CN108280806A - The DVC measurement methods of interior of articles deformation - Google Patents
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- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
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Abstract
The present invention provides a kind of DVC measurement methods of interior of articles deformation, includes the following steps:S1, the whole pixel displacement for positioning initial point, and Displacement localization method of the use based on gradient finds out the Displacement field of the initial point；S2, the three-dimensional shaped variable field that the initial point is calculated using Newton iteration method；S3, basis calculate the initial point of three-dimensional shaped variable field, and the three-dimensional shaped variable field of other pixels is calculated by Newton iteration method.Compared with the relevant technologies, quick high accuracy of the DVC measurement methods of interior of articles deformation provided by the invention for interior of articles deformation measures, this method is calculated and is realized simply, and noise resisting ability is strong, there is good measurement effect for the tiny deformation of interior of articles, realize efficient calculating of the DVC algorithms under serial design simultaneously, calculating of its complexity well below the whole pixel displacement field of a point is calculated firstly for center of gravity, and multiple global search is avoided by expanded search so that computation complexity substantially reduces.
Description
Technical field
The present invention relates to digital pictures to measure interior of articles deformation field more particularly to a kind of DVC of interior of articles deformation
Measurement method.
Background technology
X-ray microcomputer tomoscan (uCT) imaging is a kind of permission researcher not destroy object structures visual
The digital method for changing the internal structure of feature is widely used in various data acquisitions, typical such as bone.With grinding
Study carefully development and the progress of computer performance, for example micro- finite element method of many numerical methods based on CT image procossings, digitized map
As related (DVC) etc. is suggested and is applied in experimental simulation.
Bay in 1999 et al. proposes related (DVC) method of number font image, after this method can directly measure bone tissue reconstruction
The internal pressure deformation of body image.As the direct extension of 2D loading by means of digital image correlation method (2D-DIC), this method is by comparing bone
Group is woven in before and after stress and deformation two groups of number font images under state, and it is internal complete under specified pressure effect to obtain the bone tissue
Field deformation and displacement.Recently as the continuous development of 3 D digital imaging equipment, DVC method is in Experimental Mechanics, biomedicine
The research fields such as engineering and material engineering obtain extensive concern and application.
Similar with the principle of 2D-DIC methods, the principle of DVC method is volume data same position before and after contrast sample's deformation
Point obtain three-dimensional shaped variable field.In practical calculating process, researcher would ordinarily be encountered computation complexity and measurement accuracy etc.
Problems.From the point of view of computation complexity, 2D-DIC methods are needed at (2N+1)2Font block K is calculated in the cube of size2It is a
Point, and DVC method is needed at (2N+1)3The cube of size is fallen into a trap operator body block K3A, complexity is 2D-DIC methods
K (2N+1) times, in practice, the numerical value is usually in x1000 or more.From the point of view of measurement accuracy, since sample data is discrete
Pixel, integer grade deviates before and after can only calculating sample deformation, but the object actually in reality is not discrete, so
Only integer grade offset is far from being enough.
The research emphasis of DVC method has been focused into computational accuracy and computational efficiency in recent years.In the research of whole element
Middle discovery, the calculating due to cross correlation algorithm in spatial domain are equivalent to the point-by-point multiplication of frequency domain, and one kind being based on Fast Fourier Transform
Cross correlation algorithm be widely used.In order to reach higher precision, many Asias based on Newton iteration method and its deriving method
Voxel grade method is suggested, such as Levenberg-Marquardt algorithms and Broyden-Fletcher-
GoldfarbShanno (BFGS) algorithm etc. so that DVC method has reached the precision of 0.1voxel ranks.Pan et al. is carried in recent years
The thinking of three acceleration DVC algorithms is gone out：First, passing through inverse approach approximation volume data when calculating sub- voxel gradient
Hessian matrixes, so as to avoid complicated Hessian Matrix Solvings；Second is that proposing that searching one is more feasible before iteration
Offset pre-estimation, to more rapid convergence and obtain better result in iteration；Third, when recording sub- voxel interpolation
The interpolation coefficient of each voxel is avoided and is calculated again to directly be inquired in follow-up calculate.Pass through these methods, DVC
It is per second that the calculating speed of algorithm has reached 41 point-of-interests (POI).Generally speaking, current sub- voxel displacement algorithm still has
There is accuracy insufficient and the higher disadvantage of computation complexity, it is contemplated that the growing application demand of DVC algorithms, it is a kind of high-precision
Degree and efficient method are urgently demands.
