CN108280806A - The DVC measurement methods of interior of articles deformation - Google Patents

Abstract

The present invention provides a kind of DVC measurement method of internal deformation of object, comprises the following steps: S1, locate the integer pixel displacement of initial point, and use the sub-pixel displacement positioning method based on gradient to obtain the sub-pixel displacement field of described initial point; S2 . Calculate the three-dimensional deformation field of the initial point by using the Newton iterative method; S3. Calculate the three-dimensional deformation field of other pixel points by the Newton iterative method according to the initial point for which the three-dimensional deformation field is calculated. Compared with the related technology, the DVC measurement method of the internal deformation of the object provided by the present invention is used for fast and high-precision measurement of the internal deformation of the object. At the same time, it realizes the efficient calculation of the DVC algorithm under the serial design. First, the calculation of the center of gravity is far less complex than the calculation of the entire pixel displacement field of a point, and multiple global searches are avoided by extending the search. The computational complexity is greatly reduced.

Description

DVC Measurement Method of Internal Deformation of Object

technical field

The invention relates to the field of digital image measurement of internal deformation of objects, in particular to a DVC measurement method for internal deformation of objects.

Background technique

X-ray micro-computed tomography (uCT) imaging is a digital method that allows researchers to visualize the internal structure of object structure without destroying the characteristics of objects, and is widely used in various data acquisition, such as bones. With the development of research and the improvement of computer performance, many numerical methods based on CT image processing, such as micro-finite element method, digital image correlation (DVC), etc., have been proposed and applied to experimental simulations.

In 1999, Bay et al proposed the digital volume image correlation (DVC) method, which can directly measure the internal pressure deformation of the volume image after bone tissue reconstruction. As a direct extension of the 2D digital image correlation method (2D-DIC), this method obtains the internal full-field deformation and displacement. In recent years, with the continuous development of 3D digital imaging equipment, the DVC method has been widely concerned and applied in the research fields of experimental mechanics, biomedical engineering and material engineering.

Similar to the principle of the 2D-DIC method, the principle of the DVC method is to compare the points at the same position of the volume data before and after the sample deformation to obtain a three-dimensional deformation field. In the actual calculation process, researchers usually encounter many problems such as computational complexity and measurement accuracy. From the perspective of computational complexity, the 2D-DIC method needs to calculate ² points of font block K in a cube of (2N+1) ² size, while the DVC method needs to calculate sub-volume blocks in a cube of size (2N+1) ³ K ³ points, its complexity is K(2N+1) times of the 2D-DIC method, in practice, this value is usually above x1000. From the perspective of measurement accuracy, since the sample data are discrete pixels, only integer-level offsets before and after sample deformation can be calculated, but in fact, real objects are not discrete, so only integer-level offsets are far from enough of.

In recent years, the research focus of DVC method has been concentrated on the calculation accuracy and calculation efficiency. In the study of the whole element, it is found that a cross-correlation algorithm based on fast Fourier transform is widely used because the calculation of the cross-correlation algorithm in the space domain is equivalent to the point-by-point multiplication in the frequency domain. In order to achieve higher accuracy, many subvoxel-level methods based on the Newton iterative method and its derivative methods have been proposed, such as the Levenberg-Marquardt algorithm and the Broyden-Fletcher-GoldfarbShanno (BFGS) algorithm, etc., making the DVC method reach the 0.1voxel level accuracy. Pan et al. proposed three ideas to accelerate the DVC algorithm in recent years: one is to approximate the Hessian matrix of the volume data by the reverse method when calculating the subvoxel gradient, thereby avoiding the complicated Hessian matrix solution; the other is to find A more feasible pre-estimation of the offset, so as to converge faster and get better results during iterations; the third is to record the interpolation coefficients of each voxel during sub-voxel interpolation, so that they can be directly queried in subsequent calculations to avoid Calculate again. Through these methods, the calculation speed of the DVC algorithm reaches 41 points of interest (POI) per second. In general, the current subvoxel displacement algorithm still has the shortcomings of insufficient accuracy and high computational complexity. Considering the increasing application requirements of the DVC algorithm, a high-precision and high-efficiency method is urgently needed.

Contents of the invention

The technical problem solved by the present invention is to provide a DVC measurement method for internal deformation of an object, which solves the problems of relatively low accuracy and calculation efficiency of the current DVC algorithm.

