CN104655041B - A kind of industrial part contour line multi-feature extraction method of additional constraint condition - Google Patents
A kind of industrial part contour line multi-feature extraction method of additional constraint condition Download PDFInfo
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Abstract
The present invention provides a kind of industrial part contour line multi-feature extraction method of additional constraint condition, it is characterized in that using the contour line feature of traditional method for extracting as initial value, then circular arc and the constraint conditions such as straight line is tangent, adjacent circular arc and circular arc are tangent in additional outlines, and the error equation of parts profile line multiple features primary condition and constraint condition is established on this basis, realize that the Global Iterative Schemes of contour feature accurately solve, thus each feature that profile will be formed（Such as straight line, circular arc and circle）Accurate segmentation identification is carried out, the parameter of each feature is obtained.The present invention focuses on the precision for improving parts profile line drawing, as a result proves that the introducing of the constraint relationship can effectively improve the accuracy of contour line multi-feature extraction.
Description
Technical field
The present invention relates to a kind of multi-feature extraction methods of the industrial part contour line of additional constraint condition, belong to industry zero
Part field of visual inspection.
Background technique
With making constant progress for computer and computer vision etc., in the detection of current industrial part,
The demand for replacing human eye to detect part machine vision is more more and more urgent.Have using Computer Vision Detection many excellent
Point, for example detection accuracy is high, speed is fast, contactless, accuracy is also relatively good, along with hardware such as current computer, video cameras
It is inexpensive, and the price of human resources constantly increases, and in contrast, replaces human eye to detect part using machine vision
Cost can be greatly lowered, improve the efficiency of production, and then improve the competition and survival ability of enterprise.
In part vision detection process, after Edge extraction, from the available face wheel of part image to be measured
Wide pixel collection, the contour pixel point set for belonging to the same pel may make up such as basic geometric graphic element of straight line, circular arc.Two
In dimension measurement when to parameter detectings such as part shape sizes, typically according to the position of the size of pel, shape and each pel
It sets relationship etc. to be detected, therefore must first identify the feature of each pel of component part profile before detecting.In three-dimensional measurement,
Also there is the research that vision measurement reconstruction is carried out using the contour line of part, so carrying out accurate Ground Split knowledge to profile element figure
It is not a committed step in vision inspection process, will have a direct impact on the accuracy of part dimension measurement.Lot of domestic and international scholar
This is conducted extensive research, such as Hsin-Teng Sheu, Wu-Chih Hu, Alexander Kolesnikov, Wu Ji
Steel et al. combines the methods of curvature, standoff height, merging division to extract feature angle point, realizes and is retouched with pels such as circular arc and straight lines
State the characteristic information of profile.But existing intrinsic relationship between pel is not made full use of during the extraction process（Such as tangent relation）,
This necessarily will affect the accuracy of angle point grid.The precision for improving contour line multi-feature extraction, is that industrial part detection field mentions
High measurement accuracy technical problem urgently to be resolved.
Therefore the characteristics of considering industrial part processing, the present invention are comprehensively utilizing existing contour feature angular-point detection method
On the basis of be added relevant constraint, realize using straight line and circular arc and Accurate Segmentation carried out to profile, how special improve contour line
Levy the precision extracted.
Summary of the invention
It is insufficient that present invention aims to solve the prior art, improves in industrial part vision-based detection and wants commonly used profile
Line multi-feature extraction precision provides the multi-feature extraction scheme for the additional constraint condition of industrial part contour line.Mentioning
Take on the basis of the initial multiple features of parts profile line in additional outlines circular arc with straight line is tangent, adjacent circular arc and circular arc are tangent etc. about
Beam condition is iterated accurate extraction to the feature on profile, will form each feature such as straight line, circular arc and the circle of profile, carries out
Accurate segmentation identification, obtains the parameter of each feature.