Invention content
The technical problem to be solved by the present invention is to provide a kind of DVC measurement methods of interior of articles deformation, solve current DVC
The more low problem of the precision and computational efficiency of algorithm.
In order to solve the above technical problems, the present invention provides a kind of DVC measurement methods of interior of articles deformation, including walk as follows
Suddenly:
S1, the whole pixel displacement that initial point is positioned by the center of gravity of body interesting image regions before and after deformation, and use base
The Displacement field of the initial point is found out in the Displacement localization method of gradient；
S2, the three-dimensional shaped variable field for calculating the initial point using Newton iteration method according to Displacement field；
S3, basis calculate the initial point of three-dimensional shaped variable field, are calculated around the initial point by Newton iteration method
The three-dimensional shaped variable field of each pixel, to any one uncalculated pixel in body interesting image regions, according to it
Surrounding has calculated the pixel of three-dimensional shaped variable field to calculate its three-dimensional Deformation Field, until obtaining interior of articles whole pixel
The three-dimensional shaped variable field of point.
Preferably, in step sl, the calculation formula of the center of gravity of the body interesting image regions is：
Wherein, GTaBody image T is indicated in the center of gravity of a axis, a can select x, y, z-axis, and T (p) indicates body image T in p points
Pixel value.
Preferably, in step sl, the calculation formula of the Displacement field Δ of the initial point is：
fG=round (Gfx,Gfy,Gfz)
gG=round (Ggx,Ggy,Ggz)
Δ=(Δ u, Δ v, Δ w)=fG-gG
Wherein, round is the function to round up, and f and g respectively represent the body image before and after deformation, fGWith gGFor object shape
Become the center of gravity of front and back body interesting image regions.
Preferably, in step sl, the step that finds out of the Displacement field of the initial point includes：
To formula f (p)=g (p') p ∈ D and p'=p+ Δ+Δ ' carry out Taylor's single order expansion, obtain g (p+ Δs+Δ ')=
G (p+ Δs)+Δ ' g'(p+ Δs), wherein D indicates the pixel collection in k distance of current pixel, p D in body image f
In a pixel, p' indicates corresponding points of the pixel p in body image g, Δ ' for desired Displacement field, g'(p+
Δ) it is single order shade of gray of the body image g on pixel p+ Δs；
Extreme value is taken to least square correlation function (SSD)：
CSSD(Δ ')=∑p∈D(f(p)-g(p+Δ+Δ'))2
Utilize formula Δ '=∑ g'(g') ∑ (f-g) g' be calculated Displacement field Δ '.
Preferably, the shade of gray is calculated using Barron operators.
Preferably, in step s 2, the Newton iteration method uses zero-mean to normalize sum of squares function (ZNSSD) conduct
Correlation function.
Preferably, in step s 2, grey value interpolation is carried out to body image using ternary cubic interpolation method.
Compared with the relevant technologies, the DVC measurement methods of interior of articles deformation provided by the invention are used for interior of articles shape
The quick high accuracy of change measures, and this method is calculated and realized simply, and noise resisting ability is strong, has for the tiny deformation of interior of articles
Good measurement effect, while realizing efficient calculating of the DVC algorithms under serial design, firstly for the calculating of center of gravity, it is multiple
It is miscellaneous to spend the calculating of the whole pixel displacement field well below a point, and multiple global search is avoided by expanded search, make
Computation complexity is obtained to substantially reduce.
Description of the drawings
To describe the technical solutions in the embodiments of the present invention more clearly, make required in being described below to embodiment
Attached drawing is briefly described, and drawings in the following description are only some embodiments of the invention, common for this field
For technical staff, without creative efforts, other attached drawings are can also be obtained according to these attached drawings,
In：
Fig. 1 is the flow chart of the DVC measurement methods of interior of articles deformation provided in an embodiment of the present invention.
Specific implementation mode
The technical scheme in the embodiments of the invention will be clearly and completely described below, it is clear that described implementation
Example is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, this field is common
All other embodiment that technical staff is obtained without making creative work belongs to the model that the present invention protects
It encloses.
