CN105205826B - A kind of SAR image azimuth of target method of estimation screened based on direction straight line - Google Patents
A kind of SAR image azimuth of target method of estimation screened based on direction straight line Download PDFInfo
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Abstract
The invention discloses a kind of SAR image azimuth of target method of estimation screened based on direction straight line, comprise the following steps：S1, SAR targets are extracted from input picture；S2, extraction object boundary, a binary border matrix is expressed as by its information；S3, in unidirectional straight line, find the straight lines most with the intersection point number of object boundary, be used as the direction straight line of the direction；S4, in all directions straight line, screen optimum orientation straight line；S5, the angle for determining optimum orientation straight line are azimuth of target to be estimated.The inventive method does not make excessive requirement to the shape of target, so as to reduce the dependence to Objective extraction process；By the screening of two-stage direction straight line, deficiency of the conventional method on vertically and horizontally orientation is distinguished is compensate for, estimated accuracy is improved, and evaluated error is reduced in the case of long and short primary edge length difference is smaller；In addition, the inventive method computation complexity is low, estimation is quick.
Description
Technical field
The invention belongs in technical field of image processing, be related to image steganalysis method, and in particular to one kind is based on side
The estimation side of synthetic aperture radar (Synthetic Aperture Radar, the SAR) image goal position angle screened to straight line
Method.
Background technology
Synthetic aperture radar has the advantages that round-the-clock, all-weather and strong penetration capacity, has become a kind of important army
Thing investigation.In recent years, automatic target detection (Automatic Target are carried out using high-resolution SAR image
Recognition, ATR) research continue to bring out.
SAR target images are very sensitive to the orientation of radar imagery, image difference of the same target obtained by different azimuth
It is very not big.The SAR template images of a large amount of different azimuths are stored in traditional SAR ATR systems, by by target to be identified with
Template is matched to realize the identification of target.Therefore, the azimuth of target is pre-estimated out, search graph can be efficiently reduced
The quantity of picture, improves the recognition efficiency and accuracy rate of ATR systems.
The estimation procedure of SAR azimuth of targets generally includes two links of Objective extraction and angle estimation.Objective extraction is
SAR targets are extracted as precisely as possible from image；Angle estimation is analyzed extracting target, estimation
Go out the azimuth of target.At present, main SAR azimuth of target methods of estimation have：Method of principal axis, boundary rectangle method and primary edge
Method.
Method of principal axis is come estimation orientation angle by the main shaft of target scattering center.Because the mathematical modeling being related to is simple,
Calculate complicated small, and for a certain degree of target occlusion, hidden and be hinged with robustness.But a base of this kind of method
This hypothesis is that SAR targets are symmetrical on main shaft.And in practical situations both, due to the shadow by image scene or object construction
Ring, symmetry is assumed not necessarily to set up, and causes orientation angular estimation inaccurate.Boundary rectangle method is fitted mesh using minimum enclosed rectangle
Mark, always determines azimuth of target according to walking for boundary rectangle, this method has higher requirement to the shape of target, that is, needs to carry
The target of taking-up has relatively regular shape, and there may be larger angle estimation deviation for irregular shape；In addition, this method
It is related to series of rectangular rotation, amount of calculation is larger.Primary edge rule is by detecting the primary edge of target come the side of estimation
Parallactic angle.Two methods are high earlier above for the estimated accuracy of this method, and the acquisition of primary edge does not need complicated matrix rotation, speed
Comparatively fast, its major defect is when the short primary edge of target is vertical with radar beam, the estimation in vertically and horizontally orientation
Upper generation is obscured, and this problem fails to be well solved always, have impact on widely using for algorithm；Moreover, this method exists
When long and short primary edge length difference is smaller, larger estimated bias is easily produced.
The content of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of quick and estimated accuracy is higher based on side
The SAR image azimuth of target method of estimation screened to straight line.
