Weighted Background Suppression Target Detection Using Sparse Image Enhancement Technique for Newly Grown Tree Leaves

Abstract

The process from leaf sprouting to senescence is a phenological response, which is caused by the effect of temperature and moisture on the physiological response during the life cycle of trees. Therefore, detecting newly grown leaves could be useful for studying tree growth or even climate change. This study applied several target detection techniques to observe the growth of leaves in unmanned aerial vehicle (UAV) multispectral images. The weighted background suppression (WBS) method was proposed in this paper to reduce the interference of the target of interest through a weighted correlation/covariance matrix. This novel technique could strengthen targets and suppress the background. This study also developed the sparse enhancement (SE) method for newly grown leaves (NGL), as sparsity has features similar to newly grown leaves. The experimental results suggested that using SE-WBS based algorithms could improve the detection performance of NGL for most detectors. For the global target detection methods, the SE-WBS version of adaptive coherence estimator (SE-WBS-ACE) refines the area under the receiver operating characteristic curve (AUC) from 0.9417 to 0.9658 and kappa from 0.3389 to 0.4484. The SE-WBS version of target constrained interference minimized filter (SE-WBS-TCIMF) increased AUC from 0.9573 to 0.9708 and kappa from 0.3472 to 0.4417; the SE-WBS version of constrained energy minimization (SE-WBS-CEM) boosted AUC from 0.9606 to 0.9713 and kappa from 0.3604 to 0.4483. For local target detection methods, the SE-WBS version of adaptive sliding window CEM (ASW SE-WBS-CEM) enhanced AUC from 0.9704 to 0.9796 and kappa from 0.4526 to 0.5121, which outperforms other methods.

1. Introduction

Protecting wild tree coverage for sustainable forest ecosystem resources is crucial to relieve the effects of global warming and climate change. To be specific, according to a forest resource assessment report, changes in wooded areas, the accumulation of forest biomass/carbon storage, and healthier forests have been used as indices to periodically evaluate sustainable global forest resources (Food and Agriculture Organization) [1]. Therefore, monitoring the health standards of forest ecosystems by remote sensing can alleviate the global warming problem, as climate change may influence phenological events, such as sprouting and senescence [2].

When trees perceive ongoing growth signals in early spring, they begin to sprout [3]. After the leaf sprouting stage, the newly sprouted leaflets develop gradually and promote growth of the crown size, height, diameter, and carbon storage of trees [4]. Therefore, newly grown tree leaves can be regarded as the priority target of a tree’s response to temperature change and could provide key information for the early detection of climate change [5]. In forestry, a distribution map of tree species can be derived by classification approaches, as based on the spectral signatures and texture features of tree crowns [6,7,8], as well as tree delineation techniques [9,10,11,12] using high-resolution images. In addition to the use of an effective chlorophyll indicator [13], as well as appropriate spectral signatures and a canopy height model, it is possible to derive reliable chlorophyll estimates and biomass productivity [14,15,16]. Detection of newly grown leaves is a relatively new application that may further derive the flow of stand dynamics [17]. As a target may have low probability for detection or may be smaller than the size of the background, e.g., the damaged part of a forest canopy (meaning the sprouts of the forest canopy), traditional spatial domain image processing techniques [18,19,20,21] may not be able to effectively locate these targets, especially when the target dimension is smaller than the pixel resolution [5]. On the contrary, detection at the subpixel level using spectral characteristics is one of the more appropriate methods. Based on multi/hyperspectral images, an active target detection technique based on spectral information [22,23,24,25,26,27,28,29,30,31,32] may solve these problems. Active target detection algorithms such as constrained energy minimization (CEM) [25,26], the adaptive coherence estimator (ACE) [27,28], the target-constrained interference-minimized filter (TCIMF) [29], and adaptive window-based constrained energy minimization (AW-CEM) [30] all require a certain level of prior knowledge to locate specific targets of interest. CEM and ACE only require one target signature information; TCIMF can detect multiple targets and AW-CEM can adjust window size to detect small targets.