Referring to Fig. 1, the present invention provides a kind of DVC measurement methods of interior of articles deformation, include the following steps:
S1, the whole pixel displacement that initial point is positioned by the center of gravity of body interesting image regions before and after deformation, and use base
The Displacement field of the initial point is found out in the Displacement localization method of gradient；
S2, the three-dimensional shaped variable field for calculating the initial point using Newton iteration method according to Displacement field；
S3, basis calculate the initial point of three-dimensional shaped variable field, are calculated around the initial point by Newton iteration method
The three-dimensional shaped variable field of each pixel, to any one uncalculated pixel in body interesting image regions, according to it
Surrounding has calculated the pixel of three-dimensional shaped variable field to calculate its three-dimensional Deformation Field, until obtaining interior of articles whole pixel
The three-dimensional shaped variable field of point.
In step sl, under normal circumstances, due between body image before and after object deformation relative deformation and displacement it is smaller,
Corresponding points of the deformation precursor interesting image regions center of gravity after deformation in body image are inevitable in deformation Hou Ti interesting images area
Near the center of gravity of domain, therefore the present invention selects the focus point of body interesting image regions before and after deformation as a pair of initial related
The calculation formula of point, the center of gravity of the body interesting image regions is：
Wherein, GTaBody image T is indicated in the center of gravity of a axis, a can select x, y, z-axis, and T (p) indicates body image T in p points
Pixel value.The center of gravity that the formula calculates is fractional value, later by being rounding to integer：
fG=round (Gfx,Gfy,Gfz)
gG=round (Ggx,Ggy,Ggz)
Wherein, round is the function to round up, and f and g respectively represent the body image before and after deformation, fGWith gGFor object shape
Become the center of gravity of front and back body interesting image regions, Gfx,Gfy,GfzIndicate body image f in x, y, the center of gravity of z-axis, G respectivelygx,Ggy,
GgzBody image g is indicated respectively in x, and y, the center of gravity of z-axis, then, whole pixel displacement field Δ is：
Δ=(Δ u, Δ v, Δ w)=fG-gG
After finding out initial o'clock sharp pixel displacement field, the more accurate offset in deformable body image in order to obtain needs to ask
Go out the displacement field of sub-pix.It is 0 to 255 under normal conditions since volumetric pixel tonal range is limited, a pixel can not be tracked
Precise displacement, so must be centered on current pixel point, it is whole right that the pixel in the distance of center pixel k of adjusting the distance is done
Than k is the natural number more than zero.Present invention preferably uses the methods based on gradient to find out sub-pix position according to whole pixel displacement field
Move field, it is contemplated that when above-mentioned k is sufficiently small and deformation is smaller, the deformation in the region can regard approximate rigid body displacement as, and
The grey scale change of same corresponding points is little before and after deformation.Therefore, the step that finds out of the Displacement field of the initial point includes：
To formula f (p)=g (p') p ∈ D and p'=p+ Δ+Δ ' carry out Taylor's single order expansion, obtain g (p+ Δs+Δ ')=
G (p+ Δs)+Δ ' g'(p+ Δs), wherein D indicates the pixel collection in k distance of current pixel, p D in body image f
In a pixel, p' indicates corresponding points of the pixel p in body image g, and Δ is whole pixel displacement field, Δ ' for what is required
Displacement field, g'(p+ Δs) it is single order shade of gray of the body image g on pixel p+ Δs；
Extreme value is taken to least square correlation function (SSD)：
CSSD(Δ ')=∑p∈D(f(p)-g(p+Δ+Δ'))2
Utilize formula Δ '=∑ g'(g')T∑ (f-g) g' be calculated Displacement field Δ '.
By above-mentioned Displacement field Δ ' calculation formula it is found that at this time the Displacement field of initial point only with deformation
The shade of gray of body image g is related afterwards, so different shade of gray algorithms has a major impact the measurement accuracy of sub-pix.This
The higher Barron operators of invention service precision calculate shade of gray, and the gray scale for body image g in pixel p (x, y, z) is terraced
Degree is：
Wherein gx,gy,gzX, y respectively, the shade of gray component in z-axis.
In step s 2, the calculating of above-mentioned displacement field thinks that deformation is only rigid body displacement movement, it is clear that in real scene
Middle object may rotate in three dimensions and shear, so three-dimensional shaped variable field must be calculated by more accurate method.
