CN106122430B - A kind of fine module gear edge detection accuracy computation method of feature based image - Google Patents
A kind of fine module gear edge detection accuracy computation method of feature based image Download PDFInfo
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- CN106122430B CN106122430B CN201610659308.6A CN201610659308A CN106122430B CN 106122430 B CN106122430 B CN 106122430B CN 201610659308 A CN201610659308 A CN 201610659308A CN 106122430 B CN106122430 B CN 106122430B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/17—Toothed wheels
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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Abstract
The invention discloses a kind of fine module gear edge detection accuracy computation methods of feature based image.Steps are as follows for specific technical solution of the present invention：One, the characteristic function at involute gear edge is established；Two, the benchmark image of each feature of involute gear is built according to characteristic function；Three, the strategy and evaluation index of benchmark image edge detection effect assessment are established；Four, selection edge detection algorithm carries out edge detection, the deviation of deliberated index the quantization edge detection results and true edge of comprehensive each characteristic image to benchmark image.The present invention can be between quantized image edge detection results and true edge deviation, to select suitable edge detection detection method.In combination with the local edge of involute gear, multiple and different gear edge characteristic images is constructed, the workload smaller compared with the high-resolution benchmark image of structure gear entirety is lower to hardware requirement.
Description
Technical field
The invention belongs to technical field of image processing, and in particular to a kind of fine module gear edge inspection of feature based image
Survey accuracy computation method.
Background technology
Fine module gear is often referred to the gear that modulus is less than 1mm, is usually used in the transmission device in precision instrumentation.It is small
Gear due to the mechanical equivalent of light feature such as size is small, tooth socket gap is small, measured using conventional contact it is very difficult, and it is non-contacting
Vision measuring method can solve the problems, such as this from principle, and machine vision achievement, which is introduced gear measurement field, to be had become for one
A important development trend.Edge detecting technology is all the research hotspot in vision measurement field all the time, common edge inspection
Method of determining and calculating is the variation for examining or check gray scale in image pixel neighborhood, and edge is located in Pixel-level using single order, second derivative operator
In precision.With cannot be satisfied actual needs to the increase of required precision, the edge detection algorithm of Pixel-level in practical application, more
The research of sub-pixel algorithm is dedicated to come more experts.And numerous edge detection algorithms is faced, it is suitable how to select
The solution of detection method, this problem depends on the evaluation to edge detection results.
To evaluate the effect of edge detection and vision measurement, need, when carrying out edge detection, to quantify the essence of testing result
Degree.Judge the accuracy that various edge detection operators extract profile information, needs one to be capable of objective evaluation testing result
Standard.Objective edge evaluation method can be divided into two classes：One kind is no reference map evaluation method, this kind of method is normally based on side
The local correlations of edge neighborhood of pixels carry out the quality at evaluation image edge；Another kind of is the evaluation assessment based on reference map, is usually needed
Generate edge reference figure, then with this judge the missing inspection of testing result, false retrieval, again inspection and situations such as edge offset to complete
Evaluation.The objective edge evaluation method of two classes is compared, first kind method can not judge the false edge of edge detection；Second class side
Method can more comprehensively, reliably quantify the deviation of edge detection results, but relatively inefficient.
According to the evaluation criteria of national standard GBT 10095.1-2008 middle gear precision it is found that evaluate the ginseng of the accuracy of gear
Number result of calculation is micron level, therefore vision measurement system needs to provide high-resolution image to meet accuracy of gear evaluation
Demand.Therefore realize the evaluation of edge detection effect in fine module gear vision measurement system, difficult point is to build gear entirety
High-resolution benchmark image heavy workload, computer hardware is required high.
Invention content
The present invention is in order to overcome the above deficiency, it is proposed that a kind of fine module gear optimal edge detection of feature based image
It determines method, edge feature image is established according to the relevant design parameter and mathematical model of gear feature, and in this, as base
Prospective edge figure comes quantized image edge detection testing result and the deviation of true edge.
The present invention is as follows：
Step 1: establishing the characteristic function at involute gear edge.