This paper uses images taken by an unmanned aerial vehicle (UAV) as the detection images. UAV is rapidly becoming an important tool in various areas such as crop inspection, environmental surveillance, and surveillance of various earth surfaces. As UAVs can monitor different environments, they have been extensively used in various fields, including climate change, changes in the ecosystem, urbanization, and habitats, etc. However, UAV bitmap images only provides Red-Green-Blue bands which is a major challenge for detecting targets with very limited spectral information.

According to previous studies [5,30], the detection rate of multispectral images can be improved by various filters and detectors. The most important issue for target detection is how to enhance the target while suppressing background noise. Background suppression [22] is an important issue for both anomaly detection and target detection. As shown by [22] in the experimental results of synthetic images, it has been proven that removing the target signatures in the inverse of correlation matrix R or covariance matrix K significantly suppresses the abundance of background fractions. However, real images have very limited target information. In this case, it is not possible to remove all the target signatures in R or K. Therefore, this paper proposes weighted background suppression (WBS) to improve the interference of the target of interest through background suppression; the effect of background suppression is not considered when adjusting parameters. Moreover, background suppression is likely to be disturbed by the target pixel when detecting the target, meaning it will fail to implement better background suppression, which will lead to misrecognition of the final results. Referring to the method proposed by [25,26,27,28,29,30], if the common spectral algorithm is deformed and improved, the accuracy of the detection results can be effectively increased. Therefore, this paper proposes the WBS method with weighting parameters, in which the weighting parameters are adjusted according to the relative relationship between the background and the target; the closer to the target, the less the effect on background suppression. This concept is completely different from other methods found in literature [33], as it only enhances newly grown leaves (NGL) but does not consider the background suppression issue. Our experimental results show that the proposed WBS method could improve performance and is even better than [33].

Another major contribution of this study is the development of sparse enhancement (SE) to enhance the contrast of NGL. Robust Principal Component Analysis (RPCA) [34,35,36,37,38,39] or sparse and low-rank matrix decomposition [40,41,42] have mostly been used for exploratory data analysis and classification in different applications of a variety of scientific and data analytics’ problems. Discussion and further analysis have been conducted on the domains of video surveillance [36], subspace tracking [37], anomaly detection [38,42], edge-preserving rain removal [39], automatic target detection [40], burn scar detection [43], blood vessel extraction [44], and cloud removal [45]. Moreover, there are several optimal approaches to solve the equations of sparse and low-rank matrix decomposition [46,47,48,49] for the above applications. Robust PCA was used in forest remote sensing for the first time in this paper, and NGL was effectively enhanced by the sparse matrix. As the features of NGL are coincident with the characteristics of sparsity, the sparse matrix separated by [46] was superposed in the original image, in order to enhance the NGL signal, and with the WBS technique, the proposed new method of sparse enhancement-weighted background suppression (SE-WBS) was used in various target detection algorithms, such as ACE, TCIMF, CEM, and adaptive sliding window (ASW)-CEM. The experimental results show that all the target detection algorithms were significantly improved after the application of the SE-WBS technique, especially ASW-CEM, which performed better than others found in literature [33], as proposed in previous references, and the original ASW-CEM [30].

The remainder of this paper is structured as follows. Section 2 contains the materials and methods that provided our UAV data collection, as well as the detailed algorithms that were used and developed. Section 3 includes the experimental results and advanced analysis. Section 4 contains further discussion, as based on the experimental results in Section 3. Section 5 concludes and summarizes the contributions and future works of this study.

2. Materials and Methods

2.1. UAV Data Collection

In 2002, there were 17 species of trees planted in Taiwan, and the area of the hardwood forest was 188.59 ha [5]. The 17 species included the tropical species Swietenia macrophylla in the south of Taiwan, which experiences defoliation for one to two weeks during the middle of March. New leaves grow rapidly within one to two days and are observable in the air. This study used an eBee Real-Time Kinematic (RTK) drone (SenseFly, Switzerland) carrying a Canon PowerShot S110 camera to take photographs of the area on 12 July 2014.

The spatial resolution or ground sample distance of the images was 6.75 cm (known as the centimeter-level Very High Resolution (VHR) image). The research site is located in Baihe District, Tainan City, Taiwan (N23°20′, E120°27′), as shown in Figure 1. This image includes the Red, Green, and Blue bands, with a dimension of 1000 × 1300 pixels. In terms of the desired target d used in the target detection algorithms in this study, the NGL, as selected by professors from the Department of Forestry of the National Chiayi University, was used as the desired target d for NGL detection.

