**4. Discussion**

A variety of target detection techniques have been published during the last few decades [12–15,25,59], with several studies applying support vector machines (SVM) [60] or Fisher's linear discriminant analysis (FLDA) [60] to solve target detection problems as a binary classification problem [61–65]. These algorithms require a number of classes, and their class distribution model must be known in advance. In order to avoid any biased selection of training samples, the partition must be performed randomly. In other words, training samples must be randomly selected from a dataset to form a training sample set for cross validation. As a result, such a validation is not repeatable and cannot be re-produced. The results are inconsistent. To alleviate this dilemma, this paper proposes a novel Constrained Energy Minimization (CEM) based technique that takes advantage of spectral and spatial information and developed Optimal Signature Generation Process (OSGP) in terms of the iterative process point of view to solve the issues mentioned above. CEM only requires one desired target information for the specific target of interest, regardless of other background information, which is its major advantage. Theoretically, CEM subpixel detection is generally performed by two operations that involve background suppression and matched filter [16]. First, it performs background suppression via the inverse of **R** so as to enhance a detected target contrast against the background. Second, CEM operates a matched filter using **d** as the desired matched signature so as to increase intensity of the target of interest. Since only one target signature can be used as the **d** in Equation (5), selecting an appropriate **d** is a very crucial step for detection results. Although CEM has many applications [27,30,31], very few studies investigated the issues of selecting a desire target signature. Therefore, this paper developed the Optimal Signature Generation Process (OSGP) to resolve this issue.

When compared to the classification based approaches that require very precise prior knowledge to generate a set of training samples and features, applying OSGP on the proposed CEM based methods required only one target signature information and provided stable results even if the initial desire target information is bias or not reliable. In the iterative process of OSGP in Figure 24, the iteration results of different desired signatures **d** after different numbers of iterations give a stable AUC result, so that the originally worse desired target obtains a relatively better desired target. Figure 25 shows different **d'**s have different results in the same algorithm. However, the **d'** iterated by OSGP used in CEM, Subset CEM, SW CEM, and ASW CEM can enhance the original desired target to some extent. Moreover, the results are approximately identical, meaning OSGP can determine the appropriate desired target automatically when selecting inappropriate **d** as initial, and the result is still very stable.

**Figure 24.** Iterative process of OSGP and corresponding AUC detection result.

**Figure 25.** AUC detection results of various algorithms executing five different **d** and corresponding **d'** generated by OSGP (**a**) CEM; (**b**) Subset CEM; (**c**) SW CEM; and, (**d**) ASW CEM.

CEM technique only takes advantages of spectral information to detect target of interests. However, when spectral information is insufficient to distinguish between targets and some materials have similar spectral signature, this likely causes false alarms in the multispectral images. In this case, our proposed window-based techniques actually include spatial information into the CEM algorithms via fixed or adaptive windows to compensate for the insufficient spectral information. According to the experimental results and the resulting images in Figures 14–17, among our proposed local CEM algorithms, the Subset CEM, Sliding Window-based CEM (SW CEM) of the fixed window size, or Adaptive Window-based CEM (ASW CEM) enhances the contrast between the target and the background better than the general CEM. Because the autocorrelation matrix **R** of the CEM algorithm is different, CEM uses **R** of the full image, whereas our proposed local CEMs uses local autocorrelation matrix **S** in Equation (10) to suppress the background. According to effect of the background suppression [58], it is obvious that using local autocorrelation **S** is better than global

autocorrelation **R** in this study. Figures 26 and 27 show the RGB signatures corresponding to different objects in the study site. As seen, some RGB signatures of leaves and grass are very close to NGL. In the upper left of Region 1, as the grass is too similar to the sprout shown in Figure 26, the CEM detection is likely to give a false alarm. Because the **R** that is used by CEM is generated according to the pixel value of the full image, the difference between NGL and grass is not obvious in the full image. In the entire image, the house and soil are larger than the RGB difference between grass and the sprout, and so the grass is likely to be misrecognized as NGL. On the contrary, in our proposed CEM based algorithms using **S**, because **S** is generated by pixels around the current pixel value and the proportion of soil and house is not high in a small area, the difference in RGB values between grass and NGL is enlarged, and the grass is likely to be suppressed, thus reducing the false alarm rate. In the same way, the lower right of Region 2 also easily gives a false alarm. Because the pixel values of some leaves are very similar to NGL in the region shown in Figure 27, when **R** is used to suppress the background, it is likely to be influenced by pixel values with a larger difference, and this problem can be solved by using **S**.

**Figure 26.** RGB signatures corresponding to different objects in Region 1 [4].

**Figure 27.** RGB signatures with different objects in Region 2 [4].

ASW CEM can change the size of the sliding window, according to the ratio of NGL around the current pixel. When there are too many NGL in the window, the difference between them is likely to be enlarged, and NGL that is very different from the desired target will be suppressed, leading to detection omission. Therefore, the sliding window shall be enlarged to reduce the rate of NGL and enhance the difference from the background, thus increasing the detected value. On the contrary, if the rate of NGL is too low, then the difference between backgrounds increase, and the RGB values that are

similar to NGL is likely to be misrecognized. At this point, the sliding window is shrunk, the rate of NGL increases, the difference between NGL and background are more apparent, and the result value of the non-NGL is reduced for suppression. When NGL are enhanced and background is suppressed; their difference is enlarged, so as to highlight NGL.

Briefly, CEM technique was originally designed to catch (1) low probability of infrequent occurrence, (2) relatively small sample size, and (3) most importantly, the target pixel has spectrally distinct from its surrounding pixels [16]. Obviously, the NGL in RGB images shows the same features. This explains why the window-based CEM techniques can achieve satisfied results of NGL detection even only three spectral signatures is used.
