CN105157594A - Half-subarea-segmentation-method-based digital image correlation method - Google Patents
Half-subarea-segmentation-method-based digital image correlation method Download PDFInfo
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Abstract
Provided in the invention is a half-subarea-segmentation-method-based digital image correlation method. The correlation method comprises: a certain number of measurement points are distributed on a picture before deformation, a deformation field, containing two kinds of deformation modes, of a picture after deformation is obtained by using a sub-pixel digital image correlation method, and measuring points with poor results are selected; a square sample subarea is selected by using each measuring point with a poor result as a center, the subarea is segmented into two half subareas by using one line segment crossing the center point of the subarea, an optimum target subarea among all subareas at different segmentation angles is searched by using an overall-pixel digital image correlation method, and rough measurement displacement and a rough segmentation angle are obtained; and with the rough measurement displacement and rough segmentation angle as initial values, measurement displacement and a segmentation angle are searched precisely by using the sub-pixel digital image correlation method and a convex function extreme seeking method. Compared with the traditional digital image correlation method, the provided digital image correlation method enables displacement of measuring points near a boundary of two kinds of deformation modes to be searched and the application range is expanded.
Description
Technical field
The present invention relates to a kind of Digital Image Correlation Method being suitable for deformation measurement near two kinds of deformation patterns boundaries, particularly relate to a kind of Digital Image Correlation Method based on half son district split plot design.
Background technology
Digital Image Correlation Method is a kind of measuring method, by carrying out to two width speckle patterns of the forward and backward body surface of distortion displacement and the strain measurement that relevant treatment realizes body surface.The method has significant advantage: noncontact, precision are high, measurement of full field and having no special requirements to measurement environment.At present, the method has become the advanced observation method in the fields such as rock mechanics, the mechanics of materials, Experimental Mechanics.
Digital Image Correlation Method according to body surface speckle image before being deformed, after correlativity determine displacement that object is put and strain.In order to calculate any displacement and strain, before being deformed image is chosen centered by this point coordinate square image subsection and be called sample subarea, the image subset of the same size after deformation image chosen is called target subarea, and the difference of the center point coordinate of the two is displacement a little.Use centered Finite Difference Methods, can strain field be obtained according to displacement field.
Affect Digital Image Correlation Method precision because have picture quality, sub-pixel interpolation method, related search method, deformation pattern etc.In ideal conditions, displacement accuracy can up to about 0.01 pixel.In traditional Digital Image Correlation Method, it is generally acknowledged that all available Same Function of the displacement of each point in sample subarea represents, namely deformation pattern only has one.When being out of shape more even, strain is constant, and displacement is the function of first order of coordinate, and deformation pattern only has one.And when being out of shape uneven, the distortion possibility more complicated in subarea, deformation pattern may be not only a kind of.In order to reduce the enterolithic heterogeneity in subarea, the size in subarea can be reduced, but this can be subject to the threat that search precision reduces.Even, when distortion increase to a certain degree develop crackle afterwards time, in the subarea near crackle, continuous modification becomes Discontinuous Deformation, and deformation pattern is more complicated.In addition, when measuring point is at model boundary, comprise inactive area and effective coverage in subarea, the deformation pattern in two kinds of regions is not identical yet.Under these conditions, in square subregions, not only have a kind of deformation pattern, if use conventional digital image correlation technique to search for, comparatively big error can be brought.
In order to solve the problem, the present invention proposes a kind of Digital Image Correlation Method based on subarea split plot design.First, use sub-pix Digital Image Correlation Method to calculate measuring point, when measuring point is positioned near two kinds of deformation patterns boundaries, the correlativity of the measuring point of calculating is poor, is picked out.Then, square sample subarea is chosen centered by the measuring point that each result is poor, utilized subarea central point line segment that subarea is divided into two and half subareas, use Integer Pel Digital Image Correlation Method, the optimum target subarea in all half subareas during search different segmentation angle, obtains rough measuring point displacement and segmentation angle.Finally, with rough measuring point displacement and segmentation angle for initial value, utilize sub-pix Digital Image Correlation Method and convex function to ask the method for extreme value, fine search measuring point displacement and segmentation angle.When the segmentation angle calculated is close to actual value, half subarea that only comprises a kind of deformation pattern can be obtained, therefore, the displacement field that precision is higher can be obtained.Superiority of the present invention is, the displacement field of the measuring point near can having a common boundary to two kinds of deformation patterns is searched for, and improves the scope of application of Digital Image Correlation Method.