In step 1, considers the diversity of fine module gear image border, need to establish multiple and different gear edges
Characteristic image, including bore circle, involute profile and tooth top corner.
The characteristic function of 1.1 structure endoporus circles, is expressed by round function formula：
(x-x0)2+(y-y0)2=r2 (1)
Wherein：
(x, y) is the edge coordinate that characteristic function indicates；
(x0,y0) be characteristic function central coordinate of circle, be build benchmark image design parameter；
R is the radius of circle that characteristic function indicates, is the design parameter for building benchmark image.
The characteristic function of 1.2 structure involute profiles is as follows by taking left flank profil as an example：
1.2.1 the starting point A (x of involute profile are determineda,ya) and involute gear geometric center O (x0,y0), point A
On the basic circle of involute gear, calculateWith the angle β of positive direction of the y-axis：
1.2.2 the pressure angle α of involute gear is determinedkWith exhibition angle θk, and the relationship of the two is acquired by following formula：
θk=tan αk-αk (4)
1.2.3 since the corresponding angle beta of same involute profile is constant, it is possible thereby to determine that the left flank profil of involute is taken up an official post
One point K (x, y) of meaning meets following formula：
Above formula is the characteristic function at the left flank profil edge of involute, wherein rbFor base radius.It is needed in this feature function
Determining design parameter includes the modulus m of gear, number of teeth z, pressure angle αk, geometric center O (x0,y0), the starting of involute profile
Point A (xa,ya)。
With the computational methods of left flank profil, can be expressed as in the hope of the characteristic function of right flank profil：
The characteristic function of 1.3 structure tooth top corners, tooth top are characterized in by two cross linears and its intersection point (xl,yl) constitute,
The calculating of characteristic function is as follows：
Wherein k1、k2It is the slope of two straight lines, slope and intersection point (x respectivelyl,yl) coordinate is to build benchmark image to set
Count parameter.
Step 2: building the benchmark image of each feature of involute gear according to characteristic function, need by step
One obtains the characteristic function that each characteristic image edge meets, and determines the design parameter in each characteristic image.
Step 3: establishing the Evaluation Strategy and deliberated index of edge detection effect assessment.
The edge detection precision of 3.1 evaluation circle characteristic images, if the collection of marginal point is combined into (xi,yi), i=1,2 ..., n,
(xi,yi) distance to the ideal center of circle is ri.It is as follows then to evaluate calculating process：
Δri=(xi-x0)2+(yi-y0)2-r(8)
Wherein Δ riFor marginal point to the distance r in the ideal center of circleiThe difference of and function model ideal radius r, with all edges
Point Δ riAverage valueStandard as evaluating precision.
The edge detection precision of 3.2 evaluation involute characteristic images, feature is established according to the characteristic function of involute profile
Image, the flank profil edge feature in image is ideal, tooth profile total deviation Fα(contain two standards at practical tooth edge gradually
Distance between bursting at the seams) it is 0, therefore the F of actual edge testing resultαIt can be used as the standard of evaluating precision.
If the collection of flank profil marginal point is combined into (xi,yi), i=1,2 ..., n cross arbitrary profile point (xi,yi) fitting gradually open
The angle of straight line and positive direction of the y-axis between line starting point and coordinate origin is βi.Thereby determine that βmin=min { βi| i=1,2 ...,
N }, βmax=max { βi| i=1,2 ..., n }, it is acquired according to tooth profile total deviation definition：
Fα=rb(βmax-βmin) (10)
The edge detection precision of 3.3 evaluation tooth top characteristic images, according to intersection point (xl,yl) by edge detection extract edge
Point on different straight lines according to being divided into two classes.Calculate marginal point between the line correspondence function model of foundation at a distance from, if
The collection of marginal point is combined into (xi,yi), the slope of i=1,2 ..., n, straight line are k, then the distance of marginal point to straight line is：
Calculate all marginal points between linear function at a distance from, using its average value as the standard of evaluating precision.
