CN101813693A

CN101813693A - Cell in-situ active deformation measurement method

Info

Publication number: CN101813693A
Application number: CN 201010170691
Authority: CN
Inventors: 黄建永; 潘晓畅; 秦雷; 朱涛; 熊春阳; 方竞
Original assignee: Peking University
Current assignee: Peking University
Priority date: 2010-05-06
Filing date: 2010-05-06
Publication date: 2010-08-25

Abstract

The invention relates to an cell in-situ active deformation measurement method, which comprises the following measurement steps: (1) dividing square sampling grids on a cell-base fluorescent reference image and a corresponding deformation image; (2) determining the sizes of a reference subarea and a searching area; (3) establishing four global summation table; (4) calculating the cross correlation coefficient between the image reference subarea and the corresponding searching area, which take a sampling point as a center, by recurrence; (5) quickly calculating a zero-mean normalization related coefficient matrix by looking up the summation table according to the result of the step (4), and determining the overall pixel displacement of the sampling point; (6), performing subpixel interpolation by using a gradient method; and (7) recurring and calculating the displacement of the sampling point to obtain an accurate displacement field of a whole deformed image. The method has the advantages of accurate and high-efficiency measurement and high time-space resolution. The method can be used in cell in-situ active deformation measurement with high time-space resolution.

Description

A method for measuring active deformation of cells in situ

技术领域technical field

本发明涉及一种细胞显微变形测量方法，特别是关于一种用于定量分析细胞与细胞外基质(弹性基底)之间物理相互作用的细胞原位主动变形测量方法。The invention relates to a method for measuring cell microscopic deformation, in particular to a method for measuring the active deformation of cells in situ for quantitative analysis of the physical interaction between cells and extracellular matrix (elastic substrate).

背景技术Background technique

细胞是研究生命科学的基础，也是现代生命科学发展的重要支柱。一般来说，动物组织中的细胞不仅与相邻细胞接触和作用，同时也与由分泌蛋白和多糖组成的充满胞外空间的复杂网络结构，即细胞外基质相互接触和作用。细胞与细胞外基质等物理环境相互作用涉及许多复杂的生化信号转导通路，定量研究这种相互作用行为具有重要的生理病理意义。研究细胞与胞外基质相互作用的一类常用方法是采用弹性硅胶基底膜来模拟细胞外基质微环境，把细胞培养在其上面，通过牵拉硅胶膜的方式促使细胞发生被动变形，以此研究胞外基质环境变化对与细胞粘附、铺展及生长、分化等生物学行为的影响。1999年，Dembo(丹博)和王毓立等人通过把细胞培养在表面掺有荧光颗粒的聚丙烯酰胺薄膜弹性基底上，观察到了由细胞主动变形(包括细胞的周期性收缩和迁移)所导致的基底膜微纳尺度形变，以此为基础研究细胞的自主收缩、定向迁移规律，探索单细胞对外界环境的感知机理(Dembo M，Wang YL.Stresses at the cell-to-substrate interface duringlocomotion of fibroblasts.Biophysical Journal，1999；76：2307-2316.丹博，王毓立，成纤维细胞迁移过程中细胞-基底界面应力表征，生物物理，1999，76：2307-2316)。Cells are the basis of life science research and an important pillar for the development of modern life science. In general, cells in animal tissues not only contact and interact with adjacent cells, but also interact with a complex network structure filled with extracellular space, that is, the extracellular matrix, composed of secreted proteins and polysaccharides. The interaction between cells and the physical environment such as the extracellular matrix involves many complex biochemical signal transduction pathways, and the quantitative study of this interaction behavior has important physiological and pathological significance. A commonly used method to study the interaction between cells and extracellular matrix is to use elastic silica gel basement membrane to simulate the microenvironment of extracellular matrix, culture cells on it, and promote the passive deformation of cells by pulling the silica gel membrane, so as to study The influence of changes in the extracellular matrix environment on biological behaviors such as cell adhesion, spreading, growth, and differentiation. In 1999, Dembo (Danbo) and Wang Yuli and others observed the active deformation of cells (including periodic contraction and migration of cells) by culturing cells on the elastic substrate of polyacrylamide film doped with fluorescent particles. Based on the micro-nano-scale deformation of the basement membrane, the self-contraction and directional migration of cells are studied, and the mechanism of single cells' perception of the external environment is explored (Dembo M, Wang YL. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophysical Journal, 1999; 76: 2307-2316. Danbo, Wang Yuli, Characterization of cell-substrate interface stress during fibroblast migration, Biophysics, 1999, 76: 2307-2316).

目前，定量测量这种薄膜变形的方法主要有基于光流的区域特征匹配方法(Marganski WA，Dembo M，Wang YL.Measurements of cell-generated deformationson flexible substrata using correlation-based optical flow.Methods Enzymol.2003；361：197-211.马甘斯基，丹博，王毓立，运用基于相关的光流方法测量细胞导致的软基底变形，酶学方法，2003；361：197-211.)以及基于模式识别的荧光粒子点跟踪方法(Yang ZC，Lin JS，Chen JX，Wang J.Determining substrate displacement andcell traction fields-a new approach.J.Theor.Biol.2006；242：607-616.杨兆春，林津尚，陈建新，王慧聪，确定细胞牵引力场——一种新的方法，理论生物学，2006；242：607-616)。然而，基于光流的区域特征匹配方法搜索计算量大，计算速度很难满足要求；基于模式识别的荧光粒子点跟踪方法计算速度稍快，但由于单个的荧光粒子光斑几何光学特征相同，实际处理过程中极易出现错误跟踪，计算结果的准确性很难保证。At present, the methods for quantitatively measuring the deformation of such thin films mainly include optical flow-based regional feature matching methods (Marganski WA, Dembo M, Wang YL. Measurements of cell-generated deformation on flexible substrate using correlation-based optical flow. Methods Enzymol.2003; 361:197-211. Magansky, Danbo, Wang Yuli, Measuring cell-induced deformation of soft substrates using correlation-based optical flow methods, Methods in Enzymology, 2003; 361:197-211.) and fluorescence based on pattern recognition Particle point tracking method (Yang ZC, Lin JS, Chen JX, Wang J. Determining substrate displacement and cell traction fields-a new approach. J. Theor. Biol. 2006; 242: 607-616. Yang Zhaochun, Lin Jinshang, Chen Jianxin, Wang Huicong, Determining the cell traction force field—a new method, Theoretical Biology, 2006;242:607-616). However, the area feature matching method based on optical flow has a large amount of search calculation, and the calculation speed is difficult to meet the requirements; the calculation speed of the fluorescent particle point tracking method based on pattern recognition is slightly faster, but due to the same geometric and optical characteristics of a single fluorescent particle spot, the actual processing Error tracking is very easy to occur in the process, and the accuracy of calculation results is difficult to guarantee.

发明内容Contents of the invention

针对上述问题，本发明的目的是提供一种具有较高的准确率、效率及高时间-空间分辨率的细胞原位主动变形测量方法。In view of the above problems, the object of the present invention is to provide a method for measuring active deformation of cells in situ with high accuracy, efficiency and high time-space resolution.

