## 4 Image Fusion Applications in NDT Inspection  
### General Algebraic Approaches  
General algebraic (basic mathematical) approaches have been utilised to combine the source signals, features or estimations pixel-wise as a fusion rule. The selection of the appropriate fusion rule might depend on the target that needs to be achieved and the nature of the data collected from different sources. For instance, while division and subtraction are suitable for detecting temporal changes in different measurements, the maximum approach might be more applicable to finding complementary information, as seen in [48]. The study  
Figure 3: (c) An example representation for signal-level combination for a noise-free defect simulation and defect-free experimental noise. (a) Simulated noise-free defect. (b) Experimentally measured defect-free noisy back wall [43]. performed a porosity and distribution analysis for concrete structures using ultrasonic and ground-penetrating radar (GPR). After the processing (weighting and filtering datasets) and reconstruction (synthetic aperture focusing technique (SAFT)) steps for both individual methods, the amplitude values of both methods are added to obtain improved depth information, adapting the depth point of the maximum amplitude. The size of the dataset is another crucial parameter in selecting the fusion rule that will be implemented. For example, the data size must be the same for an addition or division operation. In addition, a data acquisition system might affect the selection of fusion methods due to the nature of the produced data. A bimodal imaging system may need supervision to prevent interference while using two separate imaging systems. Dual-imaging fusion based on X-ray and neutron images has been offered for material identification using attenuation differences [19]. It has been used as a single-electron linear acceleration system with a slight time delay to prevent the system from that type of interference. It should be noted that here, the acquisition systems for X-ray and neutron inspection have almost the same beam geometry, and data are ready to fuse directly. Pixel-wise matching has been performed using extracted neutron attenuation and photon attenuation values compared with the neutrons and photons of air. As a result of this pixel-wise fusion, a bivariate histogram has been provided to identify different materials and their thicknesses without prior knowledge. The basic mathematical fusion rules can also be used mainly for comparison or complementary with other fusion rules. A good example application of this is in [49], which includes the basic rules, wavelets and decision-level fusion (kernel density estimation (KDE)) together. A steel-bearing shell specimen with 15 surface grooves and specific dimensions was used experimentally. Although the sum and max fusion rules provided poor performance, all other rules showed a satisfactory flaw detection capability rather than the single-sensor yield. Another study in the manufacturing field [50] proposed pixel-based image merging to improve object measurement using the multi-energy stacks of computed tomography (CT) images. The primary purpose behind the fusion process is to eliminate measurement difficulties caused by the sample's high aspect ratio (thickness to length) and the variety of absorbing materials. Fusion was applied by finding outshined pixels of different energy stacks, followed by replacing those pixels. A mean deviation-based evaluation was applied, and the fusion results showed less deviation than the mono-energetic measurement. Table 2 presents information on the material, defect and source details of the aforementioned studies. There are more studies available in the papers [46; 51; 52; 53] that used these basic rules in a complementary manner. However, the details provided in the papers are limited. In addition, Table 3 has given mathematical expressions of related fusion rules.