Summary of the invention
The problem of distortion near two kinds of deformation patterns boundaries can not be calculated in order to solve existing Digital Image Correlation Method, the invention provides a kind of Digital Image Correlation Method based on half son district split plot design, the method can calculate the measuring point of following three kinds of situations that conventional digital image correlation technique can not calculate: (1) is positioned at the point on model boundary; (2) point of 2 kinds of homogeneous deformations is comprised near; (3) point near crackle is positioned at.The common feature of these 3 kinds of measuring points is: comprise 2 kinds of deformation patterns in the sample subarea chosen centered by measuring point.
The invention is characterized in, comprising:
Before being deformed picture is arranged the measuring point of some, centered by measuring point, choose square sample subarea, utilize sub-pix Digital Image Correlation Method, obtain the deformation field comprising picture after the distortion of two kinds of deformation patterns, and pick out the poor measuring point of result;
Square sample subarea is chosen centered by the measuring point that each result is poor, utilized subarea central point line segment that subarea is divided into two and half subareas, the angle of multiple segmentation line segment is set, use Integer Pel Digital Image Correlation Method, the optimum target subarea in all half subareas during search different segmentation angle, obtains rough measuring point displacement and segmentation angle;
With rough measuring point displacement and segmentation angle for initial value, utilize sub-pix Digital Image Correlation Method and convex function to ask the method for extreme value, fine search measuring point displacement and segmentation angle.
Further, wherein,
As shown in the schematic of Figure 1,1 is image before distortion to the described picture comprising two kinds of deformation patterns, 2 for comprise two kinds of deformation patterns distortion after image, in deformation process, before distortion, in image 1, comprise two kinds of deformation patterns.Wherein, in this schematic diagram, deformation pattern is set as: in the I of region, and deformation pattern is horizontal shear; In region il, deformation pattern is vertical shear.At region I, region II, and subarea 1-1,1-2 and the 1-3 on the boundary in two regions, it is respectively subarea 2-1,2-2 and 2-3 in image 2 after deformation.
In traditional Digital Image Correlation Method, it is generally acknowledged that the deformation pattern in subarea only has a kind, therefore, for the central point of subarea 1-1 and 1-2
o 1with
o 2, the central point of subarea 2-1 and 2-2 can be searched
o'
1with
o'
2.But the deformation pattern due to subarea 1-3 has 2 kinds, therefore, the central point of subarea 2-3 can not usually be searched
o'
3.
Further, wherein,
Before being deformed picture is arranged the measuring point of some, square sample subarea is chosen centered by measuring point, utilize sub-pix Digital Image Correlation Method, obtain the deformation field comprising picture after the distortion of two kinds of deformation patterns, and pick out the poor measuring point of result and be further:
First, before being deformed on picture, embark on journey according to level, equidistant arrangement mode vertically in column arranges the measuring point of some.Then, centered by measuring point, choose square sample subarea, adopt sub-pix Digital Image Correlation Method, by calculating the correlativity in the target subarea in the rear image of sample subarea and distortion, the deformation field of search measuring point, comprises displacement field and strain field.The precision of sub-pix Digital Image Correlation Method must be higher, about 0.01 pixel.Finally, according to the distribution situation of the related coefficient that Digital Image Correlation Method calculates, pick out correlativity and be significantly less than most measuring point, prepare to re-start calculating.The correlativity of these measuring points is poor, shows that measuring point may be positioned near two kinds of deformation patterns boundaries.
Further, wherein, centered by the measuring point that each result is poor, choose square sample subarea, utilize subarea central point line segment to be divided in subarea two and half subareas to be further:
First, analyze choosing square sample subarea centered by the poor measuring point of each result.As shown in Figure 2, the subarea 1-3 on the boundary in two regions comprises 3-1 and 3-2 two regions, in these 2 regions, all only has a kind of deformation pattern.Desirable dividing method is that subarea is divided into 3-1 and 3-2 completely.Subarea central point
p 0the subarea 3-1 at place is called boss district, and another subarea 3-2 is called secondary subarea.Use sub-pix Digital Image Correlation Method, can measuring point be obtained by the target subarea searching for boss district
p 0displacement and measuring point around strain.
Although desirable dividing method is better, the process more complicated realized, reason has 2: first, and the equation of cut-off rule has 2 parameters at least, and this brings difficulty to solving; Secondly, boss district comprises the central point of atomic region, and secondary subarea does not comprise, then the way of search of two seed zones is not identical, which increases difficulty in computation.