为实现上述目的，本发明采取以下技术方案：一种细胞原位主动变形测量方法，其包括以下步骤：(1)分别在未发生弹性变形及发生弹性变形的细胞基底荧光图的参考图像F(x，y)和变形图像G(x，y)上，以设定的采样间距S为边长划分方形采样网格，单位为像素；(2)分别以各采样点(α，β)为中心，在参考图像F(x，y)上设定边长为(2N+1)的方形相关子区f_α，β(x，y)，在变形图像G(x，y)上选择边长为(2M+1)的方形搜索区域G_α，β(x，y)，其中N的取值范围为15～30之间的整数，M的取值范围为20～80之间的整数，单位均为像素，且M＞N；(3)根据参考图像F(x，y)和变形图像G(x，y)的数字图像灰度分布结构表f(x，y)和g(x，y)，利用递推方法分别建立图像灰度全局求和结构表S_f、S_g及图像能量全局求和结构表

(4)根据数字图像灰度分布结构表f(x，y)和g(x，y)，计算以采样点(α，β)为中心的相关子区f_α，β(x，y)与相应的搜索区域G_α，β(x，y)之间的互相关系数矩阵P_α，β，得到其快速递推关系式为：P_α+S，β(u，v)＝P_α，β(u，v)-I_α-D，β(u，v)+I_α，β(u，v)，其中，令

(u，v)表示参考图像的相关子区f_α，β(x，y)中采样点(α，β)在变形图像的搜索区域G_α，β(x，y)中的位移；D是相关子区f_α，β(x，y)的边长，D＝2N+1；(5)根据所述步骤(3)、(4)的结果，计算参考图像的相关子区f_α，β(x，y)与相应变形图像的搜索区域G_α，β(x，y)的变形子区g_α，β(x，y)之间的零均值归一化互相关系数矩阵G_α，β(u，v)；(6)采用基于梯度的亚像素位移定位算法，在零均值归一化互相关系数矩阵的最大峰值所在位置附近进行亚像素插值运算，求得参考图像中采样点(α，β)在变形图像中的准确位置为：式中，(U_α，β，V_α，β)表示采样点(α，β)在变形图像中的总位移大小，(u_α，β，v_α，β)是由所述零均值归一化相关系数矩阵C_α，β(u，v)中最大元素所确定的整像素位移，(Δu_α，β，Δv_α，β)是(u_α，β，v_α，β)相应的亚像素位移；(7)重复所述步骤(4)～步骤(6)，计算所有采样点在变形图像中的准确位置，进而得到整张变形图像位移场。In order to achieve the above object, the present invention adopts the following technical solutions: a method for measuring the active deformation of cells in situ, which includes the following steps: (1) the reference images F( x, y) and the deformed image G(x, y), divide the square sampling grid with the set sampling interval S as the side length, and the unit is pixel; (2) take each sampling point (α, β) as the center , on the reference image F(x, y), set a square related sub-region f _{α, β} (x, y) with a side length of (2N+1), on the deformed image G(x, y), select a side length of (2M+1) square search area G _{α, β} (x, y), where the value range of N is an integer between 15 and 30, the value of M is an integer between 20 and 80, and the unit is is a pixel, and M>N; (3) According to the digital image grayscale distribution structure table f(x, y) and g(x, y) of the reference image F(x, y) and the deformed image G(x, y) , use the recursive method to establish the global summation structure table of image gray level S _f , S _g and the global summation structure table of image energy

(4) According to the digital image gray scale distribution structure table f(x, y) and g(x, y), calculate the relevant sub-area f _{α, β} (x, y) and The cross-correlation coefficient matrix P _{α, β} between the corresponding search area G _{α, β} (x, y), and its fast recurrence relation is obtained: P _{α+S, β} (u, v)=P _{α, β} (u, v)-I _{α-D, β} (u, v)+I _{α, β} (u, v), where, let

(u, v) represents the displacement of the sampling point (α, β) in the relevant sub-region f _{α, β} (x, y) of the reference image in the search area G _{α, β} (x, y) of the deformed image; D is Correlation subregion f _{α, the side length of β} (x, y), D=2N+1; (5) according to the result of described step (3), (4), calculate the correlation subregion f _{α of reference image, β} The zero-mean normalized cross-correlation coefficient matrix G _α,β between (x,y) and the deformed sub-region g _α,β (x,y) of the search region G α,β(x,y) _of the corresponding deformed image (u, v); (6) Using a gradient-based sub-pixel displacement positioning algorithm, sub-pixel interpolation is performed near the position of the maximum peak of the zero-mean normalized cross-correlation coefficient matrix to obtain the sampling point (α , β) The exact position in the deformed image is: In the formula, (U _{α, β} , V _{α, β} ) represents the total displacement of the sampling point (α, β) in the deformed image, and (u _{α, β} , v _{α, β} ) is normalized by the zero-mean The integer pixel displacement determined by the largest element in the correlation coefficient matrix C _{α, β} (u, v), (Δu _{α, β} , Δv _{α, β} ) is the corresponding sub-pixel of (u _{α, β} , v _{α, β} ) Displacement; (7) Repeat steps (4) to (6) to calculate the exact positions of all sampling points in the deformed image, and then obtain the displacement field of the entire deformed image.

所述步骤(4)中，所述互相关系数矩阵P_α，β快速递推关系式由以下步骤得到：①对于采样点(α，β)，令相关子区f_α，β(x，y)与相应的搜索区域G_α，β(x，y)之间构成互相关系数矩阵为P_α，β；②与采样点(α，β)相邻的采样点(α+S，β)，其对应的相关子区f_α+S，β(x，y)与相应的搜索区域G_α+S，β(x，y)之间的互相关系数矩阵为P_α+S，β；③将两个互相关系数矩阵P_α，β和P_α+S，β对比得到：P_α+S，β(u，v)＝P_α，β(u，v)-J_α，β(u，v)+I_α，β(u，v)，其中，令

得到J_α，β(u，v)＝I_α-D，β(u，v)，D是相关子区f_α，β(x，y)的边长，D＝2N+1；④由所述步骤①～③中各式能建立快速递推关系为：P_α+S，β(u，v)＝P_α，β(u，v)-I_α-D，β(u，v)+I_α，β(u，v)。In the step (4), the correlation coefficient matrix P _{α, β} fast recursive relation is obtained by the following steps: 1. For the sampling point (α, β), make the correlation sub-area f _{α, β} (x, y ) and the corresponding search area G _{α, β} (x, y) form a cross-correlation coefficient matrix P _{α, β} ; ② The sampling point (α+S, β) adjacent to the sampling point (α, β), The correlation coefficient matrix between its corresponding correlation sub-area f _{α+S, β} (x, y) and the corresponding search area G _{α+S, β} (x, y) is P _{α+S, β} ; Two cross-correlation coefficient matrices P _{α, β} and P _{α+S, β} are compared to get: P _{α+S, β} (u, v) = P _{α, β} (u, v)-J _{α, β} (u, v )+I _{α, β} (u, v), where, let

Obtain J _{α, β} (u, v)=I _{α-D, β} (u, v), D is the side length of relevant sub-area f _{α, β} (x, y), D=2N+1; ④ by the The various formulas in the above steps ①～③ can establish a fast recursive relationship as: P _{α+S, β} (u, v)=P _{α, β} (u, v)-I _{α-D, β} (u, v)+ I _α,β (u,v).