As shown in Figure 2, the red circle is the target d used in this paper, while the blue circle is the undesired target, meaning non-targeted pixels, such as soil, mature leaves, and other sundries. The undesired target was used as the undesired target in the TCIMF algorithm.

In order to effectively quantize and compare the efficiencies of various target detection algorithms, an NGL distribution map was used as the standard and measurement. According to a row of several years of inventory, the ground truth of the NGL over the images were visually interpreted and validated in situ. Figure 2 shows the ground truth in the original images.

2.2. Adaptive Coherence Estimator (ACE)

ACE [27,28] is used to calculate the standard deviation around each pixel as a new pixel value. The invariant of ACE is the relative scaling of the input spectrum, and there is constant false alarm rate (CFAR). This false alarm rate can remove background noise and interference. According to the ACE equation, r is the image pixel, d is the target pixel, and K is the background, which are expressed as follows:

$$ACE\left(r,d\right)=\frac{r^T{K}^{-1}d{\left(d^T{K}^{-1}d\right)}^{-1}{d}^T{K}^{-1}r}{r^T{K}^{-1}r}$$

(1)

It could be observed that the closer the present pixel to the target, the larger the value calculated by ACE, which is why ACE can suppress noise while maintaining details.

2.3. Target Constrained Interference Minimized Filter (TCIMF)

TCIMF [29] uses the given undesired signal source to detect multiple target signal sources, while a whole set of undesired signal sources is neglected. This can enhance the desired target, eliminate the effect of undesired signals, and suppress the background, which is identical to the combination of CEM [22,23,24] and Orthogonal subspace projection (OSP) [25]. The equation is expressed as follows.

Assume an image has three components: D (desired target), U (undesired target), and I (noise). If $D=\left[d_{1 }{d}_2\dots d_{n_d}\right]$ and $U=\left[u_{1 }{u}_2\dots u_{n_u}\right]$, they are the desired target feature matrix and undesired target feature matrix, respectively.

${\mathsf{\delta }}^{\mathbf{TCIMF}}\left(\mathbf{r}\right)$ can be expressed as:

$${\delta }^{TCIMF}\left(r\right)=r^T{R}_{L\times L}^{-1}\left(DU\right){\left[{\left(DU\right)}^T{R}_{L\times L}^{-1}\left(DU\right)\right]}^{-1}\left[\begin{array}{l}{1}_{p\times 1}\\ 0_{q\times 1}\end{array}\right].$$

(2)

2.4. Constrained Energy Minimization

Constrained Energy Minimization (CEM) [22,23,24,25] is stable and excellent for subpixel detection. An advantage of CEM is that, during the course of target detection, the CEM algorithm only requires one spectral signature (the desired signature or target of interest) as parameter d, while other prior knowledge (e.g., multiple targets of interest or background) is not required. Another advantage of CEM is that many signals are unidentifiable or unobservable by the naked eye, meaning that some materials may be detected by sensors but cannot be identified. However, CEM transposes the data correlation matrix R, which can be defined as $R=\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{N}$}\right.\right){{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{r}_i{r}_i{}^T$. The background is suppressed by correlation matrix R, while feature d is used to match the customized Finite impulse response (FIR), in order to enhance its ability to detect features.

CEM is derived from Linearly Constrained Minimum Variance (LCMV), as proposed by Frost [26]. If a hyperspectral image with N pixels r is defined as $\left\{r_{\mathbf{1}},r_{\mathbf{2}},r_{\mathbf{3}},\dots ,r_N\right\}$, each pixel has L dimensions expressed as $r_i={\left(r_{i\mathbf{1}},r_{i\mathbf{2}},r_{i\mathbf{3}},\dots ,r_{iL}\right)}^T$, the desired target d can be defined as ${\left(d_{\mathbf{1}},d_{\mathbf{2}},d_{\mathbf{3}},\dots ,d_L\right)}^T$, and FIR performs filtering to detect the desired target. The filter coefficient is defined as $\mathbf{w}={\left({\mathbf{w}}_{\mathbf{1}},{\mathbf{w}}_{\mathbf{2}},{\mathbf{w}}_{\mathbf{3}},\dots ,{\mathbf{w}}_{\mathbf{L}}\right)}^{\mathbf{T}}$. The value of w can be obtained when the average energy is constrained. The constraint is defined as $d^{T}w=w^{T}d=1$. The result of CEM is:

$${\delta }^{CEM}={\left(w^{CEM}\right)}^{T}r={\left(d^T{R}_{L\times L}^{-\mathbf{1}}d\right)}^{-1}{\left(R_{L\times L}^{-\mathbf{1}}d\right)}^{T}r.$$