Disagreeing three-D displacement, only only there are three parameter, (Δ u, Δ v, Δ w), three dimensions deformation one share 12 parameters：
Q=(ux,uy,uz,u,vx,vy,vz,v,wx,wy,wz,w)
Wherein, H (q) is displacement parameter, and T (q) is rotation parameter, and rotation parameter is also the displacement gradient component of body image, T
For using q as the spin matrix of parameter.In order to more preferably assess the similarity before and after daughter block deformation, method provided by the invention uses
Zero-mean normalizes sum of squares function (ZNSSD) and is used as correlation function, the scale and offset of function pair illumination fluctuation unwise
Sense is widely used in cross-correlation comparison.For one (2k+1)3Daughter block, formula is：
Wherein CZNSSD(q) it is zero-mean normalized function, p is the pixel of deformation premise image, and q is deformation parameter, p'
For the corresponding pixel points by symmetrical centre of central pixel point pc after the mapping function that deformation parameter is q acts on：
P'=T (q) (p-pc)+H(q)+Δ
fmWith gmThe gray average of body image daughter block, calculation formula are respectively before and after deformation：
It can be seen that ZNSSD functions are the nonlinear functions to q, include 12 parameters in q.Most for nonlinear equation
Optimization problem, we carry out rapid solving usually using Newton iteration method：
Wherein qtIt is the parameter of preceding an iteration, the initial value of the parameter is normally provided as full 0.In DVC measurement methods
In, it is little by the Gray Correlation of different zones, so leading to the calculating function of displacement parameter H (q) and rotation parameter T (q) not
It is convex function, so a good pre-estimation is the key that optimize ZNSSD functions.DVC measurement methods provided by the invention make
Use the Displacement that is found out in section as the initial value of q, i.e.,：
q0=(0,0,0, Δ u', 0,0,0, Δ v', 0,0,0, Δ w')
For the First-order Gradient of ZNSSD functions,For second order gradient, i.e. Hessian matrixes.Above-mentioned displacement parameter H
(q) and the gradient of the calculating function of rotation parameter T (q) is not intuitive, it can be seen that wherein fmWith gmAll it is constant, in derivation
It can not go to consider in journey, then single order can be abbreviated as with second order gradient：
Δ f and Δ g is respectively the denominator of displacement parameter H (q) and rotation parameter T (q) calculated in function in above formula, and is
Constant.It can be seen that the gradient of ZNSSD functions is finally only related with the shade of gray of body image after deformation, since body image is all
Whole pixel, can not directly find out the gradient fields in three-dimensional, and a kind of feasible method is to carry out grey value interpolation to body image.This
Invention preferably uses the higher ternary cubic interpolation method of precision, which, which utilizes, needs 64 whole pixels around interpolation
Half-tone information be weighted.In specific calculating process, ternary cubic interpolation method can also difference Cheng San
Primary one-dimensional cubic interpolation is respectively carried out in reference axis.The formula of body image is after reconstruction：
Wherein α is 64 (4*4*4) a interpolation coefficients, which can be by the whole of the adjacent 4*4*4 of interpolating pixel point
As number is calculated.It will be apparent that since the gray value of body image is constant, so each pixel passes through ternary cubic interpolation
64 coefficients afterwards are also certain, and 64 interpolation coefficients of each point can be calculated in pretreatment, in follow-up calculate
Directly use, and without being computed repeatedly.Body image after interpolation, which can consider, is continuous body image, at this time can be with
Simply find out its single order and second order gradient.
In step s3, after calculating the deformation of initial point, the inside whole audience deformation for calculating body image is needed.The present invention
Consider the close feature of the gray value of body image consecutive points, uses a kind of whole audience deformation calculation based on expanded search.Due to
It is all based in above-mentioned calculating (2n+1)3What the daughter block of a pixel carried out, so, come when the Deformation Field of center pixel is found out
Afterwards, position of the pixel after the deformation field action around center pixel can also be found out, as formula p'=p+ Δs+Δ ' shown in,
For any pixel point pr around center pixel, have：
Pr'=T (q) (pr-pc)+H(q)+Δ
Wherein, pr' is corresponding pixel points of the pixel pr after deformation in body image, at this time it is considered that pr is really right
Answer pixel should be near pr', it is contemplated that the continuity of ZNSSD correlation functions carries out the iteration of a new round not from pr' points
But unnecessary computing cost can be saved, good minimum can be also reached.Point is calculated centered on by pixel pr
When, the corresponding whole pixel-shifts of pr are respectively with sub-pix offset：
Δ (pr)=round (pr'-pr) Δ ' (pr)=pr'-pr- Δs (pr)
In the initial value of deformation parameter q that pixel pr can be released by above formula, T (q) is full 0, and H (q) is Δ ' (pr),
The three-dimensional shaped variable field that each pixel is computed repeatedly using Newton iteration method, to obtain the three-dimensional deformation of interior of articles whole
.