所述步骤(5)中，所述零均值归一化互相关系数矩阵C_α，β(u，v)为： $C_{α, β} (u, v) = \frac{P (α, β; u, v) - Q (α, β; u, v)}{\sqrt{F (α, β)} \sqrt{G (α, β; u, v)}},$ 令 $Q (α, β; u, v) = {\overset{&OverBar;}{f}}_{α, β} Σ_{x = α - N}^{α + N} Σ_{y = β - N}^{β + N} g (x + u, y + v),$ 其中，P(α，β；u，v)为图像参考子区f_α，β(x，y)与相应搜索区域G_α，β(x，y)之间的互相关系数矩阵，其由所述步骤(4)中的所述互相关系数矩阵P_α，β快速递推关系式得到；F(α，β)为参考图像灰度平方和；G(α，β；u，v)为变形图像灰度平方和；Q(α，β；u，v)、F(α，β)和G(α，β；u，v)通过快速查询所述步骤(3)中预先建立的四个图像灰度、图像能量全局求和结构表得到。In the step (5), the zero-mean normalized cross-correlation coefficient matrix C _{α, β} (u, v) is: $C_{α, β} (u, v) = \frac{P (α, β; u, v) - Q (α, β; u, v)}{\sqrt{f (α, β)} \sqrt{G (α, β; u, v)}},$ make $Q (α, β; u, v) = {\overset{&OverBar;}{f}}_{α, β} Σ_{x = α - N}^{α + N} Σ_{the y = β - N}^{β + N} g (x + u, the y + v),$ Among them, P(α, β; u, v) is the cross-correlation coefficient matrix between the image reference sub-region f _{α, β} (x, y) and the corresponding search area G _{α, β} (x, y), which is determined by The cross-correlation coefficient matrix P _{α in the above-mentioned step (4), β} fast recursive relation obtains; F (α, β) is the square sum of reference image gray levels; G (α, β; u, v) is deformation Image gray square sum; Q (α, β; u, v), F (α, β) and G (α, β; u, v) by quickly querying the four pre-established images in step (3) The global summation structure table of gray scale and image energy is obtained.

本发明由于采取以上技术方案，其具有以下优点：1、本发明由于采用了基于快速递推关系式和快速查询四个图像灰度、图像能量全局求和结构表的方式，快速计算零均值归一化相关系数矩阵，并根据该矩阵的峰值位置确定采样点的整像素位移大小，进而得到采样点的位移，因此实现了测量精确高效、高时间-空间分辨率的效果。2、本发明由于采用了快速查表方式和快速递推方法进行计算，因此可以有效地降低采样点位移计算的复杂性，特别是在高时间空间位移采样以及较大搜索区域尺寸情况下，能显著的提高细胞-基底位移场求解效率。3、本发明由于采用了快速递推方式进行计算，这种方法比传统数字图像相关方法的计算效率大约提高了10到50倍，特别是当采样网格边长减小时，计算效率尤为突出。因此，本发明可以应用于高时空分辨率的细胞原位主动变形测量中。Because the present invention adopts the above technical scheme, it has the following advantages: 1. The present invention quickly calculates the zero-mean return value due to the use of fast recursive relational formulas and fast query of four image grayscales and the mode of global summation structure table of image energy. The correlation coefficient matrix is normalized, and the integer pixel displacement of the sampling point is determined according to the peak position of the matrix, and then the displacement of the sampling point is obtained, thus realizing the effect of accurate and efficient measurement and high time-space resolution. 2. The present invention can effectively reduce the complexity of sampling point displacement calculation due to the adoption of fast table lookup method and fast recursive method for calculation, especially in the case of high time and space displacement sampling and large search area size. Significantly improve the efficiency of solving the cell-substrate displacement field. 3. Since the present invention uses a fast recursive method for calculation, the calculation efficiency of this method is about 10 to 50 times higher than that of the traditional digital image correlation method, especially when the side length of the sampling grid is reduced, the calculation efficiency is particularly prominent. Therefore, the present invention can be applied to in situ active deformation measurement of cells with high spatiotemporal resolution.

附图说明Description of drawings

图1是本发明的整体流程示意图Fig. 1 is the overall schematic flow chart of the present invention

图2是本发明采样点网格划分的相关子区、搜索区域示意图Fig. 2 is a schematic diagram of relevant sub-areas and search areas of sampling point grid division in the present invention

图3是本发明的实施例一中单细胞粘附在聚丙烯酰胺弹性基底上的相差图Figure 3 is a phase contrast diagram of single cells adhered to a polyacrylamide elastic substrate in Example 1 of the present invention

图4是本发明的实施例一中聚丙烯酰胺基底的变形前参考图像Fig. 4 is the reference image before deformation of the polyacrylamide substrate in Embodiment 1 of the present invention

图5是本发明的实施例一中聚丙烯酰胺基底的变形图像Fig. 5 is the deformed image of the polyacrylamide substrate in Embodiment 1 of the present invention

图6是本发明的实施例一中基于本发明测量方法计算得到的荧光基底位移场Fig. 6 is the fluorescent substrate displacement field calculated based on the measurement method of the present invention in Embodiment 1 of the present invention

具体实施方式Detailed ways

下面结合附图和实施例对本发明进行详细的描述。The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

如图1所示，本发明是基于零均值归一化互相关系数在细胞基底位移场求解过程中所表现出的内在特点，通过构建与图像灰度和图像能量密切相关的四个全局求和表，发展了一整套位移场求解快速递推方法，其步骤如下：As shown in Figure 1, the present invention is based on the inherent characteristics of the zero-mean normalized cross-correlation coefficient in the process of solving the cell substrate displacement field, by constructing four global sums closely related to image grayscale and image energy Table, developed a set of fast recursive method for solving displacement field, the steps are as follows:

1)将未发生弹性变形的细胞基底荧光图作为参考图像F(x，y)，发生弹性变形的细胞基底荧光图作为变形图像G(x，y)；设定采样间距为S，分别在参考图像F(x，y)和变形图像G(x，y)上以S为边长划分规则的方形采样网格(如图2所示)，单位为像素；1) Take the cell base fluorescence image without elastic deformation as the reference image F(x, y), and the cell base fluorescence image with elastic deformation as the deformed image G(x, y); set the sampling interval as S, respectively in the reference On the image F(x, y) and the deformed image G(x, y), divide the regular square sampling grid (as shown in Figure 2) with S as the side length, and the unit is pixel;