In order to solve the above-mentioned technical problem, present invention employs following technical solutions：
The industrial part contour line multi-feature extraction method of additional constraint condition, this method comprises the following steps：
（1）The multiple features of industrial part contour line are extracted as the initial of the method for the present invention from actual parts image
Value；
（2）The foundation of multiple features primary condition and constraint conditional error equation on parts profile line；
（3）The whole accurate solution of the contour line more characteristic parameters of attached constraint condition.
To realize goal of the invention, the contour line multi-feature extraction method of additional constraint condition, in step（1）In, due to view
Feel that detection system generally can all be arranged to semi-enclosed environment, there is good illumination condition, the silhouette target and background face of acquisition
The contrast of color is larger, it is possible to obtain initial profile using traditional Boundary extracting algorithm, then be tracked using eight neighborhood
It obtains according to from the tactic contour pixel point set of origin-to-destination, before extracting contour feature angle point, for reduction operation
Amount, the method removal for using neighborhood value to compare can not be the profile point of angle point, and utilize the rotation introduced in existing document
Redundancy angle point caused by constant angle point determination method and the determination method removal straight line resampling based on angle.But on circular arc still
So there are many redundancy angle points to need to remove, minimizing technology is：Angle point is divided into two types according to angle point neighborhood characteristics first, the
One is mutation angle points（Type）, angle point two sides curved section belongs to different characteristic, and second is smooth angle point（Type）,
It may may belong to same feature for the points of tangency or the redundancy angle point on circular arc, two sides curved section of straight line and circular arc,
It may need to remove；Then using adaptiveCurvature Methods distinguish angle point type.
Will to profile element figure carry out identification by stages, the type of pel be also predefined, that is, judge pel be straight line or
Circular arc.The present invention will differentiate the primitive types between two profile angle points based on standoff height method, to realize further by angle
Point is divided into following four type：（1）Type, i.e. straight line are to straight line (line to line)；（2）Type, i.e. circular arc are to straight line
( arc to line)；（3）Type, i.e. straight line are to circular arc (line to arc)；（4）Type, i.e. circular arc are to circular arc (arc
to arc)。
Consider and frontType andAngle point is finally divided into following a few classes by type combination, the present invention：,,,,,WithSeven subclasses.Such asIndicate the smooth angle of connection circular arc and straight line
Point,Indicate the mutation angle point of connection circular arc and straight line.For flatness feature angle point, then its both ends curved section is possible to
Belong to the same feature and is merged.
The identification of pel parameter is determined according to the angle point type of contour segment two-end-point, but in feature Corner Detection
Inevitably have omission, such as mistakeAngle point is followed byAngle point is known according to logical relationWithBetween certainly existAngle point, so at this moment needing to be inserted into therebetweenAngle point, method are as follows：It is connected with straight lineAngle point andAngle point,
Then fromAngle point andThe two angle point lines are found in profile point between angle point apart from farthest point, i.e., the point is slotting
EnterAngle point.
The case where for there is continuous circular arc feature, needs to judge whether it can be merged each other or need to be divided：It is first
First estimate the center of circle and the radius of circular arc；Then every to center of circle distance and the sum and this section of arc length of radial difference are utilized
RatioCircular arc discriminant function, merge according to following criterion or division circular arc：After two sections of circular arcs mergeValue
More hour then merges both ends circular arc, when insertion oneIt is calculated after angle pointValue more hour then divides circular arc；Finally
To the result of accurate arc fragmenting.
After identifying the feature angle point on profile, parts profile can use straight line and circular arc to be indicated.Type
WithCurved section between type angle point is expressed with straight line,Type andCurved section between type angle point is expressed with circular arc.
To realize goal of the invention, the contour line multi-feature extraction method of additional constraint condition, in step（2）In, due to
There are some researches prove only use straight line and circular arc can freedom of expression profile information well, so the present invention is to include straight line and circle
The profile of arc describes how to carry out the combined extractings of more primitive features of additional constraint condition, and detailed process includes primary condition
The foundation of error equation and constraint conditional error equation.
1）Primary condition.
（1）Linear equation expression formula is：
（1）
Then its error equation is：
（2）.