The purpose of the present invention is achieved through the following technical solutions：A kind of SAR image screened based on direction straight line
Azimuth of target method of estimation, comprises the following steps：
S1, extraction target, the SAR Objective extractions in input picture are come out, be expressed as one two with image partition method
The objective matrix of value, the line number and columns of the matrix are respectively equal to the width and length of image, each point corresponding diagram of matrix
One pixel of picture, its value is that the 1 expression pixel is target point, is that the 0 expression pixel is non-targeted point；
S2, extraction border, to each point in objective matrix, count the number of target point in its peripheral region, if mesh
Punctuate number is less than default adjacent region threshold, then judges the point as boundary point, be otherwise non-boundary point；By object boundary information table
Be shown as a binary border matrix, the line number and columns of the matrix are respectively equal to the width and length of image, matrix each
One pixel of point correspondence image, its value is that the 1 expression pixel is boundary point, is that the 0 expression pixel is non-boundary point；
S3, determine all directions straight line, including following sub-step：
S31, in target image plane make the straight line { L that one group of width is two pixelsθ,d, wherein θ be straight line with it is vertical
The angle in direction, 0 ° of ＜ θ≤180 °, θ sampling interval is Δθ, 0 ＜ Δsθ≤1；D for image top left corner apex to straight line
Distance,Wherein p, q are respectively the line number and columns of boundary matrix, and d sampling interval is Δd, 0 ＜ Δsd
≤1；
S32, every straight line L of statisticsθ,dWith the intersection point number of object boundary；
S33, to each θ, seek straight line most with boundary intersection number in all straight lines that angle is θ, define the straight line
For θ direction straight line lθ, remember lθIntersection point number with border is zθ；
S4, screening optimum orientation straight line, including following sub-step：
S41, seek zθMaximum, be designated as zmax, i.e.,
Remember zmaxCorresponding angle is θmax；
If S42, θmaxLess than 20 degree, it is determined that straight lineFor optimum orientation straight line；Otherwise travel direction straight line is screened, and is sought
Seek optimum orientation straight line；
S5, the angle for determining optimum orientation straight line are azimuth of target to be estimated.
Further, in described step S2, in statistics objective matrix in each peripheral region during the number of target point,
The area size of statistics is 5 × 5 pixels.
Further, described step S42 direction straight line screening includes the straight line screening of first order direction and second level side
Screened to straight line, described first order direction straight line screening comprises the following steps：
S421, setting intersection point number set C1 and C2, candidate direction straight line setC1, C2 andIt is ordered set,
It is 0 that three, which are gathered the element number included, when initial；
S422, by all intersection point number zθIt is added to by order from big to small in C1, if after element addition terminates, C1 is common
Include p element；
The element counter i that S423, setting initial value are 1；
S424, take the i-th element c in C1i, judge whether to meet following two conditions：
Condition 1：ci＞ η zmax, wherein 0.7 ＜ η ＜ 0.9；
Condition 2：C2 is empty set or ciCorresponding angle is poor with angle corresponding to each element in current C2
Absolute value is more than Δ, 15 ＜ Δs ＜ 25；
If condition 1 and condition 2 are met simultaneously, by ciIt is added to C2 afterbody, and by ciCorresponding direction straight line is added
To candidate direction straight line setAfterbody；Do not operated if being unsatisfactory for；
If S425, i ＜ p, counter i add 1, step S424 is gone to, the screening of second level direction straight line is otherwise carried out；
Described second level direction straight line screening comprises the following steps：
S426, setElement number be k, it is rightIn each element(wherein θiForAngle, i=1,2,
3 ..., k), a power w is seti, wiFor integer；SetThe 1st elementFor current optimal direction straight line, optimum orientation is remembered
Opt is designated as under the angle theta of straight line, i.e., current opt=1；
S427, investigationWith object boundary intersection point, the span [x of abscissa is found intersectionmin,xmax], wherein xminWith
xmaxThe respectively minimum value and maximum of intersection point abscissa；
It is S428, rightIn each elementJ=2,3,4 ..., k, make：
S4281, by current straight lineWith current best straight lineInitial weight be disposed as 0, i.e. wj=wopt=0；
S4282, to [xmin,xmax] in the range of each x make following operation：Make the hanging down for (x, 0) with transverse axis intersecting point coordinate
Straight straight line, ask the straight line withWithThe intersection point E of two straight linesjAnd Eopt；If EjAnd EoptOrdinate be respectively yjAnd yoptIf,
yj＞ yopt, wjFrom increasing 1；Otherwise woptFrom increasing 1；
S4283, seek wjWith woptPoor difw, i.e. difw=wj-wopt；
If S4284, difwMore than 1, then opt=j is made；
If S4285, difwAbsolute value be less than or equal to 1, compareWithThe angle theta of two straight linesjWith θoptIf, θjPhase
For θoptCloser to horizontal direction, then opt=j is made；
S429, determine straight lineFor optimum orientation straight line.
