# Research on Damage Localization of Steel Truss-Concrete Composite Beam Based on Digital Orthoimage
## 4 Bridge Structure Morphology Extraction
### Regression of Discontinuous Edges of Test Beam Images  
The intrinsic nature of image features is points with discontinuous grayscale variations, and the dramatic grayscale variations imply the presence of high-frequency components of the signal of interest in the vicinity of the features. The previously extracted structural image features are not enough for structural holographic deformation monitoring. The reason for this is that it is difficult to clearly delineate the high-frequency components of the signal of interest on the bridge structure images from the environmental noise. For example, in a segment of the bridge edge image signal shown in Figure 27, point A is the ideal signal identified in the feature extraction process, and there is a step in the feature gray change at this point. Since the differential operation in the feature extraction process leads to the amplification of the noise signal, whether the step signal identified at points B and C is the true edge of the structure needs to be treated with caution. In fact, points B and C are most likely the synthesis of the characteristic signal with some noise. Due to the variable environment of bridge structure monitoring, points with natural grayscale excess and continuous gradient changes, such as point A in Figure 27, are rarer on actual bridge images. The geographical and lighting environment in which the bridge is located would make most of the structural features accompanied by environmental noise, forming a large number of feature points with complex components, such as B and C. This leads to the real feature signal being smoothed out by the Gaussian spatial filter after the noise is mixed with the structural feature signal, and the actual performance of this problem on the bridge image is edge discontinuity and missing edge information (as shown in Figure 28). Structural edges are an important source of feature point generation, the missing edges cannot provide stable and rich point source data for structural holographic morphology analysis, and the missing edges need to be regressed. The dilation and erosion operations are the two most important image boundary processing methods in morphology [34; 35; 36; 37; 38], and they are also the key means to achieve the concentration of structure-extracted edges toward the actual edges and the regression of edge breakpoints in this section. We use \(f(x,y)\) to describe grayscale images, \(b(i,j)\) for structural elements, and \(D_{f}\), and \(D_{b}\) to define the domains of \(f\) and \(b\). The dilation and erosion operations are described in Equations (22) and (23). Figure 27: Schematic diagram of edge point and noise point. (1) Definition of erosion:  
\[(f\Theta b)(x,y)=\min\Bigl{\{}f(x+i,y+i)-b(i,j)\mid(x+i,y+j)\in D_{f^{i}}(i,j)\in D _{b}\Bigr{\}} \tag{22}\]  
(2) Definition of dilation:  
\[(f\oplus b)(x,y)=\max\Bigl{\{}f(x-i,y-i)-b(i,j)\mid(x-i,y-j)\in D_{f^{i}}(i,j) \in D_{b}\Bigr{\}} \tag{23}\]  
The edges of the images obtained by the erosion or dilation operations alone are rough, and the edge noise composition is complicated in the actual image processing, so it is necessary to combine the erosion and dilation operations. In order to eliminate the external discrete points of the structure edge and smooth the structure edge, the process of first erosion and then dilation is used for edge treatment. For the problem of discontinuous breaks in the edge, the process of first dilation and then erosion is used to naturally connect the edge breaks while ensuring that the edge distribution does not expand outward. The morphological process of first erosion and then dilation is called the open operation (Equation (24)), and the process of first dilation and then erosion is called the closed operation (Equation (25)), and the above basic morphological operations are shown schematically in Figure 29.  
(3) Open operation definition. \[f(x,y)\circ b(x,y)=[(f\Theta b)\oplus b](x,y) \tag{24}\]  
(4) Closed operation definition.