CN108280806B - DVC (digital video coding) measuring method for internal deformation of object - Google Patents
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Abstract
S1, positioning the whole pixel displacement of the initial point, and using the sub-pixel displacement positioning method based on gradient to calculate the sub-pixel displacement field of the initial point; s2, calculating a three-dimensional deformation field of the initial point by using a Newton iteration method; and S3, calculating the three-dimensional deformation fields of other pixel points by a Newton iteration method according to the initial point of the calculated three-dimensional deformation field. Compared with the related technology, the DVC measuring method of the internal deformation of the object provided by the invention is used for rapid high-precision measurement of the internal deformation of the object, the method is simple to calculate and realize, the noise resistance is strong, the small deformation of the internal part of the object is well measured, meanwhile, the efficient calculation of the DVC algorithm under serial design is realized, firstly, the calculation complexity of the gravity center is far lower than that of the whole pixel displacement field of one point, and multiple global searches are avoided through extended searches, so that the calculation complexity is greatly reduced.
Description
Technical Field
The invention relates to the field of measuring the internal deformation of an object by using a digital image, in particular to a DVC (digital video coding) measuring method for the internal deformation of the object.
Background
X-ray computed tomography (UCT) imaging is a digital method that allows researchers to acquire a wide variety of data, typically bones, without destroying the internal structure of the object's structural visualization features. As research progresses and computer performance advances, many numerical methods based on CT image processing such as micro finite element method, digital image correlation (DVC), etc. are proposed and applied to experimental simulation.
Bay et al, 1999 proposed a digital volume image correlation (DVC) method that directly measures the internal pressure deformation of a volume image after bone tissue reconstruction. As a direct extension of a 2D digital image correlation method (2D-DIC), the method obtains the full-field deformation and displacement of the bone tissue under the action of specific pressure by comparing two groups of digital volume images of the bone tissue in the states before and after the bone tissue is subjected to stress deformation. With the continuous development of three-dimensional digital imaging equipment in recent years, the DVC method has gained wide attention and application in the research fields of experimental mechanics, biomedical engineering, material engineering and the like.
Similar to the principle of the 2D-DIC method, the principle of the DVC method is to compare points at the same position of volume data before and after deformation of a sample to obtain a three-dimensional deformation field. In the actual calculation process, researchers often encounter many problems such as calculation complexity and measurement accuracy. From the view of computational complexity, the 2D-DIC method needs to be (2N +1)2Calculating a block K of characters in a size cube2Point, and the DVC method needs to be in (2N +1)3Calculation of the cube size for the operator block K3Points whose complexity is K (2N +1) times that of the 2D-DIC method, which in practice is usually above x 1000. From the measurement accuracy, sample data is discrete pixel points, and only integer-level offset before and after sample deformation can be calculated.
In recent years, the research focus of the DVC method has been on the calculation accuracy and the calculation efficiency. In the holistic research, 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 spatial domain is equivalent to point-by-point multiplication in the frequency domain. In order to achieve higher precision, many sub-voxel level methods based on newton's iteration method and its derivatives are proposed, such as Levenberg-Marquardt algorithm and Broyden-Fletcher-goldfarbshanno (bfgs) algorithm, etc., so that the DVC method achieves 0.1voxel level of precision. Three ideas for accelerating the DVC algorithm have been proposed in recent years by Pan et al: firstly, a Hessian matrix of volume data is approximated by an inversion method when the sub-voxel gradient is calculated, so that the complex Hessian matrix solution is avoided; secondly, a feasible offset pre-estimation is searched before iteration, so that the convergence is faster and a better result is obtained during iteration; and thirdly, recording the interpolation coefficient of each voxel during the interpolation of the sub-voxels, thereby directly inquiring in the subsequent calculation and avoiding the re-calculation. With these methods, the computation speed of the DVC algorithm reaches 41 points of Interest (POI) per second. In general, the current sub-voxel displacement algorithm still has the disadvantages of insufficient accuracy and high computational complexity, and a high-precision and high-efficiency method is urgently needed in consideration of the increasing application requirements of the DVC algorithm.
Disclosure of Invention
The invention aims to provide a DVC (digital video coding) measuring method for internal deformation of an object, which is used for solving the technical problem
In order to solve the technical problem, the invention provides a DVC measuring method for internal deformation of an object, which comprises the following steps:
s1, positioning the whole pixel displacement of the initial point through the gravity center of the region of interest of the body image before and after deformation, and solving the sub-pixel displacement field of the initial point by using a gradient-based sub-pixel displacement positioning method;
s2, calculating the three-dimensional deformation field of the initial point by using a Newton iteration method according to the sub-pixel displacement field;
s3, calculating the three-dimensional deformation field of each pixel point around the initial point by a Newton iteration method according to the initial point of the calculated three-dimensional deformation field, and calculating the three-dimensional deformation field of any non-calculated pixel point in the region of interest of the volume image according to the pixel points of which the three-dimensional deformation field is calculated around the non-calculated pixel point until the three-dimensional deformation field of all the pixel points in the object is obtained.