（2）Round equation expression formula is：
（3）
Then its error equation is：
（4）
The above two classes error equation is indicated with matrix, is obtained：
（5）
Wherein：；Indicate all
The vector of straight line parameter composition,Indicate the vector of all Circle Parameters compositions,Indicate all straight line observation error system of equations
Array at coefficient matrix,For corresponding constant item vector,It is then corresponding residual vector；Indicate all circle observations
The coefficient matrix of error equation coefficient composition,For corresponding constant item vector,It is then corresponding residual vector.
2）Constraint condition.
（1）For linear equation general type,What is represented is the normal vector of straight line, so straight line parameter
WithMeet：
（6）
It linearizes available：
（7）
To this kind of constraint conditions, i.e., all formulas（7）, being write as matrix form is：
（8）
WhereinFor its coefficient matrix,For corresponding constant vector.
（2）Circular arc and the tangent constraint condition of straight line：
（9）
It enables（10）
Then its linearised form is：
（11）
Matrix form can be write as to such constraint condition：
（12）
WhereinWithRespectivelyWithCorresponding coefficient matrix,It is corresponding constant vector.
（3）Circular arc and the tangent constraint condition of circular arc：
Two arc parameterss are enabled to be respectively,, then its Tangent Condition be（It simultaneously include interior
Cut with it is circumscribed）：
（13）
Wherein：（14）
The linearised form of the constraint condition is：
（15）
Write these constraint conditions as matrix form（All（Formula 15）The constraint condition of form）, then for
（16）
WhereinFor coefficient matrix,It is then constant vector.
To realize goal of the invention, the contour line multi-feature extraction method of additional constraint condition, in step（3）In, it builds first
The vertical parameter Estimation overall adjustment model with constraint condition, to realize the whole accurate solution of contour line more characteristic parameters, tool
Body process is as follows：
It enables, according to above error equation and constraint condition, the present invention is used
Parameter Estimation adjustment Models can be expressed as follows（Using unit weight matrix）：
（17）
Introduce the Lagrange coefficient of auxiliary, it is as follows to construct Suzanne Lenglen day function：
（18）
The criterion of extreme value is sought using Lagrange, it is rightSeeking the partial derivative of parameters and enabling it is zero, can be with
Obtain following normal equation：
（19）
All profile points are pressed into formula as the case may be（5）,（8）,（12）,（16）Calculate matrixWithThen matrix substitutes into（Formula 19）, the accurate parameters value for obtaining each primitive features of profile can be iteratively solved.
Detailed description of the invention
Fig. 1 is the part multi-feature extraction Hardware Design structural schematic diagram of the attached constraint condition of embodiment.
Fig. 2 is the part multi-feature extraction hardware system pictorial diagram of the attached constraint condition of embodiment.
Operating process when Fig. 3 is the contour line multiple features detection of attached constraint condition.
Fig. 4 is that the contour line multiple features of attached constraint condition accurately extract embodiment process.
Fig. 5 is that circular arc divides and merges schematic diagram during profile multiple features initial value extracts.
Fig. 6 is analog image profile pel Feature corner extraction result.
Fig. 7 is actual parts image outline pel multi-feature extraction result and details enlarged drawing.
Fig. 8 is the corner location comparison extracted under not attached constraint condition and appendix agreement beam condition.
Fig. 9 is the part image profile pel multi-feature extraction result detail view for having the adjacent situation of circular arc.
Figure 10 is that not attached constraint condition extracts result and attached constraint condition extracts Comparative result.
In figure：1 be telecentric lens, 2 be CCD camera, 3 be LED light source, 4 be work piece platform, 5 be column, 6 be computer,
7 it is workbench, 8 be workpiece, 9 is height adjustment knob.
Specific embodiment
For the sake of ease of implementation, the embodiment of the present invention provides the part wheel of complete attached constraint condition since shooting
Profile multi-feature extraction actual mechanical process.Wherein except style of shooting and the extraction of parts profile multiple features angle point initial value etc. are existing
Other than technology, on the basis of the initial profile angle point extracted to original image obtained by shooting part
Reason realizes the new solution for improving part multiple features detection accuracy, is the scheme that can be realized automatically using computer means.