In order to simplify subarea cutting procedure, the method that the present invention proposes as shown in Figure 3, crosses the central point comprising the subarea 1-3 of 2 kinds of deformation patterns
p 0do cut-off rule 4, when the inclination angle of cut-off rule is more reasonable, boss district 5-1 and 1 the secondary subarea 5-2 that 1 only comprises a kind of deformation pattern can be obtained.Use Digital Image Correlation Method, by search, boss district can obtain measuring point
p 0displacement and measuring point around strain.Conveniently calculate, the gray matrix in half subarea adopts following method to obtain: be set to invalid value by square subregions in the gray scale of the pixel of cut-off rule side, using the gray matrix of the gray matrix of the square subregions after change as half subarea.
Subarea of the present invention cut-off rule crosses subarea central point, has 2 significant advantages: 1. cut-off rule only has 1 undetermined parameter (cut-off rule inclination angle), is easy to solve; 2. major and minor subarea all comprises atomic region central point, and the pixel count in major and minor subarea is identical, and solution procedure is identical, this also simplifies solution procedure.
Further, wherein, the described angle arranging multiple segmentation line segment, uses Integer Pel Digital Image Correlation Method, the optimum target subarea in all half subareas during search different segmentation angle, and obtaining rough measuring point displacement with segmentation angle is further:
When segmentation angle gets arbitrary value, a sample subarea all can be divided into two and half subareas, supposes that the estimated value splitting angle has
nindividual, then can obtain 2
nindividual half subarea.Use the Digital Image Correlation Method of Integer Pel precision, search for the optimum target subarea in all half subareas.When splitting angle and being better, higher as the target subarea of calculating and the Relativity in half subarea, on the contrary lower.So displacement and the segmentation angle in the target subarea that correlativity is best are better, can as the initial value of next step fine search.In order to improve computing velocity, only using the Digital Image Correlation Method of Integer Pel precision, only considering the translation in subarea during search, do not consider rotation and the distortion in subarea.Wherein, Integer Pel search procedure is as follows: as depicted in fig. 4-a, makes the central point in this subarea of former state
p 0(
x 0,
y 0) be the measuring point of half subarea 6-1, use the Integer Pel searching method (such as, particle swarm optimization algorithm) of Digital Image Correlation Method, the Integer Pel position of the subarea 7-1 after distortion and measuring point can be obtained
p 1(
x 1,
y 1), and then obtain
p 0integer Pel displacement: horizontal shift
u 0=
x 1-
x 0and perpendicular displacement
v 0=
y 1-
y 0.When subarea correlativity after being out of shape preferably time, obtain rough displacement and segmentation angle.Using the central point in this subarea of former state all as the measuring point in half subarea, object is the displacement that the displacement obtained remains the original measuring point arranged, and the pixel quantity that each half subarea comprises is all identical.
Further, wherein, with rough measuring point displacement and segmentation angle for initial value, utilize sub-pix Digital Image Correlation Method and convex function to ask the method for extreme value, fine search measuring point displacement and segmentation angle be further:
This step is implemented specific as follows: with rough measuring point displacement and segmentation angle for initial value, use sub-pix Digital Image Correlation Method and convex function to ask the method for extreme value to solve the exact value of segmentation angle and displacement.Sub-pix Digital Image Correlation Method can the higher Newton-Raphson alternative manner of choice accuracy, and convex function asks the method for extreme value to select threefold division.
Introduce the process using threefold division to solve below.As shown in Fig. 4-b, threefold division is the method that one solves convex function (or concave function) extreme value, when know convex function general interval [
a 1,
a 2] time, in interval, choose two sound out position
a 3with
a 4, the functional value of both calculating.If
a 3functional value be greater than
a 4functional value, then the interval of extreme point be reduced into [
a 1,
a 4]; Otherwise, the interval of extreme point be [
a 3,
a 2].Circulation like this, progressively reduces interval, when sound out position closely time, think and have found extreme point.In the present invention, segmentation angle is independent variable, and related coefficient is the function that will solve, and concrete operation step is as follows:
The search procedure of sub-pix Digital Image Correlation Method is as follows: as shown in Fig. 4-a and Fig. 4-c, when the search of sub-pix Digital Image Correlation Method is carried out to subarea 6-1, the displacement of the subarea 7-1 searched for Integer Pel and segmentation angle are for initial value, through several times iteration, can obtain the information of the rear subarea 7-2 of accurate distortion, (horizontal line strains to comprise strain
ε x , perpendicular line strain
ε y and shearing strain
γ xy ) and the coordinate of subarea central point
p 2(
x 2,
y 2).Then measuring point
p 0horizontal shift
u=
x 2-
x 0, perpendicular displacement
v=
y 2-
y 0, strain field also can be obtained by the capable central difference of contraposition shift-in.Central-difference formula is
（1）
（2）
（3）
In formula,
x,
yrepresent coordinate,
i,
jrepresent line number and the columns of measuring point,
Δrepresent the spacing of adjacent measuring point.