In order to solve the above-mentioned technical problems, the invention provides a kind of DVC measuring method of internal deformation of object, comprises the steps:

S1. Locate the integer pixel displacement of the initial point through the center of gravity of the region of interest of the body image before and after deformation, and use a gradient-based sub-pixel displacement positioning method to obtain the sub-pixel displacement field of the initial point;

S2. Calculate the three-dimensional deformation field of the initial point by using the Newton iteration method according to the sub-pixel displacement field;

S3. According to the calculated initial point of the three-dimensional deformation field, calculate the three-dimensional deformation field of each pixel around the initial point by the Newton iterative method, and for any uncalculated pixel in the region of interest of the volume image, according to The surrounding pixels whose three-dimensional deformation field has been calculated are used to calculate the three-dimensional deformation field until the three-dimensional deformation field of all the pixel points inside the object is obtained.

Preferably, in step S1, the formula for calculating the center of gravity of the volumetric image region of interest is:

Among them, G _Ta represents the center of gravity of the volume image T on the a-axis, a can choose the x, y, and z axes, and T(p) represents the pixel value of the volume image T at point p.

Preferably, in step S1, the calculation formula of the sub-pixel displacement field Δ at the initial point is:

f _G ＝round(G _fx ,G _fy ,G _fz )

g _G ＝round(G _gx ,G _gy ,G _gz )

Δ=(Δu,Δv,Δw)=f _G -g _G

Among them, round is a rounding function, f and g represent the volume image before and after deformation, respectively, and f _G and g _G are the center of gravity of the region of interest in the volume image before and after object deformation.

Preferably, in step S1, the step of obtaining the sub-pixel displacement field of the initial point includes:

Taylor's first-order expansion of the formula f(p)=g(p')p∈D and p'=p+Δ+Δ' gives g(p+Δ+Δ')=g(p+Δ)+Δ 'g'(p+Δ), where D represents the set of pixels within k distances from the current pixel in the volume image f, p is a pixel in D, and p' represents the pixel point p in the volume image g Corresponding point, Δ' is the required sub-pixel displacement field, g'(p+Δ) is the first-order gray gradient of the volume image g on the pixel point p+Δ;

Take the extreme value of the least square correlation function (SSD):

C _SSD (Δ')＝∑ _p∈D (f(p)-g(p+Δ+Δ')) ²

The sub-pixel displacement field Δ' is calculated by using the formula Δ'=Σg'(g')Σ(f-g)g'.

Preferably, the gray gradient is calculated using a Barron operator.

Preferably, in step S2, the Newton iterative method uses a zero-mean normalized sum of squares function (ZNSSD) as a correlation function.

Preferably, in step S2, a ternary cubic interpolation method is used to interpolate the gray value of the volume image.

Compared with the related technology, the DVC measurement method of the internal deformation of the object provided by the present invention is used for fast and high-precision measurement of the internal deformation of the object. At the same time, it realizes the efficient calculation of the DVC algorithm under the serial design. First, the calculation of the center of gravity is far less complex than the calculation of the entire pixel displacement field of a point, and multiple global searches are avoided by extending the search. The computational complexity is greatly reduced.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings that need to be used in the description of the embodiments. The drawings in the following description are only some embodiments of the present invention. Ordinary technicians can also obtain other drawings based on these drawings without any creative effort, among which:

FIG. 1 is a flowchart of a DVC measurement method for internal deformation of an object provided by an embodiment of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Please refer to Fig. 1, the present invention provides a kind of DVC measuring method of internal deformation of object, comprises the steps:

S1. Locate the integer pixel displacement of the initial point through the center of gravity of the region of interest of the body image before and after deformation, and use a gradient-based sub-pixel displacement positioning method to obtain the sub-pixel displacement field of the initial point;

S2. Calculate the three-dimensional deformation field of the initial point by using the Newton iteration method according to the sub-pixel displacement field;

S3. According to the calculated initial point of the three-dimensional deformation field, calculate the three-dimensional deformation field of each pixel around the initial point by the Newton iterative method, and for any uncalculated pixel in the region of interest of the volume image, according to The surrounding pixels whose three-dimensional deformation field has been calculated are used to calculate the three-dimensional deformation field until the three-dimensional deformation field of all the pixel points inside the object is obtained.