2)分别以每个采样点(α，β)为中心，在参考图像F(x，y)上设定边长为(2N+1)的方形相关子区f_α，β(x，y)，在变形图像G(x，y)上选择边长为(2M+1)的方形搜索区域G_α，β(x，y)，其中N的取值范围一般为15～30之间的任意整数(其单位为像素)，而M的取值范围一般为20～80之间的任意整数(其单位也为像素)，且M＞N；2) With each sampling point (α, β) as the center, set a square related sub-area f α _{, β} (x, y) with side length (2N+1) on the reference image F(x, y) , select a square search area G _{α, β} (x, y) with a side length of (2M+1) on the deformed image G(x, y), where the value range of N is generally any integer between 15 and 30 (its unit is pixel), and the value range of M is generally any integer between 20 and 80 (its unit is also pixel), and M>N;

3)根据参考图像F(x，y)和变形图像G(x，y)的数字图像灰度分布结构表f(x，y)和g(x，y)(如表1、表2所示)，利用递推方法分别建立参考图像F(x，y)和变形图像G(x，y)的图像灰度全局求和结构表Sf、Sg及图像能量全局求和结构表

如表3～表6所示，其递推方式如下：3) According to the digital image grayscale distribution structure table f(x, y) and g(x, y) of the reference image F(x, y) and the deformed image G(x, y) (as shown in Table 1 and Table 2 ), using the recursive method to establish the global summation structure table Sf, Sg and the global summation structure table of the image energy of the reference image F(x, y) and the deformed image G(x, y) respectively

As shown in Table 3 to Table 6, the recursive method is as follows:

S_f(x，y)＝f(x，y)+S_f(x-1，y)+S_f(x，y-1)-S_f(x-1，y-1)， (1)S _f (x, y) = f (x, y) + S _f (x-1, y) + S _f (x, y-1) - S _f (x-1, y-1), (1)

${S S}_{{f f}^{22}} ((x x,, y the y)) = = {f f}^{22} ((x x,, y the y)) + + {S S}_{{f f}^{22}} ((x x - - 11,, y the y)) + + {S S}_{{f f}^{22}} ((x x,, y the y - - 11)) - - {S S}_{{f f}^{22}} ((x x - - 11,, y the y - - 11)),, - - - - - - ((22))$

S_g(x，y)＝g(x，y)+S_g(x-1，y)+S_g(x，y-1)-S_g(x-1，y-1)， (3)S _g (x, y) = g (x, y) + S _g (x-1, y) + S _g (x, y-1) - S _g (x-1, y-1), (3)

${S S}_{{g g}^{22}} ((x x,, y the y)) = = {g g}^{22} ((x x,, y the y)) + + {S S}_{{g g}^{22}} ((x x - - 11,, y the y)) + + {S S}_{{g g}^{22}} ((x x,, y the y - - 11)) - - {S S}_{{g g}^{22}} ((x x - - 11,, y the y - - 11)),, - - - - - - ((44))$

其中，当x，y≤0时，

Among them, when x, y≤0,

表1 参考数字图像灰度分布结构表f(x，y)Table 1 Reference digital image gray distribution structure table f(x, y)

f(1，1)f(1,1) …… f(1，p)f(1,p) …… f(1，w)f(1,w) …... …… …... …… …... f(q，1)f(q,1) …… f(q，p)f(q,p) …… f(q，w)f(q,w) …... …… …... …… …... f(H，1)f(H, 1) …… f(H，p)f(H,p) …… f(H，w)f(H,w)

表2 变形后数字图像灰度分布结构表g(x，y)Table 2 Deformed digital image gray distribution structure table g(x, y)

g(1，1)g(1,1) …… g(1，p)g(1,p) …… g(1，w)g(1,w) …... …… …... …… …... g(q，1)g(q,1) …… g(q，p)g(q,p) …… g(q，w)g(q,w) …... …… …... …… …... g(H，1)g(H,1) …… g(H，p)g(H,p) …… g(H，w)g(H,w)

表3 参考图相灰度求和结构表S_f Table 3 The reference image gray level summation structure table S _f

S_f(1，1)S _f (1, 1) …… S_f(1，p)S _f (1,p) …… S_f(1，w)S _f (1,w) …... …… …... …… …... S_f(q，1)S _f (q, 1) …… S_f(q，p)S _f (q, p) …… S_f(q，w)S _f (q,w) …... …… …... …… …... S_f(H，1)S _f (H, 1) …… S_f(H，p)S _f (H, p) …… S_f(H，w)S _f (H, w)

表4 变形图相灰度求和结构表S_g Table 4 Deformed image phase gray summation structure table S _g

S_g(1，1)S _g (1, 1) …… S_g(1，p)S _g (1, p) …… S_g(1，w)S _g (1, w) …... …… …... …… …... S_g(q，1)S _g (q, 1) …… S_g(q，p)S _g (q, p) …… S_g(q，w)S _g (q, w) …... …… …... …… …... S_g(H，1)S _g (H, 1) …… S_g(H，p)S _g (H, p) …… S_g(H，w)S _g (H, w)

表5 参考图像能量求和结构表 Table 5 Reference image energy summation structure table

表6 参考图像能量求和结构表

Table 6 Reference image energy summation structure table

上述各表格中，p、q、w、H均为参考的图像参考子区f_α，β(x，y)与相应搜索区域G_α，β(x，y)内任意点的取值，其单位为像素；In the above-mentioned tables, p, q, w, and H are the values of any point in the reference image reference sub-area f _{α, β} (x, y) and the corresponding search area G _{α, β} (x, y). The unit is pixel;

4)运用递推方法，根据参考图像F(x，y)和变形图像G(x，y)的数字图像灰度分布结构表f(x，y)和g(x，y)，计算以采样点(α，β)为中心的参考图像的相关子区f_α，β(x，y)与相应变形图像的搜索区域G_α，β(x，y)之间的互相关系数矩阵P_α，β，进而得到互相关系数矩阵P_α，β快速递推关系式为：4) Using the recursive method, according to the digital image gray distribution structure table f(x, y) and g(x, y) of the reference image F(x, y) and the deformed image G(x, y), calculate the sampling _The cross-correlation coefficient matrix P _α _{, β} , and then get the cross-correlation coefficient matrix P _{α, and the fast recursive relation of β} is:

P_α+S，β(u，v)＝P_α，β(u，v)-I_α-D，β(u，v)+I_α，β(u，v)， (5)P _α+S,β (u,v)=P _α,β (u,v)-I _α-D,β (u,v)+I _α,β (u,v), (5)

令 $I_{α, β} (u, v) = Σ_{x = α + N + 1}^{α + S + N} Σ_{y = β - N}^{β + N} [f (x, y) \times g (x + u, y + v)], - - - (6)$ make $I_{α, β} (u, v) = Σ_{x = α + N + 1}^{α + S + N} Σ_{the y = β - N}^{β + N} [f (x, the y) \times g (x + u, the y + v)], - - - (6)$

其中，(u，v)表示参考图像的相关子区f_α，β(x，y)中采样点(α，β)在变形图像的搜索区域G_α，β(x，y)中的位移(如图2所示)；D是相关子区f_α，β(x，y)的边长，D＝2N+1；Among them, (u, v) represents the displacement of the sampling point (α, β) in the relevant sub-region f _{α, β} (x, y) of the reference image in the search area G _{α, β} (x, y) of the deformed image ( As shown in Figure 2); D is the side length of the relevant sub-area f _{α, β} (x, y), D=2N+1;