Preferably, in step S1, the formula for calculating the center of gravity of the region of interest of the volume image is:
wherein G isTaRepresents the center of gravity of the volume image T on the a axis, a selects one of the x, y, z axes, and T (p) represents the pixel value of the volume image T at the p point.
Preferably, in step S1, the calculation formula of the sub-pixel displacement field Δ of the initial point is:
fG＝round(Gfx,Gfy,Gfz)
gG＝round(Ggx,Ggy,Ggz)
Δ＝(Δu,Δv,Δw)＝fG-gG
where round is a rounded function, f and g represent the volume images before and after deformation, respectively, and fGAnd gGAnd deforming the gravity center of the interested area of the front and back body images of the object.
Preferably, in step S1, the step of determining the sub-pixel displacement field of the initial point includes:
taylor first-order expansion is performed on the equations f (p) ═ g (p ') p ∈ D and p' ═ p + Δ + Δ ', and g (p + Δ + Δ') -g (p + Δ) + Δ 'g' (p + Δ).
Extremum is taken for the least squares correlation function SSD:
CSSD(Δ')＝∑p∈D(f(p)-g(p+Δ+Δ'))2
using the formula Δ ' ═ Σ g ' (g ')T∑(f-g) g 'to obtain a sub-pixel displacement field delta'.
Preferably, the gray scale gradient is calculated using a Barron operator.
Preferably, in step S2, the newton iteration method uses a zero-mean normalized sum of squares function ZNSSD as the correlation function.
Preferably, in step S2, the gray-scale value of the volume image is interpolated by a ternary cubic interpolation method.
Compared with the related technology, the DVC measuring method of the internal deformation of the object provided by the invention is used for rapid high-precision measurement of the internal deformation of the object, the method is simple to calculate and realize, the noise resistance is strong, the small deformation of the internal part of the object is well measured, meanwhile, the efficient calculation of the DVC algorithm under serial design is realized, firstly, the calculation complexity of the gravity center is far lower than that of the whole pixel displacement field of one point, and multiple global searches are avoided through extended searches, so that the calculation complexity is greatly reduced.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts, wherein:
fig. 1 is a flowchart of a DVC measurement method for internal deformation of an object according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the present invention provides a DVC measurement method for internal deformation of an object, including the following steps:
s1, positioning the whole pixel displacement of the initial point through the gravity center of the region of interest of the body image before and after deformation, and solving the sub-pixel displacement field of the initial point by using a gradient-based sub-pixel displacement positioning method;
s2, calculating the three-dimensional deformation field of the initial point by using a Newton iteration method according to the sub-pixel displacement field;
s3, calculating the three-dimensional deformation field of each pixel point around the initial point by a Newton iteration method according to the initial point of the calculated three-dimensional deformation field, and calculating the three-dimensional deformation field of any non-calculated pixel point in the region of interest of the volume image according to the pixel points of which the three-dimensional deformation field is calculated around the non-calculated pixel point until the three-dimensional deformation field of all the pixel points in the object is obtained.
In step S1, generally, since the relative deformation and displacement between the volume images before and after the deformation of the object are small, the corresponding point of the center of gravity of the deformed precursor image in the deformed volume image is necessarily near the center of gravity of the deformed volume image, so the center of gravity of the deformed precursor image in the region of interest of the deformed volume image is selected as a pair of initial correlation points, and the calculation formula of the center of gravity of the volume image region of interest is:
wherein G isTaRepresents the center of gravity of the volume image T on the a axis, a selects one of the x, y, z axes, and T (p) represents the pixel value of the volume image T at the p point. The center of gravity calculated by this formula is a small number, then by rounding to an integer:
fG＝round(Gfx,Gfy,Gfz)
gG＝round(Ggx,Ggy,Ggz)
where round is a rounded function, f and g represent the volume images before and after deformation, respectively, and fGAnd gGCenter of gravity, G, of the region of interest for deforming the front and rear body images of the objectfx,Gfy,GfzRespectively representing the center of gravity, G, of the volume image f in the x, y, z axesgx,Ggy,GgzRepresenting the center of gravity of the volumetric image g in the x, y, z axes, respectively, so that the integer pixel displacement field Δ is:
Δ＝(Δu,Δv,Δw)＝fG-gG
after the initial pixel-by-point displacement field is found, the sub-pixel displacement field needs to be found in order to obtain a more accurate offset in the morph image. Because the gray scale range of the volume pixel is limited, usually 0 to 255, and the accurate displacement of one pixel point cannot be tracked, the current pixel point must be taken as the center to perform integral comparison on the pixel points within k distances from the center pixel, and k is a natural number greater than zero. In the present invention, it is preferable to determine the sub-pixel displacement field from the integer pixel displacement field by using a gradient-based method, and it is considered that when k is sufficiently small and the deformation is small, the deformation in the region can be regarded as an approximate rigid body displacement, and the change in the gradation of the same corresponding point before and after the deformation is not large. Therefore, the step of determining the sub-pixel displacement field of the initial point comprises:
taylor first-order expansion is performed on the equations f (p) ═ g (p ') p ∈ D and p' ═ p + Δ + Δ ', and g (p + Δ + Δ') -g (p + Δ) + Δ 'g' (p + Δ).