In step S1, generally, since the relative deformation and displacement between the body images before and after the deformation of the object are small, the corresponding point of the barycenter of the region of interest in the deformed body image must be in the deformed body image. near the center of gravity of the region, so the present invention selects the center of gravity of the region of interest of the volume image before and after deformation as a pair of initial correlation points, and the calculation formula for the center of gravity of the region of interest of the volume image is:

Among them, G _Ta represents the center of gravity of the volume image T on the a-axis, a can choose the x, y, and z axes, and T(p) represents the pixel value of the volume image T at point p. The center of gravity calculated by this formula is a decimal value, which is then rounded to an integer:

f _G ＝round(G _fx ,G _fy ,G _fz )

g _G ＝round(G _gx ,G _gy ,G _gz )

Among them, round is a rounding function, f and g represent the volume image before and after deformation, f _G and g _G are the center of gravity of the body image region of interest before and after deformation of the object, G _fx , G _fy , G _fz represent the volume image f in The center of gravity of the x, y, and z axes, G _gx , G _gy , and G _gz represent the center of gravity of the volume image g on the x, y, and z axes respectively. Therefore, the integer pixel displacement field Δ is:

Δ=(Δu,Δv,Δw)=f _G -g _G

After calculating the initial pixel displacement field, in order to obtain a more accurate displacement in the deformable volume image, it is necessary to calculate the sub-pixel displacement field. Due to the limited range of voxel grayscale, usually 0 to 255, it is impossible to track the precise displacement of a pixel, so the current pixel must be centered on the overall comparison of the pixels within k distance from the center pixel, k is a natural number greater than zero. The present invention preferably uses a gradient-based method to obtain the sub-pixel displacement field according to the entire pixel displacement field. Considering that when the above k is small enough and the deformation is small, the deformation of this region can be regarded as an approximate rigid body displacement, and the same correspondence before and after deformation The grayscale of the dots does not change much. Therefore, the step of obtaining the sub-pixel displacement field of the initial point includes:

Taylor's first-order expansion of the formula f(p)=g(p')p∈D and p'=p+Δ+Δ' gives g(p+Δ+Δ')=g(p+Δ)+Δ 'g'(p+Δ), where D represents the set of pixels within k distances from the current pixel in the volume image f, p is a pixel in D, and p' represents the pixel point p in the volume image g Corresponding point, Δ is the entire pixel displacement field, Δ' is the required sub-pixel displacement field, g'(p+Δ) is the first-order gray gradient of the volume image g on the pixel point p+Δ;

Take the extreme value of the least square correlation function (SSD):

C _SSD (Δ')＝∑ _p∈D (f(p)-g(p+Δ+Δ')) ²

The sub-pixel displacement field Δ' is calculated by using the formula Δ'=Σg'(g') ^T Σ(fg)g'.

From the calculation formula of the sub-pixel displacement field Δ' above, it can be seen that the sub-pixel displacement field at the initial point is only related to the gray gradient of the deformed volume image g, so different gray gradient algorithms are important for the measurement accuracy of sub-pixels. influences. The present invention uses the Barron operator with higher precision to calculate the gray gradient, and the gray gradient of the volume image g at the pixel point p(x, y, z) is:

Among them, g _x , g _y , and g _z are the gray gradient components on the x, y, and z axes, respectively.

In step S2, the calculation of the above-mentioned displacement field considers that the deformation is only the displacement motion of the rigid body. Obviously, in the real scene, the object may rotate and shear in the three-dimensional space, so a more accurate method must be used to calculate the three-dimensional deformation field. Disagree that the three-dimensional displacement only has three parameters (Δu, Δv, Δw), and the three-dimensional space deformation has a total of twelve parameters:

q＝(u _x ,u _y ,u _z ,u,v _x ,v _y ,v _z ,v,w _x ,w _y ,w _z ,w)

Among them, H(q) is the displacement parameter, T(q) is the rotation parameter, the rotation parameter is also the displacement gradient component of the volume image, and T is the rotation matrix with q as the parameter. In order to better evaluate the similarity of sub-volumes before and after deformation, the method provided by the present invention uses the zero-mean normalized sum of squares function (ZNSSD) as the correlation function, which is insensitive to the scale and offset of illumination fluctuations and is widely used applied to cross-correlation comparisons. For a sub-volume block of (2k+1) ³ , the formula is:

Among them, C _ZNSSD (q) is the zero-mean normalization function, p is the pixel point of the deformation premise image, q is the deformation parameter, p' is the center pixel pc as the symmetric center and the mapping function with the deformation parameter q Corresponding pixels:

p'=T(q)(pp _c )+H(q)+Δ

f _m and g _m are the average gray values of the volume image sub-volume blocks before and after deformation, and the calculation formula is:

It can be seen that the ZNSSD function is a nonlinear function of q, and q contains 12 parameters. For the optimization problem of nonlinear equations, we usually use the Newton iterative method for fast solution:

Where q _t is the parameter of the previous iteration, and the initial value of this parameter is usually set to all 0s. In the DVC measurement method, the gray correlation of different regions is not large, so the calculation function of the displacement parameter H(q) and the rotation parameter T(q) is not a convex function, so a good pre-estimation is to optimize the ZNSSD function key. The DVC measurement method provided by the present invention uses the sub-pixel displacement obtained in the previous section as the initial value of q, namely:

q ₀ =(0,0,0,Δu',0,0,0,Δv',0,0,0,Δw')

is the first-order gradient of the ZNSSD function, is the second-order gradient, that is, the Hessian matrix. The gradient of the calculation function of the above-mentioned displacement parameter H(q) and rotation parameter T(q) is not intuitive. It can be seen that f _m and g _m are constants, which can be ignored during the derivation process, so the first-order and The second-order gradient can be abbreviated as:

In the above formula, Δf and Δg are respectively the denominators in the calculation function of the displacement parameter H(q) and the rotation parameter T(q), and are constants. It can be seen that the gradient of the ZNSSD function is only related to the gray gradient of the deformed volume image. Since the volume image is an integer pixel, it is impossible to directly calculate the gradient field in three dimensions. A feasible method is to gray the volume image degree value interpolation. The present invention preferably adopts a ternary cubic interpolation method with high precision, and the difference method uses the gray information of 64 integer pixels around the interpolation to carry out weighted calculation. In a specific calculation process, the ternary cubic interpolation method can also be divided into performing one-dimensional cubic interpolation on each of the three coordinate axes. The formula for reconstructing the posterior body image is:

Wherein α is 64 (4*4*4) interpolation coefficients, which can be obtained by calculating the integer number of 4*4*4 adjacent to the interpolation pixel. Obviously, since the gray value of the volume image is constant, the 64 coefficients of each pixel after ternary cubic interpolation are also certain, and the 64 interpolation coefficients of each point can be calculated in the preprocessing, It is used directly in subsequent calculations without double calculation. The volume image after interpolation can be regarded as a continuous volume image, and its first-order and second-order gradients can be simply calculated at this time.

In step S3, after calculating the deformation of the initial point, it is necessary to calculate the internal full-field deformation of the volume image. The present invention considers the feature that the gray values of adjacent points of the volume image are similar, and uses a full-field deformation calculation based on extended search. Since the above calculations are all based on sub-volume blocks of (2n+1) ³ pixels, after the deformation field of the central pixel is calculated, it can also be calculated that the pixels around the central pixel are affected by the deformation field After the position, as shown in the formula p'=p+Δ+Δ', for any pixel point pr around the central pixel, there are:

pr'=T(q)(pr-p _c )+H(q)+Δ

Among them, pr' is the corresponding pixel point of the pixel point pr in the deformed volume image. At this time, it can be considered that the real corresponding pixel point of pr should be near pr'. Considering the continuity of the ZNSSD correlation function, start from pr' point A new round of iterations can not only save unnecessary computational overhead, but also achieve a good minimum. When calculating with the pixel point pr as the center point, the integer pixel offset and sub-pixel offset corresponding to pr are:

Δ(pr)=round(pr'-pr)Δ'(pr)=pr'-pr-Δ(pr)

From the above formula, it can be deduced that in the initial value of the deformation parameter q of the pixel point pr, T(q) is all 0, H(q) is Δ'(pr), and the three-dimensional deformation field of each pixel point is repeatedly calculated using the Newton iterative method , so as to obtain the whole three-dimensional deformation field inside the object.

Compared with the related technology, the DVC measurement method of the internal deformation of the object provided by the present invention is used for fast and high-precision measurement of the internal deformation of the object. At the same time, it realizes the efficient calculation of the DVC algorithm under the serial design. First, the calculation of the center of gravity is far less complex than the calculation of the entire pixel displacement field of a point, and multiple global searches are avoided by extending the search. The computational complexity is greatly reduced.

The above is only an embodiment of the present invention, and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process conversion made by using the description of the present invention and the contents of the accompanying drawings, or directly or indirectly used in other related technologies fields, all of which are equally included in the scope of patent protection 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, G_TaBody 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：

f_G=round (G_fx,G_fy,G_fz)

g_G=round (G_gx,G_gy,G_gz)

Δ=(Δ u, Δ v, Δ w)=f_G-g_G

Wherein, round is the function to round up, and f and g respectively represent the body image before and after deformation, f_GWith g_GBefore 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)：

C_SSD(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.