(3)

2.5. Subset CEM

Subset CEM, as proposed by [30], divides the original image into several subsets of rectangular images. The subsets are detected by CEM and the results of all subsets are combined to obtain a complete result image. In this case, each subset image has its own correlation matrix S. Figure 3 shows the correlation matrix in the image.

2.6. Sliding Window-Based CEM (SW CEM)

Regarding the different data features around each pixel, for more specific detection, sliding window-based CEM (SW CEM) [30] performs detection pixel by pixel, as based on the concept of subsets. The pixel by pixel method has a fixed window size that slides among the pixels to obtain different messages to determine correlation matrix Sn, which is to say, SW CEM is based on detecting pixels and uses a sliding window to obtain the peripheral information of the pixel in order to determine correlation matrix Sn.

In other words, correlation matrix Sn is calculated by a sliding window for each pixel in the image, and each correlation matrix Sn is independent. SW CEM can be defined as:

$$\mathrm{SW}\_\mathrm{CEM}=\frac{d^T{R}_{mn}^{-\mathbf{1}}{r}_{mn}}{d^T{R}_{mn}^{-\mathbf{1}}d}.$$

(4)

2.7. Adaptive Sliding Window-Based CEM (ASW CEM)

According to SW CEM, as mentioned in Section 2.6, the sliding window is proposed for more specific detection; as the spectral characteristics around each pixel are different, the adaptive sliding window CEM (ASW CEM) [30] is proposed according to this method. The window size is adjusted according to the nearby characteristics of each pixel, and as the CEM algorithm needs relatively more background information for background suppression, the window is scaled according to different circumstances.

2.8. Weighted Background Suppression (WBS)

The background suppression issue has been mentioned in the literature [22]. Some detectors, such as CEM, can be decomposed into a two-stage process. The first stage is to apply the inverse of correlation matrix R or covariance matrix K to perform background suppression, and the second stage uses a match filter for detection. In this case, from the image processing point of view, enhancing the contrast of the inverse of correlation matrix R or covariance matrix K can also increase the intensity for the matched filter. As shown by [22] in the experimental results of synthetic images, it has been proven that removing the target signatures in the inverse of correlation matrix R or covariance matrix K significantly suppresses the abundance of background fractions, as compared to the original inverse of correlation matrix R or covariance matrix K. However, real images have limited target information. In this case, it is not possible to remove all the target signatures in R or K. Therefore, this paper proposes weighted background suppression to improve the interference of the target of interest through background suppression.

The main concept of WBS is that different weights are used for each pixel when calculating the correlation matrix, which is called a weighted correlation matrix, and the new nonparametric correlation matrix is redefined for feature extraction. This method aims at data with a non-gaussian distribution; because the distribution of data points is not a Gaussian distribution, the average of each class cannot represent the center of the whole; thus, the correlation matrix of the overall data cannot be directly used for background suppression, as there are calculation errors in the background of target detection.

The $w_i$ is used in calculating a correlation matrix for weight adjustment, in which the principle is to use the distance to the target pixel for weight adjustment. The shorter the distance, the closer the target spectrum; as the correlation matrix can be multiplied by distance, it reduces the effect of the spectral signature, which is similar to the target of interest in the correlation matrix. The weighted correlation matrix is used in some target detection algorithms to increase the accuracy of the target detection algorithm. The $w_i$ computing modes in this paper are divided into the Euclidean distance (ED) Weighted and Spectral Information Divergence (SID) Weighted modes.