Step 4: selection edge detection algorithm carries out edge detection to benchmark image, the precision of comprehensive each characteristic image is commented
Determine the deviation between quantification of targets edge detection results and true edge.
The beneficial effects of the invention are as follows：
1, the present invention can quantify the deviation between edge detection results and true edge, to select suitable edge detection
Detection method.
2, in conjunction with the local edge of involute gear, multiple and different gear edge characteristic images is constructed, is wrapped
Include bore circle, involute profile and tooth top corner.The workload compared with the high-resolution benchmark image of structure gear entirety
Smaller is lower to hardware requirement.
Description of the drawings
Fig. 1 is the flow chart of the present invention；
Fig. 2 is that involute profile characteristic function builds schematic diagram；
Fig. 3 is the benchmark image schematic diagram of each feature of involute gear；
Fig. 4 is involute profile characteristic image accuracy assessment strategy schematic diagram；
Fig. 5 is tooth top characteristic image accuracy assessment strategy schematic diagram.
Specific implementation mode
The invention will be further described with attached drawing with reference to embodiments.
Referring to attached drawing 1, a kind of fine module gear edge detection accuracy computation method specific steps of feature based image are such as
Under：
Step 1: establishing the characteristic function at involute gear edge.
In step 1, considers the diversity of fine module gear image border, need to establish multiple and different gear edges
Characteristic image, including bore circle, involute profile and tooth top corner.
The characteristic function of 1.1 structure endoporus circles, is expressed by round function formula, as shown in formula (1).
1.2 characteristic functions that involute profile is built referring to attached drawing 2 are as follows by taking left flank profil as an example：
1.2.1 the starting point A (x of involute profile are determineda,ya) and involute gear geometric center O (x0,y0), point A
On the basic circle of involute gear, calculateShown in angle β such as formulas (2) with positive direction of the y-axis.
1.2.2 the pressure angle α of involute gear is determinedkWith exhibition angle θk, and acquire the relationship of the two by formula (3), (4).
1.2.3 since the corresponding angle beta of same involute profile is constant, it is possible thereby to determine that the left flank profil of involute is taken up an official post
One point K (x, y) of meaning meets formula (5), the as characteristic function at the left flank profil edge of involute.In this feature function it needs to be determined that set
Meter parameter includes the modulus m, number of teeth z, pressure angle α of geark, geometric center O (x0,y0), the starting point A (x of involute profilea,
ya)。
It, can be in the hope of the expression formula of the characteristic function of right flank profil, such as formula (6) institute simultaneously according to the computational methods of left flank profil
Show.
The characteristic function of 1.3 structure tooth top corners, tooth top are characterized in by two cross linears and its intersection point (xl,yl) constitute,
Shown in the calculating of characteristic function such as formula (7).
Wherein k1、k2It is the slope of two straight lines, slope and intersection point (x respectivelyl,yl) coordinate is to build benchmark image to set
Count parameter.
Step 2: building the benchmark image of each feature of involute gear according to characteristic function referring to attached drawing 3, need
The characteristic function that each characteristic image edge meets is obtained by step 1, and determines the design parameter in each characteristic image, in Fig. 3
(a) circle characteristic model figure on the basis of, (b) on the basis of involute profile characteristic model figure, (c) on the basis of tooth top characteristic model figure.
Step 3: establishing the Evaluation Strategy and deliberated index of edge detection effect assessment.
The edge detection precision of 3.1 evaluation circle characteristic images, if the collection of marginal point is combined into (xi,yi), i=1,2 ..., n,
(xi,yi) distance to the ideal center of circle is ri.It then evaluates shown in calculating process such as formula (8), (9), acquires all marginal points to ideal
The distance r in the center of circleiThe difference DELTA r of and function model ideal radius ri, with its average valueStandard as evaluating precision.
3.2, referring to attached drawing 4, evaluate the edge detection precision of involute characteristic image, involute profile are established according to formula (5)
Characteristic image, the flank profil edge feature in image is ideal, tooth profile total deviation Fα(contain two marks at practical tooth edge
Distance between quasi- involute) it is 0, therefore the F of actual edge testing resultαIt can be used as the index of accuracy assessment.