The beneficial effects of the invention are as follows：The inventive method does not make excessive requirement to the shape of target, so as to reduce to mesh
Mark the dependence of extraction process；By the screening of two-stage direction straight line, conventional method is compensate on vertically and horizontally orientation is distinguished
Deficiency, improve estimated accuracy, and evaluated error is reduced in the case of long and short primary edge length difference is smaller；In addition,
The inventive method computation complexity is low, and estimation is quick.
Brief description of the drawings
Fig. 1 is azimuth of target method of estimation flow chart of the invention；
Fig. 2 is the flow chart for screening optimum orientation straight line of the invention；
Fig. 3 is estimated result schematic diagram of each method to image HB19820.001 azimuth of targets；
Fig. 4 is estimated result schematic diagram of each method to image HB03790.004 azimuth of targets.
Embodiment
Below in conjunction with the accompanying drawings technical scheme is further illustrated with specific embodiment.
MSTA of the test image of the embodiment of the present invention both from the advanced research project office (DARPA) of U.S. national defense
(Moving and Stationary Target Acquisition and Recognition) standard data set.With MSTAR
In image HB19820.001 (such as Fig. 3 (a) shown in) exemplified by illustrate.Image correspondence model E71 BRDM ground appearance
Mark, the angle of pitch of imaging is 17 °.
As shown in figure 1, the SAR image azimuth of target method of estimation screened based on direction straight line of the present invention, including with
Lower step：
S1, target is extracted, input picture size is 128 × 128, with image partition method by the SAR mesh in input picture
Mark is extracted, and is expressed as the objective matrix O of a two-value, and size is 128 × 128；Objective matrix O each point correspondence
One pixel of image, its value is that the 1 expression pixel is point (being referred to as target point) in target, is the 0 expression pixel
For non-targeted point.
S2, extraction border, to each point of O in objective matrix, it is target in 5 × 5 region to count size around it
The number of point, if target point number is less than default adjacent region threshold Tn=22 (22≤Tn≤ 24), then the point is judged as boundary point,
Otherwise it is non-boundary point；By object boundary information be expressed as a size be 128 × 128 binary border matrix A, A line numbers and
Columns is respectively equal to the width and length of image, and a pixel of its each point correspondence image, its value represents the picture for 1
Vegetarian refreshments is boundary point, is that the 0 expression pixel is non-boundary point.
S3, determine all directions straight line, including following sub-step：
S31, in target image plane make the straight line { L that one group of width is two pixelsθ,d, wherein θ be straight line with it is vertical
The angle in direction, 0 ° of ＜ θ≤180 °, θ sampling interval Δθ=0.5 (0 ＜ Δsθ≤1)；D is the top left corner apex of image to directly
The distance of line,D sampling interval Δd=1 (0 ＜ Δsd≤1)；
S32, every straight line L of statisticsθ,dWith the intersection point number of object boundary；
S33, to each θ, seek straight line most with boundary intersection number in all straight lines that angle is θ, define the straight line
For θ direction straight line lθ, remember lθIntersection point number with border is zθ；The present embodiment correspondence angle theta is 0.5,1.0,1.5 ...,
180；Try to achieve direction straight line l0.5, l1.0, l1.5..., l180；Intersection point number z corresponding to themθRespectively；24,28,23 ...,
28。
S4, screening optimum orientation straight line, including following sub-step：
S41, seek zθMaximum, be designated as zmax, i.e.,
Remember zmaxCorresponding angle is θmax；The z of the present embodimentθMaximum zmaxFor 31, corresponding angle thetamaxFor
92.5；
If S42, θmaxLess than 20 degree, it is determined that straight line lθmaxFor optimum orientation straight line；Otherwise travel direction straight line is screened,
Seek optimum orientation straight line；The θ of the present embodimentmaxMore than 20 degree, therefore travel direction straight line is needed to screen；Described direction straight line
Screening includes the screening of first order direction straight line and the screening of second level direction straight line, described first order direction straight line screening including with
Lower step：
S421, setting intersection point number set C1 and C2, candidate direction straight line setC1, C2 andIt is ordered set,
It is 0 that three, which are gathered the element number included, when initial；