5)根据步骤3)和步骤4)的结果，计算参考图像的相关子区f_α，β(x，y)与相应变形图像的搜索区域G_α，β(x，y)的变形子区g_α，β(x，y)之间的零均值归一化互相关系数矩阵(Zero-normalized cross-correlation coefficient，ZNCC)，该零均值归一化互相关系数矩阵C_α，β(u，v)为：5) According to the results of step 3) and step 4), calculate the relevant sub-area f _{α, β} (x, y) of the reference image and the deformed sub-area g of the search area G _{α, β} (x, y) of the corresponding deformed image The zero-normalized cross-correlation coefficient matrix (ZNCC) between _{α, β} (x, y), the zero-normalized cross-correlation coefficient matrix C _{α, β} (u, v )for:

${C C}_{α α,, β β} ((u u,, v v)) = = \frac{P P ((α α,, β β;; u u,, v v)) - - Q Q ((α α,, β β;; u u,, v v))}{\sqrt{F f ((α α,, β β))} \sqrt{G G ((α α,, β β;; u u,, v v))}},, - - - - - - ((77))$

$Q Q ((α α,, β β;; u u,, v v)) = = {\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β} {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} g g ((x x + + u u,, y the y + + v v))$

令 $= \frac{1}{{(2 N + 1)}^{2}} [Σ_{x = α - N}^{α + N} Σ_{y = β - N}^{β + N} f (x, y)] [Σ_{x = α - N}^{α + N} Σ_{Y = β - N}^{β + N} g (x + u, y + v)], - - - (8)$ make $= \frac{1}{{(2 N + 1)}^{2}} [Σ_{x = α - N}^{α + N} Σ_{the y = β - N}^{β + N} f (x, the y)] [Σ_{x = α - N}^{α + N} Σ_{Y = β - N}^{β + N} g (x + u, the y + v)], - - - (8)$

$= = \frac{11}{{((22 N N + + 11))}^{22}} [[{Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} f f ((x x,, y the y))]] [[{Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{Y Y = = β β - - N N + + v v}^{β β + + N N + + v v} g g ((x x,, y the y))]]$

$F f ((α α,, β β)) = = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {[[f f ((x x,, y the y)) - - {\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β}]]}^{22}$

$= = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {f f}^{22} ((x x,, y the y)) - - 22 {\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β} {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} f f ((x x,, y the y)) + + {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {\overset{&OverBar; &OverBar;}{f f}}^{22}_{α α,, β β}$

$= = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {f f}^{22} ((x x,, y the y)) - - 22 {\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β} [[{((22 N N + + 11))}^{22} {\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β}]] + + {((22 N N + + 11))}^{22} {\overset{&OverBar; &OverBar;}{f f}}^{22}_{α α,, β β},, - - - - - - ((99))$

$= = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {f f}^{22} ((x x,, y the y)) - - \frac{11}{{((22 N N + + 11))}^{22}} {[[{Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} f f ((x x,, y the y))]]}^{22}$

$G G ((α α,, β β;; u u,, v v)) = = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {[[g g ((x x + + u u,, y the y + + v v)) - - {\overset{&OverBar; &OverBar;}{g g}}_{α α,, β β;; u u,, v v}]]}^{22}$

$= = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {g g}^{22} ((x x + + u u,, y the y + + v v)) - - 22 {\overset{&OverBar; &OverBar;}{g g}}_{α α,, β β;; u u,, v v} {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} g g ((x x + + u u,, y the y + + v v)) + + {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {\overset{&OverBar; &OverBar;}{g g}}^{22}_{α α,, β β;; u u,, v v}$

$= = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {g g}^{22} ((x x + + u u,, y the y + + v v)) {- - ((22 N N + + 11))}^{22} {\overset{&OverBar; &OverBar;}{g g}}^{22}_{α α,, β β;; u u,, v v},, - - - - - - ((99))$

$= = {Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} {g g}^{22} ((x x,, y the y)) - - \frac{11}{{((22 N N + + 11))}^{22}} {[[{Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} g g ((x x,, y the y))]]}^{22}$

其中，P(α，β；u，v)为图像参考子区f_α，β(x，y)与相应搜索区域G_α，β(x，y)之间的互相关系数矩阵；F(α，β)为参考图像灰度平方和；G(α，β；u，v)为变形图像灰度平方和；Among them, P(α, β; u, v) is the cross-correlation coefficient matrix between the image reference sub-area f _{α, β} (x, y) and the corresponding search area G _{α, β} (x, y); F(α , β) is the gray-scale sum of the reference image; G(α, β; u, v) is the gray-scale sum of the deformed image;

公式(7)可由标准的零均值归一化互相关系数表达式经化简得到下式：Formula (7) can be simplified from the standard zero-mean normalized cross-correlation coefficient expression to obtain the following formula:

${C C}_{α α,, β β} ((u u,, v v)) = = \frac{{Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) - - {\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β}]] [[g g ((x x + + u u,, y the y + + v v)) - - {\overset{&OverBar; &OverBar;}{g g}}_{α α,, β β;; u u,, v v}]]}{\sqrt{{Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {[[f f ((x x,, y the y)) - - {\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β}]]}^{22}} \sqrt{{Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {[[g g ((x x + + u u,, y the y + + v v)) - - {\overset{&OverBar; &OverBar;}{g g}}_{α α,, β β;; u u,, v v}]]}^{22}}},, - - - - - - ((1111))$

${\overset{&OverBar; &OverBar;}{f f}}_{α α,, β β} = = \frac{11}{{((22 N N + + 11))}^{22}} {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} f f ((x x,, y the y)),, - - - - - - ((1212))$

${\overset{&OverBar; &OverBar;}{g g}}_{α α,, β β;; u u,, v v} = = \frac{11}{{((22 N N + + 11))}^{22}} {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} g g ((x x + + u u,, y the y + + v v))$

$= = \frac{11}{{((22 N N + + 11))}^{22}} {Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} g g ((x x,, y the y)),, - - - - - - ((1313))$

上述公式中，和

分别表示参考图像灰度和变形图像灰度的均值；In the above formula, and

respectively represent the mean value of the reference image grayscale and the deformed image grayscale;

6)采用基于梯度的亚像素位移定位算法，在步骤5)中的ZNCC系数矩阵最大峰值所在位置附近进行亚像素插值运算，这样可以把荧光弹性基底的位移测量精度由整像素水平延伸至亚像素水平，即求得参考图像中采样点(α，β)在变形图像中的准确位置为：6) Using a gradient-based sub-pixel displacement positioning algorithm, a sub-pixel interpolation operation is performed near the position of the maximum peak value of the ZNCC coefficient matrix in step 5), so that the displacement measurement accuracy of the fluorescent elastic substrate can be extended from the whole pixel level to the sub-pixel level Level, that is, to obtain the exact position of the sampling point (α, β) in the reference image in the deformed image is:

$\{\begin{matrix} {U u}_{α α,, β β} = = {u u}_{α α,, β β} + + Δ Δ {u u}_{α α,, β β} \\ {V V}_{α α,, β β} = = {v v}_{α α,, β β} + + Δ Δ {v v}_{α α,, β β} \end{matrix},, - - - - - - ((1414))$