If the collection of flank profil marginal point is combined into (xi,yi), i=1,2 ..., n cross arbitrary profile point (xi,yi) fitting gradually open
The angle of straight line and positive direction of the y-axis between line starting point and coordinate origin is βi.Thereby determine that βmin=min { βi| i=1,2 ...,
N }, βmax=max { βi| i=1,2 ..., n }, formula (10) is acquired according to tooth profile total deviation definition.
3.3, referring to attached drawing 5, evaluate the edge detection precision of tooth top characteristic image, according to intersection point (xl,yl) by edge detection
The marginal point of extraction on different straight lines according to being divided into two classes.It calculates between marginal point and the line correspondence function model of foundation
Distance, if the collection of marginal point is combined into (xi,yi), the slope of i=1,2 ..., n, straight line are k, then the distance of marginal point to straight line
As shown in formula (11), calculate all marginal points between linear function at a distance from, using its average value as accuracy assessment index.
Step 4: selection edge detection algorithm carries out edge detection to benchmark image, the precision of comprehensive each characteristic image is commented
Determine the deviation between quantification of targets edge detection results and true edge.It can be with according to the deviation size of different edge detection algorithms
Select suitable edge detection algorithm.
Claims (9)
1. a kind of fine module gear edge detection accuracy computation method of feature based image, which is characterized in that specific steps are such as
Under：
One, the characteristic function at involute gear edge is established；
Two, the benchmark image of each feature of involute gear is built according to characteristic function；
Three, the strategy and deliberated index of benchmark image edge detection effect assessment are established；
Four, selection edge detection algorithm carries out edge detection, the accuracy assessment index amount of comprehensive each characteristic image to benchmark image
Change the deviation between edge detection results and true edge.
2. fine module gear edge detection accuracy computation method according to claim 1, which is characterized in that in step 1
In, consider the diversity of fine module gear image border, needs to establish multiple and different gear edge characteristic images, including gear
Endoporus circle, involute profile and tooth top corner.
3. fine module gear edge detection accuracy computation method according to claim 2, which is characterized in that structure endoporus circle
Characteristic function, expressed by round function formula：
(x-x0)2+(y-y0)2=r2
Wherein：(x, y) is the edge coordinate that characteristic function indicates；(x0,y0) be characteristic function central coordinate of circle, be structure benchmark
The design parameter of image；R is the radius of circle that characteristic function indicates, is the design parameter for building benchmark image.
4. fine module gear edge detection accuracy computation method according to claim 2, which is characterized in that structure involute
The characteristic function of flank profil is as follows by taking left flank profil as an example：
1) the starting point A (x of involute profile are determineda,ya) and involute gear geometric center O (x0,y0), point A, which is located at, gradually to be opened
On the basic circle of line gear, calculateWith the angle β of positive direction of the y-axis：
2) the pressure angle α of involute gear is determinedkWith exhibition angle θk, and the relationship of the two is acquired by following formula：
θk=tan αk-αk
3) since the corresponding angle beta of same involute profile is constant, thereby determine that any point K in the left flank profil of involute (x,
Y) meet following formula：
Above formula is the characteristic function at the left flank profil edge of involute, wherein rbFor base radius；Calculate rbIn it needs to be determined that design
Parameter includes the modulus m of gear, number of teeth z, pressure angle αk, geometric center O (x0,y0), the starting point A (x of involute profilea,ya)；
With the computational methods of left flank profil, can be expressed as in the hope of the characteristic function of right flank profil：
5. fine module gear edge detection accuracy computation method according to claim 2, which is characterized in that structure tooth top turns
The characteristic function at angle, tooth top are characterized in by two cross linears and its intersection point (xl,yl) constitute, the following institute of calculating of characteristic function
Show：
Wherein k1、k2It is the slope of two straight lines, slope and intersection point (x respectivelyl,yl) coordinate be build benchmark image design ginseng
Number.