Illustrate technical solution of the present invention below in conjunction with drawings and examples.
Referring to attached drawing 1, the parts profile line multi-feature extraction detection hardware system of embodiment is consisted of the following parts：
（1）Camera with telecentric lens.With USB or 1394 data lines, computer is transferred data in real time, through reality
It is negligible to verify bright telecentric lens distortion；
（2）Computer.The equipment for connecting camera, the part multi-feature extraction method that the present invention provides attached constraint condition can adopt
It is loaded on computer with software technology；
（3）Backlight.The backlight of embodiment is LED light source, and the brightness of LED is adjusted in an external adjustable power line.Back
Scape light refers to that camera and light source are placed on a kind of not ipsilateral lighting method of measurand, and the image which obtains is mostly not
The projection of transparent substance, the part being blocked are black, otherwise to be white, therefore it is in sharp contrast on image, edge is prominent, therefore special
Not Li Yu edge detection, be suitable for opaque article shape recognition and position dimension and the fields such as measure；
（4）Part platform.For putting detected industrial part；
（5）Total bracket.It is used to support and fixed camera, camera lens, backlight, part platform.Referring to attached drawing 2, specific implementation
When adjustable bracket, so as to the industrial part on the alignment lens part platform of camera, backlight can be equably industry
The clear acquisition of parts profile image provides light.
Operating process specific steps when detection are referring to attached drawing 3：Plane industrial part to be detected is placed on part platform
Table top on, back light source brightness is adjusted by adjustable power line（Brightness is properly then not required to adjust）, with camera to industry after mixing up
Part is photographed.Part original image is obtained on shooting industrial part, is connected by camera with intercomputer and is transferred to calculating
Machine, computer execute appendix agreement on the basis of in image basis using the initial parts profile Feature corner extraction in existing document
After the profile multiple features detection of beam condition, output test result.
The parts profile multiple features detection technique scheme of additional constraint condition performed by computer of the embodiment of the present invention is such as
Under.
Step 1. obtains characteristic angle on profile from actual parts image, using contour line Feature corner extraction method
The initial value of point, using obtained initial profile line feature as the initial value of the method for the present invention.
Step 1.1, the extraction and identification of parts profile line segment segmentation angle point.
Since vision detection system generally can all be arranged to semi-enclosed environment, there is good illumination condition, so it is obtained
Generally all preferably, the contrast between target and background is big, so being extracted using image edge for the quality of image of the object to be measured taken
Algorithm carries out the initial profile that part can be obtained after edge thinning again；It is obtained after obtaining initial profile using eight neighborhood tracking
It takes according to from the tactic contour pixel point set of origin-to-destination；Before extracting contour feature angle point, to reduce operand,
First classified in advance profile point using the method for neighborhood value comparison, on the contrary it will not be possible to remove for the profile point of angle point, to what is remained
Redundancy caused by profile point is removed using the angle point determination method of invariable rotary and based on angle determination method because of straight line resampling
Angle point.
Still many redundancy angle points need on the circular arc of the angle point grid result obtained after above-mentioned steps further
Removal.Minimizing technology is：Angle point is divided into two types according to angle point neighborhood characteristics first, the first is mutation angle point（Class
Type）, angle point two sides curved section belongs to different characteristic, and second is smooth angle point（Type）, it may be straight line and circular arc
Redundancy angle point in points of tangency or circular arc, two sides curved section may belong to same feature, it may be necessary to remove；Then it utilizes
AdaptivelyCurvature Methods distinguish angle point type.