When searching for, in order to ensure that related function is convex function in the region of search, with rough measuring point displacement and angle need be split for initial value.To split the initial value of angle
θcentered by, with [
θ-45 °,
θ+ 45 °] be the region of search of threefold division, determine multiple half subarea with rough segmentation angle, utilize sub-pix Digital Image Correlation Method and threefold division, progressively solved by iteration.Wherein, the function in threefold division is related function, and the present invention adopts cross correlation function, and value is larger, represents correlativity better, when getting maximal value 1, represents completely relevant; The process finding a function value is carried out in sub-pix search.Along with the increase of iterations, the increasing extent of segmentation angle is little, approaches optimal value gradually.When the scope splitting angle is less than threshold value, thinks and reach optimal value.When optimum segmentation angle, the displacement using sub-pix Digital Image Correlation Method to calculate is optimum displacement.
Accompanying drawing explanation
Fig. 1 is the forward and backward schematic diagram comprising the picture of 2 kinds of deformation patterns of distortion; Image before 1-distortion, comprise two kinds of deformation patterns, wherein, in the I of region, deformation pattern is horizontal shear; In region il, deformation pattern is vertical shear; The subarea of 1-1-in the I of region, central point is
o 1; The subarea of 1-2-in the II of region, central point is
o 2; 1-3-in region I and the borderline subarea of region II, central point is
o 3; Image after 2-distortion; The subarea of 2-1-subarea 1-1 after deformation on image, central point is
o'
1; The subarea of 2-2-subarea 1-2 after deformation on image, central point is
o'
2; The subarea of 2-3-subarea 1-3 after deformation on image, central point is
o'
3;
Fig. 2 is the desirable Fractionation regimen of subarea 1-3, and the boss district of a kind of deformation pattern of 3-1-only comprise, comprises atomic region central point
o 3; The secondary subarea of a kind of deformation pattern of 3-2-only comprise, does not comprise atomic region central point;
Fig. 3 is the partitioning scheme of subarea 1-3 in the present invention, 4-cross subarea central point
p 0cut-off rule; The boss district of a kind of deformation pattern of 5-1-only comprise, comprises former central point
o 3; The secondary subarea of 5-2-comprise two kinds of deformation patterns, comprises former central point
o 3;
Fig. 4-a is the search procedure of Integer Pel Digital Image Correlation Method, and 6-1-any one half subarea, central point is
p 0(
x 0,
y 0); The target subarea of 7-1-search, central point is
p 1(
x 1,
y 1); Then
p 0horizontal shift
u=
x 1-
x 0, perpendicular displacement
v=
y 1-
y 0; Fig. 4-b is the schematic diagram of threefold division,
a 1the left margin of-the region of search;
a 2the right margin of-the region of search;
a 3first cut-point of-region of search;
a 4second cut-point of-region of search; Fig. 4-c is the search procedure of sub-pix Digital Image Correlation Method, half subarea that 7-1-Integer Pel searches, and central point is
p 1(
x 1,
y 1); The target subarea that 7-2-sub-pix searches, central point is
p 1(
x 2,
y 2); Then measuring point
p 0total horizontal shift
u=
x 2-
x 0, perpendicular displacement
v=
y 2-
y 0;
Fig. 5-a is the speckle pattern before and after the distortion of use affine transformation method making, speckle pattern before 8-1-distortion; Speckle pattern after 8-2-the comprise distortion of two kinds of deformation patterns; The measuring point distributing position of 9-1-setting; Position after the distortion of the measuring point of 9-2-in theory; Fig. 5-b is the speckle pattern before and after the distortion of use affine transformation method making, speckle pattern before 8-3-distortion; Speckle pattern after 8-4-the comprise distortion of crackle; The measuring point distributing position of 9-3-setting; Position after the distortion of the measuring point of 9-4-in theory; Fig. 5-c be use affine transformation method to make distortion before and after speckle pattern, speckle pattern before 8-5-the comprise distortion of inactive area; Speckle pattern after 8-6-the comprise distortion of inactive area; The measuring point distributing position of 9-5-setting; Position after the distortion of the measuring point of 9-6-in theory;
Fig. 6-a is by the displacement vector field of measuring point 9-1 in traditional Digital Image Correlation Method (hereinafter referred to as classic method) calculating chart 5-a; Fig. 6-b is the displacement vector field calculated by the present invention; Fig. 6-c is the related coefficient that two kinds of methods calculate, the result of 10-1-classic method, and 10-2 is result of the present invention; Fig. 6-d is the horizontal shift that two kinds of methods calculate, the result of 10-3-classic method, 10-4-result of the present invention, 10-5-theoretical value; Fig. 6-e is the perpendicular displacement that two kinds of methods calculate, the result of 10-6-classic method, 10-7-result of the present invention, 10-8-theoretical value;