6. fine module gear edge detection accuracy computation method according to any one of claim 1 to 5, feature exist
In, in step 2, according to characteristic function build each feature of involute gear benchmark image, need by step 1
The characteristic function that each characteristic image edge meets is obtained, and determines the design parameter in each characteristic image.
7. fine module gear edge detection accuracy computation method according to claim 3, which is characterized in that in step 3
The edge detection precision of evaluation circle characteristic image, if the collection of marginal point is combined into (xi,yi), i=1,2 ..., n, (xi,yi) arrive ideal
The distance in the center of circle is ri；It is as follows then to evaluate calculating process：
△ri=(xi-x0)2+(yi-y0)2-r
Wherein △ riFor marginal point to the distance r in the ideal center of circleiWith the difference of characteristic function model ideal radius r, with all edges
Point △ riAverage valueStandard as evaluating precision.
8. fine module gear edge detection accuracy computation method according to claim 4, which is characterized in that in step 3
The edge detection precision for evaluating involute characteristic image establishes characteristic image, in image according to the characteristic function of involute profile
Flank profil edge feature be ideal, tooth profile total deviation FαIt is 0, therefore the F of actual edge testing resultαIt can be used as evaluating precision
Standard；
If the collection of flank profil marginal point is combined into (xi,yi), i=1,2 ..., n cross arbitrary profile point (xi,yi) fitting involute starting point
The angle of straight line and positive direction of the y-axis between coordinate origin is βi；Thereby determine that βmin=min { βi| i=1,2 ..., n }, βmax=
max{βi| i=1,2 ..., n }, it is acquired according to tooth profile total deviation definition：
Fα=rb(βmax-βmin)。
9. fine module gear edge detection accuracy computation method according to claim 5, which is characterized in that in step 3
The edge detection precision for evaluating tooth top characteristic image, according to intersection point (xl,yl) by edge detection extraction marginal point according to positioned at not
It is divided into two classes on same straight line；Calculate marginal point between the line correspondence characteristic function model of foundation at a distance from, if marginal point
Collection is combined into (xi,yi), the slope of i=1,2 ..., n, straight line are k, then the distance of marginal point to straight line is：
Calculate all marginal points between linear function at a distance from, using its average value as the standard of evaluating precision.
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| CN107424164B (en) * | 2017-07-19 | 2019-09-27 | 中国计量大学 | A kind of Image Edge-Detection Accuracy Assessment |
| CN108447071B (en) * | 2018-03-16 | 2021-12-21 | 中国一拖集团有限公司 | Gear tooth profile boundary extraction method based on meshing-pixel image edge tracking method |
| CN111062879B (en) * | 2019-11-13 | 2023-11-14 | 南京工业大学 | Image method for detecting involute in image |
| CN112432612B (en) * | 2020-10-22 | 2022-08-16 | 中国计量科学研究院 | High-precision micro rotation angle measuring method based on monocular vision |
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| CN103712567A (en) * | 2013-05-27 | 2014-04-09 | 北京理工大学 | Small module arc gear non-contact optical fine measurement method |
| JP5480413B1 (en) * | 2013-02-12 | 2014-04-23 | 株式会社トヨタコミュニケーションシステム | Finite element method analysis method and finite element method analyzer |
| CN105043288A (en) * | 2015-05-04 | 2015-11-11 | 天津科技大学 | Machine vision-guided laser gear chamfering contour measurement apparatus and measurement method thereof |
| CN105046650A (en) * | 2015-07-12 | 2015-11-11 | 中国计量学院 | Machine vision-based image mosaic method for small module gear detection process |
| CN204788270U (en) * | 2015-07-12 | 2015-11-18 | 中国计量学院 | Fine module gear precision measurement device |
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| JP5480413B1 (en) * | 2013-02-12 | 2014-04-23 | 株式会社トヨタコミュニケーションシステム | Finite element method analysis method and finite element method analyzer |
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| CN105043288A (en) * | 2015-05-04 | 2015-11-11 | 天津科技大学 | Machine vision-guided laser gear chamfering contour measurement apparatus and measurement method thereof |
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