024
All hour, this zone is approximately the flat region;
(2) if ,
Figure 456738DEST_PATH_IMAGE024
When differing larger, illustrate that this zone is fringe region;
(3) if
Figure 2013100897012100001DEST_PATH_IMAGE026
The time, illustrate that this point is the validity feature point, wherein, Be the threshold value of oneself setting;
Step 5: utilize
Figure 2013100897012100001DEST_PATH_IMAGE030
The whole image of window gradient matrix traversal is chosen the window of texture-rich, namely chooses local irregularities in image and the window that has regular characteristic on macroscopic view, and the validity feature point the chosen size according to its eigenwert is sorted;
Step 6, the calculating of picture point side-play amount, any at image
Figure 2013100897012100001DEST_PATH_IMAGE032
The time chart picture frame
Figure 2013100897012100001DEST_PATH_IMAGE034
With
Figure 2013100897012100001DEST_PATH_IMAGE036
The time chart picture frame
Figure 2013100897012100001DEST_PATH_IMAGE038
In the position satisfy Wherein
Figure 106025DEST_PATH_IMAGE014
,
Figure 971213DEST_PATH_IMAGE018
, be the coordinate of the pixel of image,
Figure 2013100897012100001DEST_PATH_IMAGE042
Be a bit of moment,
Figure 2013100897012100001DEST_PATH_IMAGE044
,
Figure 2013100897012100001DEST_PATH_IMAGE046
For the horizontal ordinate of pixel and the displacement of ordinate, namely exist
Figure 483971DEST_PATH_IMAGE038
In each pixel, can by
Figure 67400DEST_PATH_IMAGE034
The pixel translation of middle respective window
Figure 2013100897012100001DEST_PATH_IMAGE048
Obtain, purpose is obtained the pixel translational movement exactly
Figure 2013100897012100001DEST_PATH_IMAGE050
Step 7: carry out consistency check with Affine arithmetic for following the tracks of successful unique point;
step 8, above-mentioned algorithm is resolved into several parts, respectively the level and smooth of image, calculate pyramid diagram, computed image gray difference value, unique point is selected, feature point tracking, six modules of unique point consistency check, these six modules are transplanted in multi-core DSP, core of each module assignment wherein, maintenance data stream mode is processed, being task moves according to the transmission of data, a task promotes the another one task run, specifically the data handled well of first core pass to second core, the data of successively previous core being handled well pass to next core, the communication of intermodule realizes by message passing mechanism.
2. the implementation method of KLT Moving Target Tracking Algorithm based on multi-core DSP described according to right 1, be characterised in that: step 1 is described, utilization has the video acquisition plate of network interface and SRIO interface, by SRIO with transmission of video images to DSP, video acquisition plate and dsp board carry out data transmission by udp protocol.
3. the implementation method of KLT Moving Target Tracking Algorithm based on multi-core DSP described according to right 1 is characterised in that: the side-play amount of computed image unique point, and with the tracking of realization character point, specifically being calculated as follows of side-play amount:
Suppose Characteristic window constantly is
Figure 2013100897012100001DEST_PATH_IMAGE052
, wherein
Figure 2013100897012100001DEST_PATH_IMAGE054
Be window coordinates,
Figure 177755DEST_PATH_IMAGE032
Characteristic window constantly is
Figure 2013100897012100001DEST_PATH_IMAGE056
, due to reasons such as noises, have , wherein For in the time
Figure 799098DEST_PATH_IMAGE042
The interior noise that produces that changes due to illumination condition,
Will Square and in whole window upper integral, just obtained the gray scale difference quadratic sum of video in window
Figure 2013100897012100001DEST_PATH_IMAGE062
(1)
Wherein,
Figure 2013100897012100001DEST_PATH_IMAGE064
,
Figure 2013100897012100001DEST_PATH_IMAGE066
,
Figure 2013100897012100001DEST_PATH_IMAGE068
Usually can be taken as 1, if emphasize the effect of core texture adopt gauss of distribution function, this patent
Figure 798595DEST_PATH_IMAGE068
Adopt gauss of distribution function;
When
Figure 638375DEST_PATH_IMAGE050
For with
Figure DEST_PATH_IMAGE070
When comparing insignificant a small amount of, will Taylor expansion is removed high-order term, obtains
Figure DEST_PATH_IMAGE074
(2)
With formula (2) substitution formula (1), and right simultaneously to the both sides of formula (1)
Figure 181352DEST_PATH_IMAGE050
Get 0 after differentiate, can obtain
Figure DEST_PATH_IMAGE076
(3)
At this moment The minimal value of getting, variable being changed to of formula (3)
Figure DEST_PATH_IMAGE080
(4)
If order
Figure DEST_PATH_IMAGE082
(5)
Figure DEST_PATH_IMAGE084
(6)
Formula (4) can be expressed as
Figure DEST_PATH_IMAGE086
(7)
For every two width images, solve an equation (7) can obtain the displacement of characteristic window
Figure 660744DEST_PATH_IMAGE048
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