上式中，(U_α，β，V_α，β)表示采样点(α，β)在变形图像中的总位移大小，(u_α，β，v_α，β)是由步骤5)中的零均值归一化相关系数矩阵C_α，β(u，v)中最大元素所确定的整像素位移，(Δu_α，β，Δv_α，β)是(u_α，β，v_α，β)相应的亚像素位移；In the above formula, (U _{α, β} , V _{α, β} ) represents the total displacement of the sampling point (α, β) in the deformed image, and (u _{α, β} , v _{α, β} ) is derived from step 5) The integer pixel displacement determined by the largest element in the zero-mean normalized correlation coefficient matrix C _α,β (u,v), (Δu _α,β ,Δv _α,β ) is (u _α,β ,v _α,β ) The corresponding sub-pixel displacement;

7)重复步骤4)～步骤6)，计算所有采样点在变形后图像中的准确位置，进而得到整张变形图像位移场。7) Repeat steps 4) to 6) to calculate the exact positions of all sampling points in the deformed image, and then obtain the displacement field of the entire deformed image.

上述步骤4)中，互相关系数矩阵P_α，β快速递推关系式通过以下步骤得到：In the above step 4), the cross-correlation coefficient matrix P _{α, β} fast recursive relation is obtained by the following steps:

①对于采样点(α，β)，令参考图像的相关子区f_α，β(x，y)与相应的变形图像的搜索区域G_α，β(x，y)之间构成的互相关系数矩阵P_α，β为：① For the sampling point (α, β), let the correlation coefficient formed between the relevant sub-region f _{α, β} (x, y) of the reference image and the search area G _{α, β} (x, y) of the corresponding deformed image The matrix P _{α, β} is:

$= = [\begin{matrix} {P P}_{α α,, β β} [[- - ((M m - - N N)),, - - ((M m - - N N))]] & \cdot \cdot \cdot \cdot \cdot \cdot & {P P}_{α α,, β β} [[u u,, - - ((M m - - N N))]] & \cdot &Center Dot; \cdot \cdot \cdot \cdot & {P P}_{α α,, β β} [[((M m - - N N)),, - - ((M m - - N N))]] \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot \cdot & \cdot \cdot \\ \cdot &Center Dot; & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; \\ {P P}_{α α,, β β} [[- - ((M m - - N N)),, v v]] & \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; & {P P}_{α α,, β β} [[u u,, v v]] & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {P P}_{α α,, β β} [[((M m - - N N)),, v v]] \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; \\ {P P}_{α α,, β β} [[- - ((M m - - N N)),, ((M m - - N N))]] & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {P P}_{α α,, β β} [[u u,, ((M m - - N N))]] & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {P P}_{α α,, β β} [[((M m - - N N)),, ((M m - - N N))]] \end{matrix}];;$

②同理，对于与采样点(α，β)相邻的采样点(α+S，β)而言，其对应的相关子区f_α+S，β(x，y)与相应的搜索区域G_α+S，β(x，y)之间的互相关系数矩阵P_α+S，β可以表示为：②Similarly, for the sampling point (α+S, β) adjacent to the sampling point (α, β), its corresponding relevant sub-area f _{α+S, β} (x, y) and the corresponding search area The cross-correlation coefficient matrix P _{α+S, β between G α+S} _, β (x, y) can be expressed as:

$= = [\begin{matrix} {P P}_{α α + + S S,, β β} [[- - ((M m - - N N)),, - - ((M m - - N N))]] & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {P P}_{α α + + S S,, β β} [[u u,, - - ((M m - - N N))]] & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {P P}_{α α + + S S,, β β} [[((M m - - N N)),, - - ((M m - - N N))]] \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {P P}_{α α + + S S,, β β} [[- - ((M m - - N N)),, v v]] & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {P P}_{α α + + S S,, β β} [[u u,, v v]] & \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; & {P P}_{α α + + S S,, β β} [[((M m - - N N)),, v v]] \\ \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; \\ {P P}_{α α + + S S,, β β} [[- - ((M m - - N N)),, ((M m - - N N))]] & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {P P}_{α α + + S S,, β β} [[u u,, ((M m - - N N))]] & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {P P}_{α α + + S S,, β β} [[((M m - - N N)),, ((M m - - N N))]] \end{matrix}]$

③将上述两个互相关系数矩阵P_α，β和P_α+S，β进行对比后，可以得到：③ After comparing the above two cross-correlation coefficient matrices P _{α, β} and P _{α+S, β} , we can get:

${P P}_{α α + + S S,, β β} ((u u,, v v)) = = {Σ Σ}_{x x = = α α + + S S - - N N}^{α α + + S S + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) \times \times g g ((x x + + u u,, y the y + + v v))]]$

$= = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) \times \times g g ((x x + + u u,, y the y + + v v))]] - - {Σ Σ}_{x x = = α α - - N N}^{α α - - N N + + S S + + 11} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) \times \times g g ((x x + + u u,, y the y + + v v))]]$

$= = {Σ Σ}_{x x = = α α + + N N + + 11}^{α α + + S S + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) \times \times g g ((x x + + u u,, y the y + + v v))]]$

$= = {P P}_{α α,, β β} ((u u,, v v)) - - {J J}_{α α,, β β} ((u u,, v v)) + + {I I}_{α α,, β β} ((u u,, v v))$

其中，令 $J_{α, β} (u, v) = Σ_{x = α - N}^{α - N + S - 1} Σ_{y = β - N}^{β + N} [f (x, y) \times g (x + u, y + v)];$ Among them, order $J_{α, β} (u, v) = Σ_{x = α - N}^{α - N + S - 1} Σ_{the y = β - N}^{β + N} [f (x, the y) \times g (x + u, the y + v)];$

显然，将J_α，β(u，v)与公式(6)进行对比后可知，J_α，β(u，v)＝I_α-D，β(u，v)，D是相关子区f_α，β(x，y)的边长，即D＝2N+1；Obviously, after comparing J _{α, β} (u, v) with formula (6), it can be seen that J _{α, β} (u, v) = I _{α-D, β} (u, v), D is the relevant sub-area f _{α, the side length of β} (x, y), namely D=2N+1;

④由上述步骤中各式可建立如下快速递推关系：④ From the above steps, the following fast recursive relationship can be established:

P_α+S，β(u，v)＝P_α，β(u，v)-I_α-D，β(u，v)+I_α，β(u，v)。P _α+S,β (u,v)=P _α,β (u,v)-I _α-D,β (u,v)+I _α,β (u,v).