Will to profile element figure carry out identification by stages, the type of pel be also predefined, that is, judge pel be straight line or
Circular arc.The present invention will differentiate the primitive types between two profile angle points based on standoff height method, to realize further by angle
Point is divided into following four type：（1）Type, i.e. straight line are to straight line (line to line)；（2）Type, i.e. circular arc are to straight line
( arc to line)；（3）Type, i.e. straight line are to circular arc (line to arc)；（4）Type, i.e. circular arc are to circular arc (arc
to arc)。
Consider and frontType andAngle point is finally divided into following a few classes by type combination, the present invention：,,,,,WithSeven subclasses.Such asIndicate the smooth angle of connection circular arc and straight line
Point,Indicate the mutation angle point of connection circular arc and straight line.
Step 1.2, in industrial part common element figure parameter identification.
After identifying the feature angle point on profile, so that it may by parts profile straight line and arc representation.If feature
A possibility that angle point is mutation angle point, then its both ends curved section does not merge, if feature angle point is smooth type, angle point two
End curved section is then likely to belong to the same feature, it is possible to be merged.Type andCurved section straight line table between type angle point
It reaches,Type andCurved section between type angle point is expressed with circular arc, needs to be inserted into new angle if being unsatisfactory for both of these case
Point.
Step 1.2.1, linear feature differentiate.
The identification of pel parameter is determined according to the angle point type of contour segment two-end-point, but in feature Corner Detection
Inevitably have omission, such as mistakeAngle point is followed byAngle point is known according to logical relationWithBetween certainly existAngle point needs to be inserted into therebetween at this timeAngle point, method are：It is connected with straight lineAngle point andAngle point, then fromAngle point andThe two angle point lines are found in profile point between angle point apart from farthest point, i.e., the point is insertion
Angle point.Angle point * on profileWith angle point* the line segment between is linear feature（* it indicatesOr）, quasi- with linear equation
It closes.
Step 1.2.2, the segmentation of circular arc with merge.
In view of continuous circular arc feature has a possibility that merging and segmentation simultaneously, therefore continuous circular arc is needed to judge
Whether it can be merged each other or need to be divided：The center of circle and the radius of circular arc are estimated first；Then every to circle is utilized
The ratio of the sum and this section of arc length of the distance and radial difference of the heartCircular arc discriminant function, merge according to following criterion
Or division circular arc：After two sections of circular arcs mergeIt is worth more hour, then merges both ends circular arc；When insertion oneAfter angle point,
It is calculatedValue more hour then divides circular arc.
Specific step is as follows for the split degree method of circular arc in the present invention：
Such as attached drawing 5（a）It is shown, it usesIndicate one section of continuous arc section, wherein
WithFor,,,Or,Indicate i-th sectionAngle point, then：
（1）Utilize equation of a circle pairBetween profile point be fitted to obtainThe center of circle of this section of circular arc and
Radius, and calculate itValue enables,；
（2）It willIt is added, utilizesBetween the profile point center of circle of the Fitting Calculation circular arc and radius again, that is, count
It calculatesThe center of circle and radius, and calculate itValue；
（3）If, then mergeFor one section of circular arc, and enable,, then return to step 2；Otherwise it enables；
（4）?Between be inserted intoIt divides this section of arc section, then calculatesThe center of circle and radius, and calculate itValue；
（5）If, explanationIt uniquely determines, then can jump directly to（7）Step；
（6）If, then,, otherwise it enables, return to（4）Step；
（7）?One new angle point of place's insertion, and removeBetween all angle points.Then followed by
It is continuous to determineWithBetween the case where：It enables, it is then return to the first step and judges newlyBetween circular arc merge
Situation is divided, until terminating.
As can be seen that step from above method（2）,（3）For merging circular arc, step（4）,（6）For dividing circle
Arc can reach two purposes of merging and segmentation simultaneously.Plane industrial part profile can directly make to come with the aforedescribed process
It realizes circular arc division or merges.
Step 2. has the contour line more characteristic parameters integrated solution of constraint condition, and calculating process is specific as follows.
1）Primary condition.
（1）Linear equation expression formula is：
（1）
Then its error equation is：
（2）.
