**5.1 Spatial feature extraction performance**

In grayscale, we tested the performances of kICA versus nICA algorithms and the effect of feature overlaps (shadow effects) on image segmentation. An example of PCA and ICA procedures is presented in **Figure 7**. We simulated and evaluated the feature extraction processes on an overlapped photo that is mixed with three images: a human face, fruits, and vegetable scenes (features **f**1, **f**2, and **f**<sup>3</sup> in **Figure 7**). The problem can be formulated as the extraction of the human face (feature **f**2) from the mixed images (**g**1, **g**2, and **g**3) without any prior information

### **Figure 7.**

*An example of independent component analysis with kurtosis and negentropy maximization on linear mixtures of three independent images (f1, f2, and f3 with 180 180 pixels). ICA goes a step further and rotates the principal components to maximize non-Gaussianity. The results are recovered original images. The column on the right side represents the cross plots of the variables.*

from the original face. This simulation helps us to evaluate the performance of the SFE2D algorithm before the implementation on more complex applications.

While PCA whitening fails to recover all three features (y1, y2, y3), the Fast-ICA algorithm could separate the latent features inside the mixed images (^*<sup>f</sup>* <sup>1</sup>, ^*<sup>f</sup>* <sup>2</sup>, ^*<sup>f</sup>* <sup>3</sup>). Further analysis of the non-Gaussianity maximization methods revealed that the Fast-ICA through negentropy maximization (nICA algorithm) compared to kurtosis maximization (kICA algorithm) is more effective and recovers more details of each original photo. The kICA converges at 50 iterations, while the nICA converges at iteration 5 (**Figure 8**). The kICA algorithm is prone to outliers and thus fails to converge to an effective solution. However, restarting the kICA each time might improve the results. Therefore, for large images, the efficiency of the nICA method is superior to the kICA, with about 10 times faster convergence and more accurate results.

Another influencing factor with the same level of added unpredictable noise is the sampling interval. This is crucially important in the geophysical sense since the sampling interval directly influences the geophysical survey budget. Large regionalscale data sets are sampled in smaller intervals and give more details about geological structures. As is shown in **Figure 9**, increasing the number of samples reduces

### **Figure 8.**

*Performance of kICA algorithm (a) compared to nICA algorithm (b). The kICA results converge at 10 iterations while the nICA results are converged at iteration 5. The nICA method is superior to the kICA, with about two times faster convergence and more accurate results (180 180 pixels).*

### **Figure 9.**

*Performance of kICA algorithm (a) compared to nICA algorithm (b) on large images with 720 720 pixels. For the kICA algorithm, a 16 times increase of pixels results in eight times slower convergence with numerous local minima. Therefore, for larger images with smaller sampling intervals, negentropy maximization is superior to kurtosis maximization.*

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

the performance of kICA compared to nICA and indicates that for large datasets with smaller sampling intervals, negentropy maximization is superior to kurtosis maximization.

However, there are two inherent ambiguities in the ICA framework: (1) Ambiguity in permutations of the recovered sources. This problem states that the order of the estimated independent components is unspecified. (2) Ambiguity in the recovered amplitudes of the sources. One can partially solve this problem by assuming unit variance for all sources. However, there is still a 50% chance that the polarities of the sources are not determined correctly. In cases where we have enough prior information, we can multiply sources by 1 to achieve the best results.

The effect of mixing on image segmentation is also explored in **Figure 10**. ICA significantly reduces the impact of feature overlaps and enhances the performance of image segmentation. The proposed approach integrates information from multiple geo-images and makes sure that the combined images are maximally independent and unique. In other words, the feature overlaps are minimal. This has an important implication in image segmentation since a slight presence of image overlaps and artifacts distort the segmentation output. As shown in **Figure 10**, the segmentation after negentropy maximization improves the human face detection.

### **5.2 Spectral feature extraction**

Further feature extraction can be performed on the images to extract spectral features like edges and lineaments inside the photos. **Figure 11a** shows the results of CWT with Cauchy mother wavelet and 20 scales on the second independent component (recovered human face). As can be seen, different spectral features appear in different CWT scales/directions. Low-level features like edges appear in higher frequencies, and high-level features appear in lower frequencies. However, the transition from each scale/direction is relatively smooth, and that allows some features from each scale/direction leak into the following scale/direction, creating unwanted spectral features' overlap. To reduce these effects, we perform source separation methods like PCA and ICA algorithms again. The results are shown in **Figure 11b**. As is shown, spectral source separation with nICA has improved the low/high-level features with crisper edges and more visible boundaries.

### **Figure 10.**

*Effect of ICA as a preprocessing step before grayscale image segmentation. (a) Segmentation on the mixture image (***g**<sup>2</sup> *in Figure 6). (b) Segmentation after negentropy maximization nICA (*^**f**<sup>2</sup> *in Figure 6).*

**Figure 11.**

*(a) Space-frequency representation with Cauchy mother wavelet in four scales on the second independent component (recovered human face). Different spectral features appear in different CWT scales/directions. (b) Separation of spectral features with nICA. The results are crisper and have more distinct features.*