2.8.1. Euclidean distance (ED) Weighted Mode

The Euclidean distance weighted method, as proposed in this paper, is based on the Euclidean distance between the target of interest and the detection image; the shorter the Euclidean distance to the target of interest, the more similar the detection pixel is to the target of interest. These characteristics are used for weight adjustment; where ${\mathbf{w}}_{\mathbf{i}}$ represents the Euclidean distance between ${\mathbf{r}}_{\mathbf{i}}$ and d. The computing equation is expressed as follows:

$$w_i=\mathrm{ED}\left(r_i,d_i\right).$$

(5)

2.8.2. Spectral Information Divergence (SID)Weighted Mode

SID [32] is derived from the concept of information divergence in information theory and is a standard for measuring spectral similarity and calculating the difference between the spectral vector probability behaviors of two pixels. SID uses the distance between the spectral signature probability distributions, as calculated by the spectral signature vectors of two pixels.

In comparison to other common similarity calculations, SID proposes a different view that uses the relative entropy to explain the spectral information and spectral similarity provided by each pixel. This paper uses the relative entropy for the weight adjustment of WBS. SID is processed by extreme normalization to 0–1 and the abundance value is used for backward suppression.

The computing equation is expressed as follows:

$$w_i=1-\mathrm{SID}\left(r_i\left|\right|d_i\right).$$

(6)

2.8.3. Weighted Background Suppression Target Detection

The weights of Section 2.8.1 and Section 2.8.2 are put in the target detection algorithm, respectively, resulting in WBS-ACE, WBS-TCIMF, and WBS-CEM, which are expressed as follows.

WBS-ACE: The weights of each point and target pixel in the image are put in the correlation matrix of ACE and calculated; thus, the original ACE equation is changed to:

$$K^{*}=w_i\times K_i$$

(7)

$$\mathrm{WACE}\left(r,d\right)=\frac{r^T{K}^{*-\mathbf{1}}d{\left(d^T{K}^{*-\mathbf{1}}d\right)}^{-\mathbf{1}}{d}^T{K}^{*-\mathbf{1}}r}{r^T{K}^{*-\mathbf{1}}r}$$

(8)

where K* represents the weighted K matrix.

WBS-TCIMF: The concept of weight is admitted into the correlation matrix of the TCIMF equation and expressed as follows:

$$R^{*}=w_i\times R_i$$

(9)

$${\mathsf{\delta }}^{\mathrm{WBS}-\mathrm{TCIMF}}\left(\mathbf{r}\right)=r^{\mathbf{T}}{R}_{L\times L}^{*-1}\left(DU\right){\left[{\left(DU\right)}^T{R}_{L\times L}^{*-1}\left(DU\right)\right]}^{-1}\left[\begin{array}{l}{1}_{p\times 1}\\ 0_{q\times 1}\end{array}\right]$$

(10)

where R* represents the weighted correlation matrix.

WBS-CEM: The weight is substituted into the correlation matrix of CEM and expressed as:

$$\mathrm{R}*=\frac{1}{N}{{\displaystyle \sum }}_{i=1}^n{w}_i{r}_i{r}_i^T.$$

(11)

The WBS-CEM equation is:

$${\mathsf{\delta }}^{\mathrm{WBS}-\mathrm{CEM}}={\left(w^{\mathrm{WBS}-\mathrm{CEM}}\right)}^{T}r={\left(d^T{R}_{L\times L}^{*-1}d\right)}^{-1}{\left(R_{L\times L}^{*-1}d\right)}^{T}r.$$

(12)

2.9. Robust Principal Component Analysis (RPCA)

RPCA [34,35,36,37,38,39] is essentially identical to PCA, as they both look for the optimum projection in a low rank space. The problem in PCA is the handling of singularities. PCA is influenced by singularities, and in order to match the singularity, the calculated projection vector will be distorted. Therefore, RPCA uses “robust statistics” for data statistics, as based on the statistics of PCA. Robust statistics have two purposes; one is to recover the optimum condition fit for most data, while the second is to detect and reject abnormal values. Calculations can therefore be prevented from being influenced by the singularity, in order to find a better low rank space.