S422, by all intersection point number zθIt is added to by order from big to small in C1, after element addition terminates, C1 is wrapped altogether
Containing 360 elements；
The element counter i that S423, setting initial value are 1；
S424, take the i-th element c in C1i, judge whether to meet following two conditions：
Condition 1：ci＞ η × 31, wherein η are set to 0.85 (0.7 ＜ η ＜ 0.9)；
Condition 2：C2 is empty set or ciCorresponding angle is poor with angle corresponding to each element in current C2
Absolute value is more than Δ, and wherein Δ is set to 20 (15 ＜ Δs ＜ 25)；
If condition 1 and condition 2 are met simultaneously, by ciIt is added to C2 afterbody, and by ciCorresponding direction straight line is added
To candidate direction straight line setAfterbody；Do not operated if being unsatisfactory for；
If S425, i ＜ 360, counter i adds 1, step S424 is gone to, the screening of second level direction straight line is otherwise carried out；
Obtained intersection point number set C2={ 31,29,28 }, candidate direction straight line collection are screened by first order direction straight line
CloseIts corresponding angle theta1=92.5, θ2=86.0, θ3=0.5；
Described second level direction straight line screening comprises the following steps：
It is S426, currentElement number be 3, it is rightIn each element(wherein θiForAngle, i=1,2,
3), a power w is seti, wiFor integer；SetThe 1st elementFor current optimal direction straight line, optimum orientation straight line is remembered
Angle theta under be designated as opt, i.e., current opt=1；
S427, investigationWith object boundary intersection point, the span for trying to achieve intersection point abscissa is [54,69]；
It is S428, rightIn each elementJ=2,3, make following iteration twice：
S4281, by current straight lineWith current best straight lineInitial weight be disposed as 0, i.e. wj=wopt=0；
S4282, make following operation to each x in the range of [54,69]：It is the vertical of (x, 0) to make with transverse axis intersecting point coordinate
Straight line, ask the straight line withWithThe intersection point E of two straight linesjAnd Eopt；If EjAnd EoptOrdinate be respectively yjAnd yoptIf, yj
＞ yopt, wjFrom increasing 1；Otherwise woptFrom increasing 1；
S4283, seek wjWith woptPoor difw, i.e. difw=wj-wopt；
If S4284, difwMore than 1, then opt=j is made；
If S4285, difwAbsolute value be less than or equal to 1, compareWithThe angle theta of two straight linesjWith θoptIf, θjPhase
For θoptCloser to horizontal direction, then opt=j is made；
S429, determine straight lineFor optimum orientation straight line；
To first time iteration, in the present embodiment, there are j=2, current opt=1, obtained by step S4281 and S4282
wj=0, wopt=w1=14, difw=wj-wopt=-14, because of difwValue be unsatisfactory for condition in step S4284 and S4285, therefore
Without corresponding operating, opt value keeps constant；
To second of iteration, in the present embodiment, there are j=3, current opt=1, obtained by step S4281 and S4282
wj=13, wopt=w1=1, difw=wj-wopt=13, because of difwMore than 1, the condition in step S4284 is met, then makes opt=
3；And in step S4285, because of difwAbsolute value be more than 1, be unsatisfactory for its condition, therefore without corresponding operating, opt value is protected
Hold constant；
Therefore the opt=3 finally given, therefore determine straight line in step S429For optimum orientation straight line.
S5, optimum orientation straight line angle theta3For 0.5, therefore azimuth of target to be estimated is 0.5 degree.
The effect of the present invention is compared with boundary rectangle method and primary edge method below.Test machine is Intel (R)
I5-5300U processors, dominant frequency is 2.3GHz.Test is divided to free hand drawing test and the step of integration test two to carry out.In all tests, the
One step extracts target using conventional threshold segmentation method.
(1) free hand drawing is tested
Free hand drawing test is with image HB19820.001 (as shown in Fig. 3 (a)) and image HB03790.004 (such as Fig. 4 (a) institutes
Show) exemplified by illustrate.Image HB03790.004 corresponds to model c71 BTR70 ground targets, and the angle of pitch of imaging is
17°.Especially, when carrying out orientation angular estimation to above two images, the implementation procedure of the inventive method covers two kinds not
Same program branch：To image HB19820.001, in step S42, because being unsatisfactory for θmaxCondition less than 20 degree, program is performed
Direction straight line screening step；And to image HB03790.004, in step S42, because meeting θmaxCondition less than 20 degree, program is jumped
Direction straight line screening step has been crossed, and then has directly determined direction straight line.