Fig. 7-a is by the displacement vector field of measuring point 9-3 in classic method calculating chart 5-b; Fig. 7-b is the displacement vector field calculated by the present invention; Fig. 7-c is the related coefficient that two kinds of methods calculate, the result of 11-1-classic method, and 11-2 is result of the present invention; Fig. 7-d is the horizontal shift that two kinds of methods calculate, the result of 11-3-classic method, 11-4-result of the present invention, 11-5-theoretical value; Fig. 7-e is the perpendicular displacement that two kinds of methods calculate, the result of 11-6-classic method, 11-7-result of the present invention, 11-8-theoretical value;
Fig. 8-a is by the displacement vector field of measuring point 9-5 in classic method calculating chart 5-c; Fig. 8-b is the displacement vector field calculated by the present invention; Fig. 8-c is the related coefficient that two kinds of methods calculate, the result of 12-1-classic method, and 12-2 is result of the present invention; Fig. 8-d is the horizontal shift that two kinds of methods calculate, the result of 12-3-classic method, 12-4-result of the present invention, 12-5-theoretical value; Fig. 8-e is the perpendicular displacement that two kinds of methods calculate, the result of 12-6-classic method, 12-7-result of the present invention, 12-8-theoretical value.
Embodiment
The problem of distortion near two kinds of deformation patterns boundaries can not be calculated in order to solve existing Digital Image Correlation Method, the invention provides a kind of Digital Image Correlation Method being suitable for deformation measurement near two kinds of deformation patterns boundaries, the method can calculate the measuring point of following three kinds of situations that conventional digital image correlation technique can not calculate: (1) is positioned at the point on model boundary; (2) point of 2 kinds of homogeneous deformations is comprised near; (3) point near crackle is positioned at.The common feature of these 3 kinds of measuring points is: comprise 2 kinds of deformation patterns in the sample subarea chosen centered by measuring point.The method comprises the following steps:
Step 1: the measuring point before being deformed picture being arranged some, square sample subarea is chosen centered by measuring point, utilize sub-pix Digital Image Correlation Method, obtain the deformation field comprising picture after the distortion of two kinds of deformation patterns, and pick out the poor measuring point of result;
This step is implemented specific as follows: first, before being deformed image is arranged the measuring point of some, and for the ease of calculating strain field, measuring point is that level is embarked on journey, grid type distribution mode vertically in column, and the spacing of measuring point is taken as 5 ~ 20 pixels; Then, square sample subarea is chosen centered by measuring point, utilize sub-pix Digital Image Correlation Method, the coordinate of search measuring point after deformation on image, obtains displacement field by the coordinate difference before and after wet environment, carries out central difference obtain strain field to displacement field, in order to obtain higher precision, Digital Image Correlation Method should select good searching method, such as, and Newton-Raphson alternative manner; Finally, pick out the poor measuring point of result according to the distribution of correlation coefficient of all measuring points, re-start calculating.The formula of related coefficient has tens kinds, and conventional has cross correlation function, minimum squared distance function etc.
Wherein, the picture comprising two kinds of deformation patterns can be obtained by experiment, also can manual manufacture.For the picture of manual manufacture, higher speckle quality can be obtained, also can accurate controlling distortion pattern, be convenient to the accuracy checking measuring point result.Use the method (PengZhou that forefathers propose, KennethEGoodson.Subpixeldisplacementanddeformationgradie ntmeasurementusingdigitalimage/specklecorrelation.Optica lEngineering, 2001,40 (8): 1613 – 1620.) make simulation speckle pattern, use affine transformation method controlling distortion pattern.
Further, wherein, described simulation speckle generation method is further:
First, in a certain size region the point of stochastic distribution some as speckle central point; Then, according to the gray scale of any point in following formula zoning
（1）
In formula,
rthe coordinate of any point,
the gray scale of any point,
sfor speckle count,
afor speckle radius,
r k for the coordinate of any one speckle central point,
for the peak gray of speckle, be generally random value.Finally, gray matrix is saved as digital picture, can speckle pattern be obtained.Work as parameter
swith
awhen arranging reasonable, high-quality speckle pattern can be obtained.
