# A Titanium Alloy Defect Detection Method Based on Optical-Acoustic Image Fusion
## 2 Principle
### Technology of Optical-Acoustic Image Information Fusion  
Belonging to the field of multi-source information fusion technology, optical-acoustic image information fusion is a technology based on the result images under two different mechanisms of optical and ultrasonic detection [25; 26; 27; 28; 29; 30]. The multi-source information fusion method is a signal processing method designed for systems with multiple sensors (or information sources), which is similar to the comprehensive information processing method used by the brain. The goal of information fusion is to obtain reliable and effective data. There is a variety of advantages in the field of the NDT of titanium alloys via information fusion technology. On the one hand, it can enhance the capabilities of monitoring and detection; on the other hand, it can reduce the fuzziness of data. In addition, it can overcome the limitations of a single detection method and obtain comprehensive, accurate, and intuitive detection results. The input of the information fusion algorithm includes the optical surface defect detection results and the acoustic internal defect detection results. Due to the fact that the optical detection mechanism and the acoustic detection mechanism are two different modes, there are some issues with temporal and spatial image registration during the fusion process. In terms of temporal image registration, the signal's post-processing can ignore the issues of temporal image registration. In terms of spatial image registration, we proposed a spatial image registration method based on coordinate mapping in this paper. The diagram of coordinate mapping is shown in Figure 6.  
Specifically, it is essential to clarify that the surface defect detection image of the titanium alloy and the key points on it are located in the plane of Cartesian coordinate system A; the acoustic detection imaging of internal defects of the titanium alloy and the key points on it are located in the plane of Cartesian coordinate system B. Also, the background field of fusion detection image information is located in the plane of Cartesian  
Figure 5: Results of three scanning methods. (**a**) A-scan; (**b**) B-scan; (**c**) C-scan. coordinate system C. Under the above premise, coordinate mapping between the optical image of surface defect detection and the internal defect detection acoustic imaging of the titanium alloy should be performed. And then obtain the correct positions of the optical image of surface defect detection and internal defect detection of the titanium alloy in Cartesian coordinate system C. Moreover, the defect symbols need to be made to obtain the optical-acoustic defect fusion detection result. The algorithm flow of optical-acoustic image fusion titanium alloy defect detection is shown in Algorithm 1. The reasoning formulas of coordinate mapping are as follows:  
\[\frac{A_{sx}}{L_{T}}=\frac{C_{sx}}{D_{1}} \tag{5}\]  
\[\frac{A_{sy}}{W_{T}}=\frac{C_{sy}}{D_{2}} \tag{6}\]  
\[\frac{B_{ix}}{L_{T}^{\prime}}=\frac{C_{ix}}{D_{1}} \tag{7}\]  
\[\frac{B_{iy}}{W_{T}^{\prime}}=\frac{C_{iy}}{D_{2}} \tag{8}\]  
In the equations, \(A_{sx}\) and \(A_{sy}\) are, respectively, the abscissa and ordinate of the points on the optical image of the surface defect detection of the titanium alloy part within planar rectangular coordinate system \(A\). \(L_{T}\) and \(W_{T}\) are, respectively, the overall length and width of the titanium alloy part reflected in planar rectangular coordinate system \(A\). \(B_{ix}\) and \(B_{iy}\) are, respectively, the abscissa and ordinate of the points on the image of the internal defect detection of the titanium alloy part within planar rectangular coordinate system \(B\). \(L_{T}^{\prime}\) and \(W_{T}^{\prime}\) are, respectively, the overall length and width of the titanium alloy part reflected in planar rectangular coordinate system \(B\). \(D_{1}\) and \(D_{2}\) are, respectively, the real length and width of the titanium alloy part.