## 4 Image Fusion Applications in NDT Inspection
### Principal Component Analysis  
Principal component analysis (PCA) is a well-known statistical technique for reducing the dimensionality of a dataset. This is carried out via appropriate coordinate transformation. Here, the main idea is to retain the maximum possible variation while reducing the dimensionality of the dataset. The new set of variables, referred to as the _principal components_ (PCs), is generated in such a way that the first few PCs retain most of the variation (in more detail, the first component retains the maximum variance, with the second one existing in the subspace that is perpendicular to the first PC) [54, 55, 56]. PCs are linear combinations or mixtures of the original data. Figure 4 illustrates the first and second uncorrelated dimensions as PCs. PCA has already been used in various domains, such as pattern recognition, image compression, dimensionality reduction and feature extraction [57, 58, 59, 60], as well as NDT applications [61, 62, 63, 64, 65]. \begin{table}
\begin{tabular}{c c c c c} \hline
**Sources** & **Material** & **Defect Types** & **Aim** & **Fusion Rule** & **Reference** \\ \hline Eddy current, active & & & & Minimum, \\ thermography and & & & Preventing & geometric mean, \\ magnetic flux & & & single-sensor & harmonic mean, \\ leakage & & & domination & product, median, \\  & & & sum, sumIgnoreMax & \\ \hline Computed & & & & and maximum \\ tomography with & & & & \\ different & & & measurement issues & \\ configurations & & & & \\ \hline \end{tabular}  
\({}^{1}\) This study tried to detect different materials for an object.  
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline
**Method** & **Equation 1** & **Remark** \\ \hline Summation & \(\tilde{F}=\sum\limits_{i}F_{i}\) & \begin{tabular}{c} Suitable for fusion of complete \\ datasets (same size or resolution) \\ \end{tabular} \\ \hline Difference & \(\tilde{F}=\sum\limits_{i}F_{i}-\sum\limits_{j}F_{j}\) & \
\begin{tabular}{c} As explained above and for fusion of \\ simulated and real datasets \\ \end{tabular} \\ \hline Quotient & \(\tilde{F}=\sum\limits_{i}F_{i}/\sum\limits_{j}F_{j}\) & as explained above \\ \hline Average & \(\tilde{F}=\sum\limits_{i}F_{i}/k\) &
\begin{tabular}{c} Fusion of incomplete datasets \\ as well \\ \end{tabular} \\ \hline Maximum & \(\tilde{F}=\max\limits_{i}F_{i}\) & as explained above \\ \hline Product & \(\tilde{F}=\prod\limits_{i}F_{i}\) & From quotient \\ \hline SumIgnoreMax & \(\tilde{F}=\sum\limits_{i}F_{i}-\max\limits_{i}F_{i}\) & From summation \\ \hline \end{tabular}  
\({}^{1}\)\(\tilde{F}=\) fused dataset; \(F_{i},F_{j}=i\) and \(j\) (source) datasets, respectively; \(k=\) number (size) of measurements of the \(i\) datasets.  
\end{table} 
Table 3: Data fusion operations at signal level (amplitudes). In the context of NDT fusion, a pixel-level fusion using the PCA and DWT methods was proposed to detect inclusive defects (copper sheets) with different depths, sizes and shapes in a GFRP material [66]. Amplitude and phase images from active thermography, extracted using a Fourier transform, were fed for fusion as inputs. The principle components and wavelet coefficients shaped the input images for combination purposes. In terms of fusion efficiency, the metric used was the signal-to-noise ratio (SNR) between the inputs and fused images. It was highlighted in the work that the PCA fusion strategy increased the SNR for the inclusive defects considerably. A similar study [45], including Teflon inclusions of different depths and sizes for GFRP composites, applied pulse compression to thermographic images. For transmission, a low peak power and long-duration modulated wave was used, rather than a short duration and high peak power, to obtain a better depth resolution and SNR for the inhomogeneities in the structure. The study compared averaging-, PCA- and wavelet-based fusions, with the latter providing the highest SNR.