Compared with the relevant technologies, the DVC measurement methods of interior of articles deformation provided by the invention are used for interior of articles shape
The quick high accuracy of change measures, and this method is calculated and realized simply, and noise resisting ability is strong, has for the tiny deformation of interior of articles
Good measurement effect, while realizing efficient calculating of the DVC algorithms under serial design, firstly for the calculating of center of gravity, it is multiple
It is miscellaneous to spend the calculating of the whole pixel displacement field well below a point, and multiple global search is avoided by expanded search, make
Computation complexity is obtained to substantially reduce.
Example the above is only the implementation of the present invention is not intended to limit the scope of the invention, every to utilize this hair
Equivalent structure or equivalent flow shift made by bright specification and accompanying drawing content is applied directly or indirectly in other relevant skills
Art field, is included within the scope of the present invention.
Claims (7)
1. a kind of DVC measurement methods of interior of articles deformation, which is characterized in that include the following steps:
S1, the whole pixel displacement that initial point is positioned by the center of gravity of body interesting image regions before and after deformation, and using based on ladder
The Displacement localization method of degree finds out the Displacement field of the initial point；
S2, the three-dimensional shaped variable field for calculating the initial point using Newton iteration method according to Displacement field；
S3, basis calculate the initial point of three-dimensional shaped variable field, are calculated by Newton iteration method each around the initial point
The three-dimensional shaped variable field of a pixel, to any one uncalculated pixel in body interesting image regions, according to around it
The pixel of three-dimensional shaped variable field has been calculated to calculate its three-dimensional Deformation Field, until obtaining interior of articles whole pixel
Three-dimensional shaped variable field.
2. the DVC measurement methods of interior of articles deformation according to claim 1, which is characterized in that in step sl, described
The calculation formula of the center of gravity of body interesting image regions is：
Wherein, GTaBody image T is indicated in the center of gravity of a axis, a can select x, y, z-axis, T (p) indicate body image T p points pixel
Value.
3. the DVC measurement methods of interior of articles deformation according to claim 2, which is characterized in that in step sl, described
The calculation formula of the Displacement field Δ of initial point is：
fG=round (Gfx,Gfy,Gfz)
gG=round (Ggx,Ggy,Ggz)
Δ=(Δ u, Δ v, Δ w)=fG-gG
Wherein, round is the function to round up, and f and g respectively represent the body image before and after deformation, fGWith gGBefore object deformation
The center of gravity of body interesting image regions afterwards.
4. the DVC measurement methods of interior of articles deformation according to claim 3, which is characterized in that in step sl, described
The step that finds out of the Displacement field of initial point includes：
To formula f (p)=g (p') p ∈ D and p'=p+ Δ+Δ ' progress Taylor's single order expansion, g (p+ Δs+Δ ')=g (p+ are obtained
Δ)+Δ ' g'(p+ Δs), wherein D indicates that the pixel collection in k distance of current pixel, p are in D in body image f
One pixel, corresponding points of the p' expressions pixel p in body image g, Δ ' be desired Displacement field, g'(p+ Δs)
For single order shade of gray of the body image g on pixel p+ Δs；
Extreme value is taken to least square correlation function (SSD)：
CSSD(Δ ')=∑p∈D(f(p)-g(p+Δ+Δ'))2
Utilize formula Δ '=∑ g'(g')T∑ (f-g) g' be calculated Displacement field Δ '.
5. the DVC measurement methods of interior of articles deformation according to claim 4, which is characterized in that the shade of gray is adopted
It is calculated with Barron operators.
6. the DVC measurement methods of interior of articles deformation according to claim 1, which is characterized in that in step s 2, described
Newton iteration method uses zero-mean to normalize sum of squares function (ZNSSD) and is used as correlation function.
7. the DVC measurement methods of interior of articles deformation according to claim 6, which is characterized in that in step s 2, use
Ternary cubic interpolation method carries out grey value interpolation to body image.
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| CN112082496A (en) * | 2020-09-08 | 2020-12-15 | 西安建筑科技大学 | Concrete internal deformation measurement method and system based on improved digital volume image correlation method |
| CN114549614A (en) * | 2021-12-21 | 2022-05-27 | 北京大学 | Digital volume correlation method, device, equipment and medium based on deep learning |
| CN114777709A (en) * | 2022-05-05 | 2022-07-22 | 东南大学 | DVC (dynamic voltage waveform) microcrack characterization method based on daughter block separation |
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