上述步骤5)中，互相关系数矩阵P(α，β；u，v)根据步骤4)中的互相关系数矩阵P_α，β快速递推关系式可以得到：In the above-mentioned step 5), the cross-correlation coefficient matrix P (α, β; u, v) according to the cross-correlation coefficient matrix P _{α in the step 4), the fast recursive relational expression of β} can be obtained:

$P P ((α α,, β β;; u u,, v v)) = = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) \times \times g g ((x x + + u u,, y the y + + v v))]],,$

公式(7)中的Q(α，β；u，v)、F(α，β)和G(α，β；u，v)可以通过快速查询步骤3)中预先建立的四个图像灰度、图像能量全局求和结构表(表3～表6)得到，即：Q(α, β; u, v), F(α, β) and G(α, β; u, v) in formula (7) can quickly query the four pre-established image gray levels in step 3) , Image energy global summation structure table (table 3～table 6) obtains, namely:

${Z Z}_{11} ((α α,, β β)) = = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} f f ((x x,, y the y))$

$= = {S S}_{f f} ((α α + + N N,, β β + + N N)) - - {S S}_{f f} ((α α - - N N - - 11,, β β + + N N)) - - {S S}_{f f} ((α α + + N N,, β β - - N N - - 11)),,$

$+ + {S S}_{f f} ((α α - - N N - - 11,, β β - - N N - - 11))$

${Z Z}_{22} ((α α,, β β)) = = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {f f}^{22} ((x x,, y the y))$

$= = {S S}_{{f f}^{22}} ((α α + + N N,, β β + + N N)) - - {S S}_{{f f}^{22}} ((α α - - N N - - 11,, β β + + N N)) - - {S S}_{{f f}^{22}} ((α α + + N N,, β β - - N N - - 11)),,$

$+ + {S S}_{{f f}^{22}} ((α α - - N N - - 11,, β β - - N N - - 11))$

${Z Z}_{33} ((α α,, β β)) = = {Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} g g ((x x,, y the y))$

$= = {S S}_{g g} ((α α + + N N + + u u,, β β + + N N + + v v)) - - {S S}_{g g} ((α α - - N N + + u u - - 11,, β β + + N N + + v v)),,$

$- - {S S}_{g g} ((α α + + N N + + u u,, β β - - N N + + v v - - 11)) + + {S S}_{g g} ((α α - - N N + + u u - - 11,, β β - - N N + + v v - - 11))$

${Z Z}_{44} ((α α,, β β)) = = {Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} {g g}^{22} ((x x,, y the y))$

$= = {S S}_{{g g}^{22}} ((α α + + N N + + u u,, β β + + N N + + v v)) - - {S S}_{{g g}^{22}} ((α α - - N N + + u u - - 11,, β β + + N N + + v v)),,$

$- - {S S}_{{g g}^{22}} ((α α + + N N + + u u,, β β - - N N + + v v - - 11)) + + {S S}_{{g g}^{22}} ((α α - - N N + + u u - - 11,, β β - - N N + + v v - - 11))$

$Q Q ((α α,, β β;; u u,, v v)) = = \frac{11}{{((22 N N + + 11))}^{22}} [[{Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} f f ((x x,, y the y))]] [[{Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} g g ((x x,, y the y))]]$

$= = \frac{{Z Z}_{11} ((α α,, β β)) \times \times {Z Z}_{33} ((α α,, β β))}{{((22 N N + + 11))}^{22}},,$

$F f ((α α,, β β)) = = {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {f f}^{22} ((x x,, y the y)) - - \frac{11}{{((22 N N + + 11))}^{22}} {[[{Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} f f ((x x,, y the y))]]}^{22},,$

$= = {Z Z}_{22} ((α α,, β β)) - - \frac{{[[{Z Z}_{11} ((α α,, β β))]]}^{22}}{{((22 N N + + 11))}^{22}}$

$G G ((α α,, β β;; u u,, v v)) = = {Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} {g g}^{22} ((x x,, y the y)) - - \frac{11}{{((22 N N + + 11))}^{22}} {[[{Σ Σ}_{x x = = α α - - N N + + u u}^{α α + + N N + + u u} {Σ Σ}_{y the y = = β β - - N N + + v v}^{β β + + N N + + v v} g g ((x x,, y the y))]]}^{22};;$

$= = {Z Z}_{44} ((α α,, β β)) - - \frac{{[[{Z Z}_{33} ((α α,, β β))]]}^{22}}{{((22 N N + + 11))}^{22}}$

上述步骤6)中，亚像素位移(Δu_α，β，Δv_α，β)为：In the above step 6), the sub-pixel displacement (Δu _{α, β} , Δv _{α, β} ) is:

$[\begin{matrix} Δ Δ {u u}_{α α,, β β} \\ Δ Δ {v v}_{α α,, β β} \end{matrix}] = = {[\begin{matrix} {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {(({g g}_{u u}^{' '}))}^{22} & {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} (({g g}_{u u}^{' '} {g g}_{v v}^{' '})) \\ {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} (({g g}_{v v}^{' '} {g g}_{u u}^{' '})) & {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} {(({g g}_{v v}^{' '}))}^{22} \end{matrix}]}^{- - 11} \times \times [\begin{matrix} {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) - - g g ((x x + + {u u}_{α α,, β β},, y the y + + {v v}_{α α,, β β}))]] {g g}_{u u}^{' '} \\ {Σ Σ}_{x x = = α α - - N N}^{α α + + N N} {Σ Σ}_{y the y = = β β - - N N}^{β β + + N N} [[f f ((x x,, y the y)) - - g g ((x x + + {u u}_{α α,, β β},, y the y + + {v v}_{α α,, β β}))]] {g g}_{v v}^{' '} \end{matrix}]$

上式中，

和

分别表示在u和v方向上灰度的一阶梯度，灰度梯度算子取为[1/12，-8/12，0，8/12，-1/12]，这时：In the above formula,

and

represent the first-order gradient of the grayscale in the u and v directions respectively, and the grayscale gradient operator is taken as [1/12, -8/12, 0, 8/12, -1/12], then:

${g g}_{u u}^{' '} = = \frac{11}{1212} g g (({u u}_{α α,, β β} - - 22,, {v v}_{α α,, β β})) - - \frac{88}{1212} g g (({u u}_{α α,, β β} - - 11,, {v v}_{α α,, β β})) + + \frac{88}{1212} g g (({u u}_{α α,, β β} + + 11,, {v v}_{α α,, β β})) - - \frac{11}{1212} g g (({u u}_{α α,, β β} + + 22,, {v v}_{α α,, β β})),,$

${g g}_{v v}^{' '} = = \frac{11}{1212} g g (({u u}_{α α,, β β},, {v v}_{α α,, β β} - - 22)) - - \frac{88}{1212} g g (({u u}_{α α,, β β},, {v v}_{α α,, β β} - - 11)) + + \frac{88}{1212} g g (({u u}_{α α,, β β},, {v v}_{α α,, β β} + + 11)) - - \frac{11}{1212} g g (({u u}_{α α,, β β},, {v v}_{α α,, β β} + + 22)) . .$

下面通过具体实施例对本发明的测量方法进行进一步的描述。The measuring method of the present invention will be further described below through specific examples.