In the cognition of RPCA, general data matrix O $=\left(r_1,r_{2,}\dots r_i\right)$ contains a primary structure and noise. The data matrix can be decomposed into two matrices. One is low rank matrix $L=\left(L_1,L_{2,}\dots L_i\right)$, and contains the primary structure information of the original matrix P, in which the rows or columns are linearly correlated. The other is sparse matrix $S=\left(S_1,S_{2,}\dots S_i\right)$, which contains the noise of the original matrix O. The result of the overall equation conversion is:

$$\underset{L, S}{\min }{\left|\left|L\right|\right|}_{*}+\mathsf{\lambda }{\left|\left|S\right|\right|}_{\mathbf{1}},\mathrm{subject}\mathrm{to}\mathbf{O}=\mathbf{L}+\mathbf{S}$$

(13)

where, P is the original data, L is the low rank matrix, S is the sparse matrix, and Norm 1 is the sum of the absolute values of the elements in the vector. The low rank matrix obtains the solution closest to the principal component in the concept approximate to Norm 0, the most principal and similar structure is maintained, and the noise is separated from the sparse matrix. Previous studies have presented numerous methods for image preprocessing and enhancement. Sparse representation has been used in many fields as mentioned in the introduction part. In these studies, the detection images had low rank backgrounds and sparse images as foreground, and the two images were separated and enhanced by the processing of sparse representation for different applications.

2.10. Sparse Enhancement-Based Weighted Background Suppression (SE-WBS)

This paper proposes SE-WBS to increase the accuracy of target detection algorithms, in which an image is preprocessed by sparse enhancement to enhance NGL, highlight the difference between elements with different features, and observe whether or not preprocessing could increase the accuracy of the target detection. In Figure 4, the image is decomposed by RPCA into L as a low rank matrix and S as a sparse matrix. Sparse enhancement, as proposed in this paper, adds sparse matrix S to the original image O to enhance NGL, and because the sparsity of NGL is similar to the characteristic of a sparse matrix, image enhancement can be implemented by simple addition. The schematic diagram is shown below.

As CEM only selects one target of interest, the wrong signature of interest may be used due to manual selection and the target detection algorithm will be inaccurate; therefore, this paper used the optimal signature generation process (OSGP) [30] to optimize the desired signature. The OSGP implements subset CEM iteratively. When the results of CEM are obtained, the image threshold is obtained by using Otsu’s method. These pixels correspond to similar RGB values in the original image and are averaged as a new target d’. This is repeated until the last spectral angle mapper (SAM) are smaller than value θ, and then, the optimal target d’ is exported. Figure 5 is the flowchart of OSGP. Reference [30] has already proven that, by applying OSGP to target detection methods which require only one target signature, it provides stable results even if the initial desired target information is biased or not reliable.

Finally, the aforementioned weighted target detection algorithm was used to detect the target, improve the effect of the misrecognition of a target of interest by the target detection algorithm, and conduct performance analysis of the staged and general results of the overall research process. Figure 6 shows the sparse enhancement-weighted background suppression (SE-WBS) process proposed in this paper.

The detection target in this paper was sprouts, which are sparse in a forest. The characteristic identical to the sparse matrix characteristic of RPCA is the spike noise. The RPCA preprocessing method, as proposed in this paper, consists of an image decomposed into two images using the characteristic of RPCA; one image is the principal component image and the other is the sparse image. The separated sparse matrix is combined with the original image to enhance the sparse image on the original image. The sprouts, i.e., the sparse parts, are enhanced using this method. The hyperspectral algorithm is performed after this preprocessing mode.

RPCA has different optimal solution methods according to the characteristics of different robust statistics [46,47,48,49]; thus, the calculated results are different. Therefore, this paper used the online probabilistic approach to robust matrix (OPRMF) kernel [46] to find the kernel with characteristics coincident with the sprout characteristics, in order to increase the accuracy of sprout detection.

After the image was preprocessed by RPCA, the four target detection algorithms were performed and the desired target used by all detection algorithms was the desired target d’, which increased the detection accuracy iterated by OSGP. The ED and SID types of WBS were used in the four algorithms to adjust the weighted correlation matrix.

3. Results

3.1. Evaluation of Detection Results

Two methods for evaluating accuracy are used in this paper. The first one is the receiver operating characteristic curve (ROC) [50,51,52], which can calculate the effect of target detection. The second method is Cohen’s kappa [53], which is an evaluation method used in the field of biology to calculate model accuracy. The theories and concepts of the two methods are as follows.