Generally, the center point coordinate of speckle is stochastic distribution, and this can cause image to occur in local the situation that speckle flocks together or lacks, thus causes the quality of speckle pattern lower; In order to improve the quality of speckle pattern, first arranged according to the mode of equidistant grid by the center point coordinate of speckle, then make the movement at random in its vicinity of all speckle central points, it is more even that this can make speckle distribute, and there is again certain randomness, the speckle pattern quality therefore generated is higher.
Further, wherein,
Described affine transformation method is a kind of conventional image conversion method, can realize the distortion such as the translation of figure, rotation, stretching, compression, shearing.
As shown in Fig. 5-a, Fig. 5-b and Fig. 5-c, utilize simulation speckle generation method to make high-quality speckle pattern 8-1,8-3 and 8-5, wherein, the hole in 8-5 is inactive area.Use affine transformation method, allow speckle pattern produce distortion, obtain 3 kinds of pictures: the picture 8-2(that (1) comprises 2 kinds of deformation patterns carries out clockwise vertical shear to the left-half of 8-1, carries out counterclockwise vertical shearing, obtain 8-2 to right half part); (2) the picture 8-4(comprising crackle is a prefabricated Incline Crack in the upper left corner of 8-3, makes triangle below translation one segment distance be left positioned at above crackle, obtains 8-4); (3) the picture 8-6(comprising circular inner edge circle, in order to produce distortion, relative to 8-5, has carried out horizontal compression to a certain degree to 8-6).
Step 2: choose square sample subarea centered by the measuring point that each result is poor, utilized subarea central point line segment that subarea is divided into two and half subareas, the angle of multiple segmentation line segment is set, use Integer Pel Digital Image Correlation Method, the optimum target subarea in all half subareas during search different segmentation angle, obtains rough measuring point displacement and segmentation angle;
When segmentation angle gets arbitrary value, a sample subarea all can be divided into two and half subareas, supposes that the estimated value splitting angle has
nindividual, then can obtain 2
nindividual half subarea.Segmentation angle gets multiple estimated value within the scope of 0 ° ~ 180 °, uses the Digital Image Correlation Method (such as, particle swarm optimization algorithm) of Integer Pel precision, searches for the optimum target subarea in all half subareas.Conveniently calculate, the gray matrix in half subarea adopts following method to obtain: be set to invalid value by square subregions in the gray scale of the pixel of cut-off rule side, using the gray matrix of the gray matrix of the square subregions after change as half subarea.When splitting angle and being better, higher as the target subarea of calculating and the Relativity in half subarea, on the contrary lower.So displacement and the segmentation angle in the target subarea that correlativity is best are better, can as the initial value of next step fine search.In order to improve computing velocity, only using the Digital Image Correlation Method of Integer Pel precision, only considering the translation in subarea during search, do not consider rotation and the distortion in subarea.Wherein, Integer Pel search procedure is as follows: as depicted in fig. 4-a, makes the central point in this subarea of former state
p 0(
x 0,
y 0) be the measuring point of half subarea 6-1, use the Integer Pel searching method (such as, particle swarm optimization algorithm) of Digital Image Correlation Method, the Integer Pel position of the subarea 7-1 after distortion and measuring point can be obtained
p 1(
x 1,
y 1), and then obtain
p 0integer Pel displacement: horizontal shift
u 0=
x 1-
x 0and perpendicular displacement
v 0=
y 1-
y 0.When subarea correlativity after being out of shape preferably time, obtain rough displacement and segmentation angle.
Step 3: with rough measuring point displacement and segmentation angle for initial value, utilize sub-pix Digital Image Correlation Method and convex function to ask the method for extreme value, fine search measuring point displacement and segmentation angle.
This step is implemented specific as follows: with rough measuring point displacement and segmentation angle for initial value, use sub-pix Digital Image Correlation Method and convex function to ask the method for extreme value to solve the exact value of segmentation angle and displacement.Sub-pix Digital Image Correlation Method can select Newton-Raphson alternative manner, and convex function asks the method for extreme value to select threefold division.