Table 1 is that the inventive method and boundary rectangle method, the azimuth estimated result of primary edge method compare.It can be seen that,
The evaluated error of the inventive method is much smaller than boundary rectangle method and primary edge method method.To HB19820.001 images, external square
Shape method and primary edge method are generated in the estimation in vertically and horizontally orientation to be obscured, so as to cause very big evaluated error；
To HB03790.004 images, because long and short primary edge length difference is smaller, the evaluated error of primary edge method is larger.And it is right
Both the above situation, the inventive method can obtain accurate estimation.
The each method of table 1 compares the azimuth of target estimated result of single image
The pattern that Fig. 3 and Fig. 4 sets forth the estimated result of table 1 is represented, wherein the azimuth direction target estimated
The straight line of exterior measuring is represented.Fig. 3 is estimated result schematic diagram of each method to image HB19820.001 azimuth of targets, wherein
Fig. 3 (a) is original HB19820.001 images, and Fig. 3 (b) is boundary rectangle method to the estimated result of HB19820.001 images, Fig. 3
(c) it is estimated result of the primary edge method to HB19820.001 images, Fig. 3 (d) is that the inventive method is schemed to HB19820.001
The estimated result of picture；
Fig. 4 is estimated result schematic diagram of each method to HB03790.004 image goal position angles, and wherein Fig. 4 (a) is original
Beginning HB03790.004 image, Fig. 4 (b) be boundary rectangle method to the estimated result of HB03790.004 images, Fig. 4 (c) is leading
Boundary method is to the estimated result of HB03790.004 images, and Fig. 4 (d) is estimation knot of the inventive method to HB03790.004 images
Really；
(2) integration test
Integration test have selected the species of BRDM, BTR70 and BMP (SN9563) three that the angle of pitch in MSTAR databases is 17 °
Type target is tested.Wherein BRDM types have 298 width target images, and BTR70 types and BMP (SN9563) type respectively have
233 width.To these test image the inventive method and boundary rectangle method, primary edge method and 2011《Computer application》
Upper issue《The SAR azimuth of target methods of estimation converted based on primary edge Radon》The method that (document 1) is proposed carries out angle
Degree estimation, its result is as shown in table 2.Number of targets of the absolute error of orientation angular estimation in the range of 5 ° and 10 ° is listed in table
Mesh accounts for the ratio of general objective number, the average of absolute error and standard deviation, run time etc..From the point of view of the accuracy of estimation, this
Inventive method evaluated error is smaller, and much smaller than boundary rectangle method and primary edge method method.All images are averaged, this
It is respectively 91.1% and 98.3% that inventive method estimation absolute error, which is less than 5 ° and the ratio less than 10 °, is all substantially better than other
Method.From the point of view of run time, the inventive method estimating speed is fast, suitable with primary edge method, and is significantly faster than that boundary rectangle
Method.It should be noted that the data of " improvement primary edge " method carry out document 1 in table.In theory, the time-consuming of this method should be with
Quite but data are much larger than this experimental result in table for former " primary edge " method time-consuming, and this is mainly due in the first step
In Objective extraction, document 1 employs increasingly complex method；In addition, document 1 is different from the machine that this experiment test is used,
It result in the difference of data.
The each method of table 2 compares the estimated result of sample image azimuth of target
One of ordinary skill in the art will be appreciated that embodiment described here is to aid in reader and understands this hair
Bright principle, it should be understood that protection scope of the present invention is not limited to such especially statement and embodiment.This area
Those of ordinary skill can make according to these technical inspirations disclosed by the invention various does not depart from the other each of essence of the invention
Plant specific deformation and combine, these deformations and combination are still within the scope of the present invention.
