## 3 Full-Field Temporal-Spatial Displacement Measurement of Large Slender Ratio Structure
### Slice Template Matching Model  
#### 3.3.1 Concept of Single Slice Template Matching Model (STMM)  
In vision-based monitoring, the slender structure, for example a beam, is captured and stored in a 2-D gray image as shown in Figure 6a, and there is good distinguishability of the gray-scale values in the vertical direction, but poor distinguishability horizontally. Without preinstalled markers, it is difficult to track the motion of the beam by DIC method or feature-based motion tracking method, but it is possible to track any motion of the single 1-D image in the \(i\)-th column of the image, as shown in Figure 6a.  
For the 1-D image composed of N pixels, the \({N_{0}}^{i}\) pixels contains the beam section and is set as the mask as shown in Figure 6b, and the transversal pixels is the mask's possible motion region in the column indicated as \({N_{i}}^{i}\), where \(i\) is the column number in the image.  
Figure 5: Degraded one-dimension template matching. (**a**) 1-D column template matching model. (**b**) 1-D row template matching model.  
Figure 6: Beam structure in image storage and the STMM. (**a**) Beam in 2-D image. (**b**) Slice template matching model.  
Therefore, a one-dimension template matching model could be set up, and the number of pixels within the transversal sections in each column can be determined by the priori geometrical, mechanical information of the beam as follows.  
The number of pixels in mask \({N_{0}}^{i}\) should be slightly larger than that of beam height, and the height of transversal section \(H_{\text{s}}\) is formulated as follows:  
\[H_{\text{S}}=h+kD\ (1.2\leq k\leq 1.5) \tag{3}\]  
where \(h\) is the height of beam, and \(D\) is the deflection value calculated theoretically from material property, priori loading and geometry information, as shown in Figure 7. \(k\) is a constant empirical coefficient between 1.2 and 1.5.  
In this way, the full-field deformation measurement of the beam can be transferred to a series of 1-D template matching models to trace the deflections of uniform measure points in Figure 4, and this one-dimensional template matching model is called Slice Template Matching Model (STMM). In practical application, the number of measurement points arranged on the beam surface can be determined according to engineering requirement, and the maximum number is the number of pixels columns \(M_{\text{f}}\) covered by the beam length in image space, i.e., one template matching model is established for each column of pixels. Then, the dynamic full-field displacement measurement of the slender structure is converted into \(M_{\text{f}}\) series of STMM per frame in the image sequence.  
It is clear that the STMM resolves the two-direction distinguishability challenge in the beam image, by converting the measurement task into multiple one-dimensional template matching processes, which require distinguishability only in the vertical dimension. This approach can be easily achieved for bridge structure located in natural light environment while maintaining high computational efficiency. Moreover, multiple one-dimension models are computed independently each column, and it helps the realization of parallel computation. Meanwhile, this computation independence between columns helps to avoid interference in the neighborhood, as in the two-dimension template matching method model or in the feature matching method, which induces computation redundancy as well as mismatching. The simplicity and interpretability of STMM are better than feature extraction-and-matching based method.