实施例一：如图3～图6所示，给出的一组细胞变形图像，其图像尺寸为1027×533像素，当参考子区边长为40和60个像素时的计算效率测试结果如表7、表8所示，Example 1: As shown in Figures 3 to 6, a set of cell deformation images is given, the image size is 1027 × 533 pixels, and the calculation efficiency test results when the side length of the reference sub-region is 40 and 60 pixels are as follows As shown in Table 7 and Table 8,

表7 传统数字图像相关方法与本发明的测量方法计算时间之比(即加速比)Table 7 Traditional digital image correlation method and the ratio (being speed-up ratio) of measuring method calculation time of the present invention

表8 传统数字图像相关方法与本发明的测量方法计算时间之比(即加速比)Table 8 The traditional digital image correlation method and the ratio (i.e. the acceleration ratio) of the measurement method calculation time of the present invention

从上述两个表中可以看到，当搜索半径介于10～50个像素，采样网格边长为5～20个像素时，传统数字图像相关方法与本发明的测量方法计算时间之比(即加速比)大约在10～50之间变化，这表明本发明的测量方法能够较传统数字图像相关方法提高计算效率大约10到50倍。特别是当采样网格边长减小时，计算效率尤为突出，这一特点预示着本发明的测量方法更适于高时空分辨率的细胞原位主动变形测量。As can be seen from the above two tables, when the search radius is between 10 to 50 pixels and the sampling grid side length is 5 to 20 pixels, the ratio of the traditional digital image correlation method to the measurement method calculation time of the present invention ( That is, the speedup ratio) varies between about 10 and 50, which indicates that the measurement method of the present invention can improve the calculation efficiency by about 10 to 50 times compared with the traditional digital image correlation method. Especially when the side length of the sampling grid is reduced, the calculation efficiency is particularly prominent, which indicates that the measurement method of the present invention is more suitable for in-situ active deformation measurement of cells with high temporal and spatial resolution.

上述各实施例仅用于说明本发明，凡是在本发明技术方案的基础上进行的等同变换和改进，均不应排除在本发明的保护范围之外。The above-mentioned embodiments are only used to illustrate the present invention, and all equivalent transformations and improvements based on the technical solutions of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. cell in-situ active deformation measurement method, it may further comprise the steps:

(1) respectively elastic deformation does not take place and the cell based of elastic deformation takes place at the bottom of the reference picture F of fluorogram (x, y) and deformation pattern G (x, y) on, be that the length of side is divided square sampling grid with the sampling interval S that sets, unit is a pixel;

(2) (α β) is the center, and (x, y) going up the setting length of side is the square relevant subarea f of (2N+1) at reference picture F with each sampled point respectively _{α, β}(x, y), (x y) goes up the moving-square search zone G that the selection length of side is (2M+1) at deformation pattern G _{α, β}(x, y), wherein the span of N is the integer between 15～30, and the span of M is the integer between 20～80, and unit is pixel, and M＞N;

(3) according to reference picture F (x, y) and deformation pattern G (x, digital picture intensity profile structural table f y) (x, y) and g (x y), utilizes recurrence method to set up the gradation of image overall situation structural table S that sues for peace respectively _f, S _gAnd image energy overall situation summation structural table

(4) according to digital picture intensity profile structural table f (x, y) and g (x y), calculates that (α β) is the relevant subarea f of the reference picture at center with sampled point _{α, β}(x is y) with the region of search G of corresponding deformation image _{α, β}(x, y) the cross correlation matrix number P between _{α, β}, obtain its quick recurrence relation formula and be:

P _α+S，β(u，v)＝P _α，β(u，v)-I _α-D，β(u，v)+I _α，β(u，v)，

Wherein, order

(u v) represents the relevant subarea f of reference picture _{α, β}(x, y) (α is β) at the region of search of deformation pattern G for middle sampled point _{α, β}(x, y) displacement in; D is relevant subarea f _{α, β}(x, length of side y), D=2N+1;

(5), calculate the relevant subarea f of reference picture according to the result of described step (3), (4) _{α, β}(x is y) with the region of search G of corresponding deformation image _{α, β}(x, distortion subarea g y) _{α, β}(x, y) the zero-mean normalized crosscorrelation matrix of coefficients C between _{α, β}(u, v);

(6) adopt sub-pix displacement location algorithm, near the peak-peak position of zero-mean normalized crosscorrelation matrix of coefficients, carry out the sub-pixel interpolation computing based on gradient, try to achieve sampled point in the reference picture (α, β) the accurate position in deformation pattern is:

\{\begin{matrix} U_{α, β} = u_{α, β} + {Δu}_{α, β} \\ V_{α, β} = v_{α, β} + {Δv}_{α, β} \end{matrix},

In the formula, (U _{α, β}, V _{α, β}) expression sampled point (α, β) the total displacement size in deformation pattern, (u _{α, β}, v _{α, β}) be by described zero-mean normalized correlation coefficient Matrix C _{α, β}(u, the v) middle determined whole pixel displacement of greatest member, (Δ u _{α, β}, Δ v _{α, β}) be (u _{α, β}, v _{α, β}) corresponding sub-pix displacement;

(7) repeating said steps (4)～step (6) is calculated the accurate position of all sampled points in deformation pattern, obtains whole deformation pattern displacement field.

2. a kind of cell in-situ active deformation measurement method as claimed in claim 1 is characterized in that: in the described step (4), and described cross correlation matrix number P _{α, β}The recurrence relation formula is obtained by following steps fast:

1. (α β), makes relevant subarea f for sampled point _{α, β}(x is y) with corresponding region of search G _{α, β}(x, constituting the cross correlation matrix number between y) is P _{α, β}

2. with sampled point (α, β) adjacent sampled point (α+S, β), the relevant subarea f of its correspondence _{α+S, β}(x is y) with corresponding region of search G _{α+S, β}(x, y) the cross correlation matrix number between is P _{α+S, β}

3. with described two cross correlation matrix number P _{α, β}And P _{α+S, β}After comparing, obtain:

P _α+S，β(u，v)＝P _α，β(u，v)-J _α，β(u，v)+I _α，β(u，v)

Wherein, order

D is relevant subarea f _{α, β}(x, length of side y), D=2N+1;

4. can set up quick recurrence relation and be by described step is various in 1.～3.:

P _α+S，β(u，v)＝P _α，β(u，v)-I _α-D，β(u，v)+I _α，β(u，v)。

3. a kind of cell in-situ active deformation measurement method as claimed in claim 1 is characterized in that: in the described step (5), and described zero-mean normalized crosscorrelation matrix of coefficients C _{α, β}(u v) is:

C_{α, β} (u, v) = \frac{P (α, β; u, v) - Q (α, β; u, v)}{\sqrt{F (α, β)} \sqrt{G (α, β; u, v)}},

Order

Q = (α, β; u, v) = {\overset{&OverBar;}{f}}_{α, β} Σ_{x = α - N}^{α + N} Σ_{y = β - N}^{β + N} g (x + u, y + v),

Wherein, P (α, β; U v) is image reference subarea f _{α, β}(x is y) with corresponding searching area G _{α, β}(it is by the described cross correlation matrix number P in the described step (4) for x, y) the cross correlation matrix number between _{α, β}The recurrence relation formula obtains fast; (α β) is reference picture gray scale quadratic sum to F; G (α, β; U v) is a deformation pattern gray scale quadratic sum; Q (α, β; U, v), F (α, β) and G (α, β; U v) obtains by four gradation of images, the image energy overall situation summation structural table of setting up in advance in the described step of fast query (3).