Extremum is taken for the least squares correlation function SSD:
CSSD(Δ')＝∑p∈D(f(p)-g(p+Δ+Δ'))2
using the formula Δ ' ═ Σ g ' (g ')TAnd sigma (f-g) g 'is calculated to obtain a sub-pixel displacement field delta'.
As can be known from the above calculation formula of the sub-pixel displacement field Δ', the sub-pixel displacement field at the initial point is only related to the gray scale gradient of the deformed body image g, so different gray scale gradient algorithms have an important influence on the measurement accuracy of the sub-pixels. The invention uses Barron operator with higher precision to calculate gray gradient, and the gray gradient of the volume image g at a pixel point p (x, y, z) is as follows:
wherein g isx,gy,gzGray scale gradient components in the x, y, z axes, respectively.
In step S2, the above-mentioned calculation of the displacement field considers that the deformation is only rigid body displacement motion, and obviously in a real scene, the object may rotate and shear in the three-dimensional space, so the three-dimensional deformation field must be calculated by a more accurate method. It is not agreed that three-dimensional displacement has only three parameters (Δ u, Δ v, Δ w), and three-dimensional deformation has a total of twelve parameters:
q＝(ux,uy,uz,u,vx,vy,vz,v,wx,wy,wz,w)
wherein, h (q) is a displacement parameter, T (q) is a rotation parameter, the rotation parameter is also a displacement gradient component of the volume image, and T is a rotation matrix with q as a parameter. In order to better evaluate the similarity before and after the subvolume deformation, the method provided by the invention uses a zero-mean normalized sum-of-squares function ZNSDS as a correlation function, and the function is insensitive to the scale and the offset of illumination fluctuation and is widely applied to cross-correlation comparison. For one (2k +1)3The sub-volume of (a), having the formula:
wherein C isZNSSD(q) is a zero-mean normalization function, p is a pixel point of a deformation precondition image, q is a deformation parameter, and p' is a corresponding pixel point which takes a central pixel point pc as a symmetric center and is subjected to the action of a mapping function with the deformation parameter as q:
p'＝T(q)(p-pc)+H(q)+Δ
fmand gmThe gray level mean values of the sub-blocks of the images of the front and rear bodies before and after deformation are respectively calculated according to the following formula:
it can be seen that the ZNSSSD function is a non-linear function to q, which contains 12 parameters. For the optimization problem of non-linear equations, we typically use newton's iteration method for fast solution:
wherein q istIs the parameter of the previous iteration, the initial value of which is typically set to all 0 s. In the DVC measurement method, the gray level correlation of different regions is not large, so that the calculation function of the displacement parameter h (q) and the rotation parameter t (q) is not a convex function, and a good pre-estimation is the key for optimizing the ZNSSD function. The DVC measurement method provided by the present invention uses the sub-pixel displacement found in the previous section as the initial value of q, namely:
q0＝(0,0,0,Δu',0,0,0,Δv',0,0,0,Δw')
in the above formula, Δ f and Δ g are denominators in the calculation functions of the displacement parameter h (q) and the rotation parameter t (q), respectively, 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, and since the volume image is a whole pixel point, the gradient field in three dimensions cannot be directly solved, and a feasible method is to perform gray value interpolation on the volume image. The invention preferably adopts a ternary cubic interpolation method with higher precision, and the difference method carries out weighting calculation by utilizing the gray information of 64 whole pixel points around the interpolation to be needed. In a specific calculation process, the ternary cubic interpolation method can also be divided into one-dimensional cubic interpolation on three coordinate axes respectively. The formula for the reconstructed volume image is:
where α is 64(4 × 4) interpolation coefficients, which can be calculated by rounding 4 × 4 adjacent to the interpolated pixel. Obviously, as the gray value of the volume image is unchanged, 64 coefficients of each pixel point after ternary cubic interpolation are also fixed, and the 64 interpolation coefficients of each point can be calculated in preprocessing and directly used in subsequent calculation without repeated calculation. The interpolated volume image can be considered as a continuous volume image, and the first and second gradients can be simply determined.
