*6.1.2 Spectral feature extraction*

CWT is performed on the magnetic data sets (**Figure 13c**). Decomposing the magnetic data sets with CWT forms raw spectral features that eventually increase dimensionality. 2D wavelet coefficients are calculated here for eight scales with Mexican Hat mother wavelet, containing several frequency-dependent raw features (**Figure 15**). However, the algorithm allows choosing any number of scales and directions (in the case of anisotropic mother wavelets), as long as the computer hardware specifications allow.

As shown in **Figure 15**, spectral decomposition reveals many latent features that are not properly visible in the spatial domain. The major difficulty arises in extracting and selecting the spectral features due to the statistical interdependence of features in various spectra. Spectral decomposition of images also overloads the computational cost of interpretation and demands a methodology to pick the best spectral representation of images. The SFE2D program tackles this problem with the

**Figure 13.**

*Three input images. (a) Digital elevation model. (b) GGMplus gravity anomalies. (c) Aeromagnetic data sets.*

### **Figure 14.**

*Color image segmentation after variance and negentropy maximization and RGB image compilation through* k*means clustering with eight segments. (a) PCA segmentation with variance maximization. (b) ICA segmentation with negentropy maximization.*

*SFE2D: A Hybrid Tool for Spatial and Spectral Feature Extraction DOI: http://dx.doi.org/10.5772/intechopen.101363*

**Figure 15.** *CWT with Mexican Hat mother wavelet with eight scales over magnetic data sets.*

spectral independent component analysis. We used Fast-ICA through negentropy maximization to separate the eight raw wavelet features to produce the spectral inputs necessary for interpretation. The Fast-ICA algorithm can reduce the dimensionality of the raw features. This is important when we produce a large number of raw features through CWT, and as a result, our computational hardware resources are not enough to handle the inevitable high dimensionality.

We reduced the dimensionality of the raw spectral features and thus produced three independent features (**Figure 16**). As shown in **Figure 16**, the program uncovered several low-frequency features in higher wavelet scales related to deep sources and high-frequency features related to shallow sources.

2D wavelet coefficients are also calculated with Cauchy mother wavelet on eight scales and eight directions, producing several directional/frequency-dependent raw features (**Figure 17**). As can be seen, most of the wavelet spectral content is redundant, and similar features are repeated in 64 subsequent directions/scales. Three independent spectral components are extracted through spectral feature extraction and dimensionality reduction (**Figure 18a**–**c**). Therefore, the 64-dimensional hyperspace is reduced to a 3D RGB space to facilitate visual interpretations

**Figure 16.**

*Spectral feature extraction and dimensionality reduction by negentropy maximization on CWT results with Mexican Hat mother wavelet. (a–c) Extracted independent spectral features.*

**Figure 17.** *CWT with Cauchy mother wavelet on eight scales and eight directions over magnetic data sets.*

(**Figure 18d**). As can be seen, the process helped to uncover several hidden lineaments in the NE–SW direction.
