Receiver Operating Characteristic (ROC)

The receiver operating characteristic (ROC), which is based on the Neyman-Pearson detection theory, is used for the evaluation of detection performance in signal processing, communication, and medical diagnosis (Chang et al., 2001; Wang et al., 2005; Miyamoto et al., 2008; Chang, 2010). The ROC curve is used to illustrate the performance of a binary classif er system, which means whether a class is detected (‘hit’) or not (‘miss’). The detection is measured by the area under the Neyman Pearson curve. The area is denoted by A. and bounded between Vi and 1. For better detection, it should be closer to 1 (Wang et al., 2005). The 2D ROC curve is plotted by the false alarm rate (FAR) on one axis (л-axis) and true positive (TP) rate on another axis (у-axis). On the other hand, the 3D ROC curve is plotted by taking the false alarm rate (FAR) on the .v-axis, detection threshold (!) on the у-axis, and true positive (TP) rate on the z-axis (Figure 7.1). The 2D ROC can be used for hard decision produced by the classif er, whereas 3D ROC can be used for the soft decision (Wang et al., 2005).

This method is also able to check the accuracy while extracting single land cover from remote sensing image classif cation, where the classif er acts like a binary or in other words, when the interest is only to know whether the classif er is able to detect a particular class or not. The 2D ROC curve is plotted by the true positive (TP) rate on one axis and the false alarm rate (FAR) on the other axis, whereas in 3D ROC

ROC curves for identif cation of wheat crop using noise clustering classif er

FIGURE 7.1 ROC curves for identif cation of wheat crop using noise clustering classif er. (a) 3-D curve showing variation of true positive (TP) with false alarm rate (FAR) and detection threshold (t) and (b) variation of TP with FAR alone.

one more axis corresponding to the detection threshold is also added to the 2D ROC curves. The TP and FAR can be def ned in Equations (7.26) and (7.27), respectively:

The area under the 2D ROC curve is used to measure the detection performance of the classif er. It is bounded between Vi and 1. For better detection, it should be closer to 1.

Method for Edge Preservation

There are methods for adding contextual information through MRF or local convolution to reduce noisy pixels in a given image. While adding contextual information, edges of the objects are affected due to smoothing effect. Therefore, it is important to verify whether any edge within a classif ed output is correct or not. An edge represents boundaries between two objects which may be characterized as a step function or slope between two regions (Wen and Xia, 1999).

As per Wen and Xia (1999), if for some specif c threshold c,

|yu, - /л2 then there is no signif cant difference between the grey levels on the two sides of the edge whereas if - ц2 > c, there will be a signif cant difference between the true averages, where and 2 are the mean value of the pixels on each side of the edges.

To verify the signif cance of an edge, the distribution of grey levels of both sides needs to be analyzed in the sense that the difference between the average values within two regions represents the steepness of the edge. To determine the value of c, edge point is examined f rst through Equation (7.28).

where X, and T represent the grey level of Ith pixel on two sides of the edge respectively. S is the standard deviation of the grey levels in the region the point. Za can be obtained from the standard distribution tables. In practice, the values of a can be assigned as 0.01, 0.05, 0.1, 0.2 depending upon different requirements. Both low and high thresholds for an edge can be identif ed by selecting two different values.

The fraction image generated using the contextual approach for a particular class has the high membership value if class exists for a known location. If it does not exist, then membership value is low. For a homogeneous area, the fraction image will have less variability among the membership values. Consequently, the mean membership value will be high and variance will be low for a homogeneous area. This concept has been suggested to verify the edge preservation.

For edge preservation method, f rst a homogeneous area of a specif c class, i.e., crop, has been selected which has a high mean value and a low variance. After selecting a homogeneous area, two sets of pixels were selected at either side of the crop class edge. Mean and variance are calculated for these two sets of pixels in each iteration. The mean difference of these two sets of pixels should be high and variance within should be low if the edge is to be preserved.

 
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