（2）Round equation expression formula is：
（3）
Then its error equation is：
（4）
The above two classes error equation is indicated with matrix, is obtained：
（5）
Wherein：；Indicate institute
The vector being made of straight line parameter,Indicate the vector of all Circle Parameters compositions,Indicate all straight line observation error equations
The coefficient matrix of coefficient composition,For corresponding constant item vector,It is then corresponding residual vector；Indicate that all circles are seen
The coefficient matrix of error equation coefficient composition is surveyed,For corresponding constant item vector,It is then corresponding residual vector.
2）Constraint condition.
（1）For linear equation general type,What is represented is the normal vector of straight line, so straight line parameter
WithMeet：
（6）
It linearizes available：
（7）
To this kind of constraint conditions, i.e., all formulas（7）, being write as matrix form is：
（8）
WhereinFor its coefficient matrix,For corresponding constant vector.
（2）Circular arc and the tangent constraint condition of straight line：
（9）
It enables（10）
Then its linearised form is：
（11）
Matrix form can be write as to such constraint condition：
（12）
WhereinWithRespectivelyWithCorresponding coefficient matrix,It is corresponding constant vector.
（3）Circular arc and the tangent constraint condition of circular arc
Two arc parameterss are enabled to be respectively,, then its Tangent Condition be（It simultaneously include interior
Cut with it is circumscribed）：
（13）
Wherein：（14）
The linearised form of the constraint condition is：
（15）
Wherein,（16）
Write these constraint conditions as matrix form（All（Formula 15）The constraint condition of form）, then for
（17）
WhereinFor coefficient matrix,It is then constant vector.
3）Parameter Estimation overall adjustment model with constraint condition
It enables, according to above error equation and constraint condition, the present invention is adopted
Parameter Estimation adjustment Models can be expressed as follows（Using unit weight matrix）：
（18）
Introduce the Lagrange coefficient of auxiliary, it is as follows to construct Suzanne Lenglen day function：
（19）
The criterion of extreme value is sought using Lagrange, it is rightSeeking the partial derivative of parameters and enabling it is zero, can be with
Obtain following normal equation：
（20）
All profile points are pressed into formula as the case may be（5）,（8）,（12）,（17）Calculate matrixWithThen matrix substitutes into（Formula 20）, the accurate parameters value for obtaining each primitive features of profile can be iteratively solved.
In order to verify additional constraint condition proposed by the present invention contour line multi-feature extraction method validity, adopt respectively
It is qualitatively and quantitatively tested with analog image and actual parts image.
It is drawn in view of the true value of actual parts can not be obtained in actual tests, therefore according to known part size design drawing
It has made analog image and has carried out quantitative analysis and verifying to method proposed by the present invention.For analog image, the method for the present invention
It extracts result such as Fig. 6 (a), shown in 6 (b), includes 5 straight lines, 2 sections of circular arcs and 3 circles, wherein for the extraction knot of two sections of circular arcs
The extraction of values of fruit, attached constraint condition and not attached constraint condition is shown in Table 1 compared with board design value（x0、y0, r unit be pixel,
Sita unit is °）.It can be found that the introducing of constraint condition is so that extraction result is more accurate, thus quantitative from the comparison of table 1
Ground illustrates that the accurate extraction of parts profile line multiple features may be implemented in the method for the present invention.
Parts profile extraction is carried out to the actual parts image obtained in embodiment, as a result as shown in attached drawing 7,9.These knots
Fruit shows：Method proposed by the present invention can correctly extract the segmentation angle point between profile pel, even for continuous circular arc phase
The part of adjacent situation, can also accurately extract circular arc points of tangency as cut-point (such as attached drawing 9)；In addition from attached drawing 8,10
In the Detail contrast figure it can be seen that extraction position of the profile pel Image Segmentation Methods Based on Features angle point of additional constraint condition is more accurate reasonable.
When carrying out quality testing to part, result will be extracted and be compared with the design value of parts profile parameter, if it is poor
Value shows part quality qualification in the range of condition is allowed, otherwise illustrates that part quality is unqualified.Judging result is as inspection
Flow gauge as a result, can be exported by computer display apparatus, prompt to handle underproof part.