Introduce the process using threefold division to solve below.As shown in Fig. 4-b, threefold division is the method that one solves convex function (or concave function) extreme value, when know convex function general interval [
a 1,
a 2] time, in interval, choose two sound out position
a 3with
a 4, the functional value of both calculating.If
a 3functional value be greater than
a 4functional value, then the interval of extreme point be reduced into [
a 1,
a 4]; Otherwise, the interval of extreme point be [
a 3,
a 2].Circulation like this, progressively reduces interval, when sound out position closely time, think and have found extreme point.In the present invention, segmentation angle is independent variable, and related coefficient is the function that will solve, and concrete operation step is as follows:
The search procedure of sub-pix Digital Image Correlation Method is as follows: as shown in Fig. 4-a and Fig. 4-c, when the search of sub-pix Digital Image Correlation Method is carried out to subarea 6-1, the displacement of the subarea 7-1 searched for Integer Pel and segmentation angle are for initial value, through several times iteration, can obtain the information of the rear subarea 7-2 of accurate distortion, (horizontal line strains to comprise strain
ε x , perpendicular line strain
ε y and shearing strain
γ xy ) and the coordinate of subarea central point
p 2(
x 2,
y 2).Then measuring point
p 0horizontal shift
u=
x 2-
x 0, perpendicular displacement
v=
y 2-
y 0, strain field also can be obtained by the capable central difference of contraposition shift-in.Central-difference formula is
（1）
（2）
（3）
In formula,
x,
yrepresent coordinate,
i,
jrepresent line number and the columns of measuring point,
Δrepresent the spacing of adjacent measuring point.
When searching for, in order to ensure that related function is convex function in the region of search, with rough measuring point displacement and angle need be split for initial value.To split the initial value of angle
θcentered by, with [
θ-45 °,
θ+ 45 °] be the region of search of threefold division, determine multiple half subarea with rough segmentation angle, utilize sub-pix Digital Image Correlation Method and threefold division, progressively solved by iteration.Wherein, the function in threefold division is related function, and the present invention adopts cross correlation function, and value is larger, represents correlativity better, when getting maximal value 1, represents completely relevant; The process finding a function value is carried out in sub-pix search.Along with the increase of iterations, the increasing extent of segmentation angle is little, approaches optimal value gradually.When the scope splitting angle is less than threshold value, thinks and reach optimal value.When optimum segmentation angle, the displacement using sub-pix Digital Image Correlation Method to calculate is optimum displacement.
embodiment 1
The present embodiment is the effect that the present invention comprises the point of 2 kinds of homogeneous deformations near calculating.Use the distortion of 8-1 to 8-2 in traditional sub-pix Digital Image Correlation Method and calculating chart 5-a of the present invention respectively, wherein, the length of side in subarea is taken as 31 pixels, lower same.Measuring point is selected on the horizontal linear 9-1 in Fig. 5-a, and the measuring point after distortion should on broken line 9-2.Fig. 6-a is the displacement vector field calculated by traditional Digital Image Correlation Method (hereinafter referred to as classic method), and Fig. 6-b is the displacement vector field calculated by the present invention.Fig. 6-c is the related coefficient that two kinds of methods calculate, and wherein, 10-1 is the result of classic method, and 10-2 is result of the present invention.Related coefficient adopts cross correlation function, and maximal value is 1, and minimum value is-1, and the larger representative of value is more relevant, lower same.Fig. 6-d is the horizontal shift that two kinds of methods calculate, and wherein, 10-3 is the result of classic method, and 10-4 is result of the present invention, and 10-5 is theoretical value.Fig. 6-e is the perpendicular displacement that two kinds of methods calculate, and wherein, 10-6 is the result of classic method, and 10-7 is result of the present invention, and 10-8 is theoretical value.
Can find, compared with classic method, the various results that the present invention calculates are all relatively good: (1) is the left side of 151 pixels at horizontal ordinate, and from left to right, the displacement of measuring point linearly increases, and all point to below; On the right side of it, the displacement of measuring point linearly reduces, and equally all points to below, and the regularity of classic method result of calculation is so unobvious; (2) related coefficient of all measuring points is all large than classic method, and all close to the maximal value 1 that related coefficient can reach, illustrates that Search Results is more accurate; (3) precision of horizontal shift of the present invention is very high, with theoretical value 0 pixel closely, the limits of error is less than 0.01 pixel, and the limits of error of classic method reaches 0.06 pixel; (4) perpendicular displacement completely linearly arranges, very identical with theoretical value, and the error of classic method is obviously very large, the most about 0.8 pixel.
embodiment 2
The present embodiment is that the present invention is in the effect calculating the point be positioned near crackle.Use the distortion of 8-3 to 8-4 in traditional Digital Image Correlation Method and calculating chart 5-b of the present invention respectively.Measuring point is selected on the vertical line 9-3 in 8-3, and the measuring point after distortion should on broken line 9-4.The related coefficient that Fig. 7-a, Fig. 7-b, Fig. 7-c, Fig. 7-e, Fig. 7-e are respectively displacement vector field that classic method calculates, the displacement vector field that the present invention calculates, two kinds of methods calculate, horizontal shift and perpendicular displacement.Wherein, 11-1,11-3 and 11-6 are respectively the result of classic method, and 11-2,11-4 and 11-7 are respectively result of the present invention, 11-5 and 11-8 is theoretical value.