In step S3, after the deformation of the initial point is calculated, the internal full-field deformation of the volume image needs to be calculated. The invention considers the characteristic 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(2n+1)3Since the sub-patches of the pixels are processed, when the deformation field of the central pixel is obtained, the positions of the pixels around the central pixel after the deformation field is applied can also be obtained, as shown in the formula p '═ p + Δ + Δ', and for any pixel pr around the central pixel, there are:
pr'＝T(q)(pr-pc)+H(q)+Δ
and considering the continuity of the ZNSSSD correlation function, a new iteration is carried out from the pr' point, so that not only can unnecessary calculation cost be saved, but also a good minimum value can be achieved. When the pixel point pr is used as a central point for calculation, the whole pixel offset and the sub-pixel offset corresponding to the pr are respectively as follows:
Δ(pr)＝round(pr'-pr)Δ'(pr)＝pr'-pr-Δ(pr)
in the initial values of the deformation parameters q of the pixel points pr, T (q) is all 0, H (q) is delta' (pr), and the three-dimensional deformation field of each pixel point is repeatedly calculated by using a Newton iteration method, so that all the three-dimensional deformation fields in the object are obtained.
Compared with the related technology, the DVC measuring method of the internal deformation of the object provided by the invention is used for rapid high-precision measurement of the internal deformation of the object, the method is simple to calculate and realize, the noise resistance is strong, the small deformation of the internal part of the object is well measured, meanwhile, the efficient calculation of the DVC algorithm under serial design is realized, firstly, the calculation complexity of the gravity center is far lower than that of the whole pixel displacement field of one point, and multiple global searches are avoided through extended searches, so that the calculation complexity is greatly reduced.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (5)
1. A DVC measurement method for internal deformation of an object is characterized by comprising the following steps:
s1, positioning the whole pixel displacement of the initial point through the gravity center of the region of interest of the body image before and after deformation, and solving the sub-pixel displacement field of the initial point by using a gradient-based sub-pixel displacement positioning method;
the calculation formula of the gravity center of the region of interest of the volume image is as follows:
wherein G isTaRepresenting the center of gravity of the volume image T on an a axis, a selecting one of x, y and z axes, and T (p) representing the pixel value of the volume image T on a point p;
the calculation formula of the sub-pixel displacement field of the initial point is as follows:
fG＝round(Gfx,Gfy,Gfz)
gG＝round(Ggx,Ggy,Ggz)
Δ＝(Δu,Δv,Δw)＝fG-gG
wherein Δ is the sub-pixel displacement field of the initial point, round is a rounded function, f and g represent the volume images before and after deformation, respectively, and fGAnd gGThe center of gravity of the region of interest of the front and back body images is deformed for the object;
s2, calculating the three-dimensional deformation field of the initial point by using a Newton iteration method according to the sub-pixel displacement field;
s3, calculating the three-dimensional deformation field of each pixel point around the initial point by a Newton iteration method according to the initial point of the calculated three-dimensional deformation field, and calculating the three-dimensional deformation field of any non-calculated pixel point in the region of interest of the volume image according to the pixel points of which the three-dimensional deformation field is calculated around the non-calculated pixel point until the three-dimensional deformation field of all the pixel points in the object is obtained.
2. A DVC measurement method of internal deformation of an object according to claim 1, wherein in step S1, the step of finding the initial sub-pixel displacement field comprises:
performing taylor first-order expansion on the formulas f (p) ═ g (p ') p epsilon D and p ' ═ p + delta ', to obtain g (p + delta ') -g (p + delta) + delta ' g ' (p + delta), wherein g ' (p + delta) is the first-order gray gradient of the volume image g on the pixel point p + delta;
extremum is taken for the least squares correlation function SSD:
CSSD(Δ')＝∑p∈D(f(p)-g(p+Δ+Δ'))2
using the formula Δ ' ═ Σ g ' (g ')TAnd sigma (f-g) g 'is calculated to obtain a sub-pixel displacement field delta'.
3. A DVC measurement of deformation inside an object according to claim 2, characterized in that said gray scale gradients are calculated using Barron's operator.
4. A DVC measuring method of deformation inside an object according to claim 1, wherein the newton' S iteration method uses a zero-mean normalized sum-of-squares function ZNSSD as a correlation function in step S2.
5. The DVC measurement method for internal deformation of an object according to claim 4, wherein in step S2, the gray value of the volume image is interpolated by using a tri-cubic interpolation method.
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