Claims (2)
1. the industrial part contour line multi-feature extraction method of additional constraint condition, it is characterised in that step is followed successively by：
(1) multiple features of industrial part contour line are extracted as initial value from actual industrial part image；
(2) multiple features primary condition and the foundation for constraining conditional error equation on parts profile line；
(3) the whole accurate solution of the contour line more characteristic parameters of attached constraint condition；
In step (2), describe how to carry out more primitive features of additional constraint condition with the profile comprising straight line and circular arc
Combined extracting, detailed process include primary condition error equation and constraint conditional error equation foundation：
1) primary condition
(1) linear equation expression formula is：
Ax+by+c=0 (1)
Then its error equation is：
V=xda+ydb+dc+ (ax+by+c) |0 (2)
(2) the equation expression formula of circle is：
Then its error equation is：
The above two classes error equation is indicated with matrix, is obtained：
V=AX-L (5)
Wherein：X1Indicate all straight lines
The vector of parameter composition, X2Indicate the vector of all Circle Parameters compositions, A1Indicate all straight line observation error equation coefficient compositions
Coefficient matrix, L1For corresponding constant item vector, V1It is then corresponding residual vector；A2Indicate all round observation error system of equations
Array at coefficient matrix, L2For corresponding constant item vector, V2It is then corresponding residual vector；
2) constraint condition
(1) for linear equation general type, what (a, b) was represented is the normal vector of straight line, so straight line parameter a and b are full
Foot：
a2+b2=1 (6)
It linearizes available：
2a·da+2b·db+0·dc+(a2+b2-1)|0≈0 (7)
To this kind of constraint conditions, i.e., all formulas (7), being write as matrix form is：
N1X1=C1 (8)
Wherein N1For its coefficient matrix, C1For corresponding constant vector；
(2) circular arc and the tangent constraint condition of straight line：
(ax0+by0+c)2-R2=0 (9)
Enable k=ax0+by0+c (10)
Then its linearised form is：
2kx0·da+2ky0·db+2k·dc+2ka·dx0+2kb·dy0-2R·dR+(k2-R2)|0≈0 (11)
Matrix form can be write as to such constraint condition：
N2X1+M2X2=C2 (12)
Wherein N1And M2Respectively X1And X2Corresponding coefficient matrix, C2It is corresponding constant vector；
(3) circular arc and the tangent constraint condition of circular arc：
Enabling two arc parameterss is respectively (x1, y1, R1), (x2, y2, R2), then it includes inscribe and circumscribed Tangent Condition is：
((R1+R2)2-D2)·((R1-R2)2-D2)=0 (13)
Wherein：
The linearised form of the constraint condition is：
Write these constraint conditions of formula (15) form as matrix form, then for
M3X2=C3 (16)
Wherein M3For coefficient matrix, C3It is then constant vector.
2. the industrial part contour line multi-feature extraction method of additional constraint condition as described in claim 1, which is characterized in that
In step (3), the parameter Estimation overall adjustment model with constraint condition is initially set up, to realize that contour line multiple features are joined
The whole accurate solution of number, detailed process is as follows：
It enablesAccording to primary condition error equation and conditional error equation is constrained,
The parameter Estimation overall adjustment model of use is as follows using weight unit expression matrix：
The Lagrange coefficient K of auxiliary is introduced, construction Suzanne Lenglen day function is as follows：
LG (X, K)=VTV+2KT(NX-W) (18)
Seek the criterion of extreme value using Lagrange, seeking the partial derivative of parameters to LG (X, K) and enabling it is zero, it is available such as
Under normal equation：
All profile points are calculated into matrix A, N, L and W matrix by formula (5), (8), (12), (16) as the case may be, then
It substitutes into the parameter Estimation overall adjustment modular form (19) with constraint condition, can iteratively solve and obtain each primitive features of profile
Accurate parameters value.
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