Can find, when measuring point is chosen at away from crackle, the result that classic method can obtain, such as, the measuring point of upper/lower terminal, its displacement field is smooth, and related coefficient is higher.But, when measuring point is near crackle, the complete mistake of displacement field, classic method complete failure.And the present invention is when calculating the measuring point near crackle, can ensure that every bit all calculates correctly.
embodiment 3
The present embodiment is that the present invention is calculating the effect of the point be positioned on model boundary.First, the distortion of 8-5 to 8-6 in traditional Digital Image Correlation Method calculating chart 5-c is used.Measuring point is selected in 8-5 on the horizontal linear 9-5 of inactive area (hole), and the measuring point after distortion should on straight line 9-6.The border of inactive area is the border of model inside, and the measuring point got in its vicinity is the point be positioned on model boundary.The related coefficient that Fig. 8-a, Fig. 8-b, Fig. 8-c, Fig. 8-e, Fig. 8-e are respectively displacement vector field that classic method calculates, the displacement vector field that the present invention calculates, two kinds of methods calculate, horizontal shift and perpendicular displacement.Wherein, 12-1,12-3 and 12-6 are respectively the result of classic method, and 12-2,12-4 and 12-7 are respectively result of the present invention, 12-5 and 12-8 is theoretical value.
Can find, for the measuring point near hole, classic method complete failure, the present invention then can search result accurately.No matter be related coefficient, or horizontal shift and perpendicular displacement, all embody the excellent characteristics of result of the present invention.
Above-mentioned 3 embodiments show, measuring point for following three kinds of situations: (1) is positioned at the point on model boundary, (2) point of 2 kinds of homogeneous deformations is comprised near, (3) point near crackle is positioned at, the result that traditional Digital Image Correlation Method can not obtain, and the result precision that the present invention calculates is higher.
Claims (5)
1., based on a Digital Image Correlation Method for half son district split plot design, the method concrete steps are as follows:
Step 1: the measuring point before being deformed picture being arranged some, square sample subarea is chosen centered by measuring point, utilize sub-pix Digital Image Correlation Method, obtain the deformation field comprising picture after the distortion of two kinds of deformation patterns, and pick out the poor measuring point of result;
Step 2: choose square sample subarea centered by the measuring point that each result is poor, utilized subarea central point line segment that subarea is divided into two and half subareas, the angle of multiple segmentation line segment is set, use Integer Pel Digital Image Correlation Method, the optimum target subarea in all half subareas during search different segmentation angle, obtains rough measuring point displacement and segmentation angle;
Step 3: with rough measuring point displacement and segmentation angle for initial value, utilize sub-pix Digital Image Correlation Method and convex function to ask the method for extreme value, fine search measuring point displacement and segmentation angle.
2. a kind of Digital Image Correlation Method based on half son district split plot design according to claim 1, it is characterized in that, the poor measuring point of described result is determined according to the correlativity of measuring point, when correlativity is poor, shows that measuring point may be positioned near two kinds of deformation patterns have a common boundary.
3. a kind of Digital Image Correlation Method based on half son district split plot design according to claim 1, is characterized in that, described half subarea is split to form by square shaped subarea, and segmentation line segment is by the central point of square subregions; A square subregions is divided into two and half subareas, each half subarea comprises the central point of former square subregions, and, when using sub-pix or Integer Pel Digital Image Correlation Method, using this point all as the measuring point in half subarea, so that the displacement obtained remains the displacement of the original measuring point arranged, and the pixel quantity that each half subarea comprises is all identical.
4. a kind of Digital Image Correlation Method based on half son district split plot design according to claim 1, it is characterized in that, the optimum target subarea in described half subarea is in relevant search, need the gray matrix using half subarea, the gray matrix in half subarea adopts following method to obtain: be set to invalid value by square subregions in the gray scale of the pixel of cut-off rule side, using the gray matrix of the gray matrix of the square subregions after change as half subarea.
5. a kind of Digital Image Correlation Method based on half son district split plot design according to claim 1, it is characterized in that, described segmentation angle and theoretical value closely time, half subarea that one after deformation image only comprises a kind of deformation pattern can be obtained, and then the higher displacement field of precision can be obtained.
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