Claims (3)
1. a kind of SAR image azimuth of target method of estimation screened based on direction straight line, it is characterised in that including following step
Suddenly：
S1, target is extracted, the SAR Objective extractions in input picture are come out with image partition method, two-value is expressed as
Objective matrix, the line number and columns of the matrix are respectively equal to the width and length of image, each point correspondence image of matrix
One pixel, its value is that the 1 expression pixel is target point, is that the 0 expression pixel is non-targeted point；
S2, extraction border, to each point in objective matrix, count the number of target point in its peripheral region, if target point
Number is less than default adjacent region threshold, then judges the point as boundary point, be otherwise non-boundary point；Object boundary information is expressed as
One binary border matrix, the line number and columns of the matrix are respectively equal to the width and length of image, each point pair of matrix
Answer a pixel of image, its value is that the 1 expression pixel is boundary point, be that the 0 expression pixel is non-boundary point；
S3, determine all directions straight line, including following sub-step：
S31, in target image plane make the straight line { L that one group of width is two pixelsθ,d, wherein θ is straight line and vertical direction
Angle, 0 ° of ＜ θ≤180 °, θ sampling interval is Δθ, 0 ＜ Δsθ≤1；D for image top left corner apex to straight line distance,Wherein p, q are respectively the line number and columns of boundary matrix, and d sampling interval is Δd, 0 ＜ Δsd≤1；
S32, every straight line L of statisticsθ,dWith the intersection point number of object boundary；
S33, to each θ, seek straight line most with boundary intersection number in all straight lines that angle is θ, define the straight line for θ
Direction straight line lθ, remember lθIntersection point number with border is zθ；
S4, screening optimum orientation straight line, including following sub-step：
S41, seek zθMaximum, be designated as zmax, i.e.,
<mrow>
<msub>
<mi>z</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
<mi>&theta;</mi>
</munder>
<msub>
<mi>z</mi>
<mi>&theta;</mi>
</msub>
</mrow>
Remember zmaxCorresponding angle is θmax；
If S42, θmaxLess than 20 degree, it is determined that straight lineFor optimum orientation straight line；Otherwise travel direction straight line is screened, and is sought most
Good direction straight line；
S5, the angle for determining optimum orientation straight line are azimuth of target to be estimated.
2. the SAR image azimuth of target method of estimation according to claim 1 screened based on direction straight line, its feature is existed
In, in described step S2, in statistics objective matrix in each peripheral region during the number of target point, the area size of statistics
For 5 × 5 pixels.
3. the SAR image azimuth of target method of estimation according to claim 1 screened based on direction straight line, its feature is existed
In described step S42 direction straight line screening includes the straight line screening of first order direction and the screening of second level direction straight line, described
The screening of first order direction straight line comprise the following steps：
S421, setting intersection point number set C1 and C2, candidate direction straight line setC1, C2 andIt is ordered set, when initial
It is 0 that three, which are gathered the element number included,；
S422, by all intersection point number zθIt is added to by order from big to small in C1, if after element addition terminates, C1 includes p altogether
Individual element；
The element counter i that S423, setting initial value are 1；
S424, take the i-th element c in C1i, judge whether to meet following two conditions：
Condition 1：ci＞ η zmax, wherein 0.7 ＜ η ＜ 0.9；
Condition 2：C2 is empty set or ciThe poor absolute value of corresponding angle and angle corresponding to each element in current C2
More than Δ, 15 ＜ Δs ＜ 25；
If condition 1 and condition 2 are met simultaneously, by ciIt is added to C2 afterbody, and by ciCorresponding direction straight line is added to time
Select direction straight line setAfterbody；Do not operated if being unsatisfactory for；
If S425, i ＜ p, counter i add 1, step S424 is gone to, the screening of second level direction straight line is otherwise carried out；
Described second level direction straight line screening comprises the following steps：
S426, setElement number be k, it is rightIn each elementWherein θiForAngle, i=1,2,3 ..., k, if
Put a power wi, wiFor integer；SetThe 1st elementFor current optimal direction straight line, the angle theta of optimum orientation straight line is remembered
Under be designated as opt, i.e., current opt=1；
S427, investigationWith object boundary intersection point, the span [x of abscissa is found intersectionmin,xmax], wherein xminAnd xmaxRespectively
For the minimum value and maximum of intersection point abscissa；
It is S428, rightIn each elementMake：
S4281, by current straight lineWith current best straight lineInitial weight be disposed as 0, i.e. wj=wopt=0；
S4282, to [xmin,xmax] in the range of each x make following operation：It is the vertical straight of (x, 0) to make with transverse axis intersecting point coordinate
Line, ask the straight line withWithThe intersection point E of two straight linesjAnd Eopt；If EjAnd EoptOrdinate be respectively yjAnd yoptIf, yj＞
yopt, wjFrom increasing 1；Otherwise woptFrom increasing 1；
S4283, seek wjWith woptPoor difw, i.e. difw=wj-wopt；
If S4284, difwMore than 1, then opt=j is made；
If S4285, difwAbsolute value be less than or equal to 1, compareWithThe angle theta of two straight linesjWith θoptIf, θjRelative to
θoptCloser to horizontal direction, then opt=j is made；
S429, determine straight lineFor optimum orientation straight line.
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