3.1.1. ROC Curve

In recent years, the ROC curve has been used for evaluation in machine learning, data mining, and signal and image processing. It is used in signal and image processing to evaluate the detection effect. The main concept of ROC analysis is a binary classification model, which has two classes of output results, e.g., correct/incorrect, match/mismatch, and target/non-target, etc. For the classification effect, a threshold is given for evaluation, the data are divided into two classes by the threshold, and threshold (τ), P_D (True Positive Rate), and P_F (False Positive Rate) are drawn to obtain the ROC curve, as shown in Figure 7.

The P_D and P_F can be obtained by Equation (14) to determine optimum threshold (τ). The accuracy is then calculated by the correction decision/classification rate, as measured according to the sum of detection power P_D, corresponding to “true positive (TP)”, and (1–P_F), corresponding to “true negative (TN)”

$$\mathsf{\tau }=\mathrm{Arg}\left\{\mathrm{Max}\left({\mathrm{P}}_{\mathrm{D}}\left(\mathsf{\tau }\right)+\left(1-{\mathrm{P}}_{\mathrm{F}}\left(\mathsf{\tau }\right)\right)\right)\right\}.$$

(14)

TPR and FPR are used as the evaluation values of target detection accuracy, which can be calculated under the optimum threshold and are another basis of evaluation. The accuracy is defined as follows:

$$\mathrm{Accuracy}=\frac{TP+TN}{\mathbf{P}+\mathbf{N}}=\frac{TP+TN}{TP+TN+FT+FN}.$$

(15)

3.1.2. Cohen’s Kappa

Cohen’s kappa coefficient can measure the consistency between two classes. In image processing, the ROC curve is used to measure the effect of the detector. Cohen’s kappa is an algorithm that evaluates the results of binarization and calculates consistency. The error matrix identical to the ROC curve is used to calculate the kappa value, as shown in

Table 1. Error matrix of Cohen’s kappa.

Error Matrix		Ground Truth		Total
		Sprout (p)	Non-Sprout (n)
Detection	Sprout (p′)	True Positive ${\mathrm{P}}_a$	False Positive ${\mathrm{P}}_b$	${\mathrm{P}}_a+{\mathrm{P}}_b$
	Non-Sprout (n′)	False Negative ${\mathrm{P}}_c$	True Negative ${\mathrm{P}}_d$	${\mathrm{P}}_c+{\mathrm{P}}_d$
Total		${\mathrm{P}}_a+{\mathrm{P}}_c$	${\mathrm{P}}_b+{\mathrm{P}}_d$	Total Pixels $\mathrm{N}$

. where, ${\mathrm{P}}_a$ is the true value of the sprout and what is detected is the sprout; ${\mathrm{P}}_b$ is the true value of the sprout but what is detected is not the sprout; ${\mathrm{P}}_c$ is not the true value of the sprout, but what is detected is the sprout; and ${\mathrm{P}}_d$ is not the true value of the sprout and what detected is not the sprout. Cohen’s kappa can be defined as follows:

$${\mathrm{P}}_o=\frac{{\mathrm{P}}_a+{\mathrm{P}}_d}{{\mathrm{P}}_a+{\mathrm{P}}_b+{\mathrm{P}}_c+{\mathrm{P}}_d}=\frac{{\mathrm{P}}_a+{\mathrm{P}}_d}{N}$$

(16)

$${\mathrm{P}}_e={\mathrm{P}}_{Yes}+{\mathrm{P}}_{No}=\frac{{\mathrm{P}}_a+{\mathrm{P}}_b}{\mathrm{N}}.\frac{{\mathrm{P}}_a+{\mathrm{P}}_c}{\mathrm{N}}+\frac{{\mathrm{P}}_c+{\mathrm{P}}_d}{\mathrm{N}}.\frac{{\mathrm{P}}_b+{\mathrm{P}}_d}{\mathrm{N}}$$

(17)

$$\mathrm{K}=\frac{{\mathrm{P}}_o-{\mathrm{P}}_e}{1-{\mathrm{P}}_e}=1-\frac{1-{\mathrm{P}}_o}{1-{\mathrm{P}}_e}.$$

(18)

Coefficient K, as calculated by Cohen’s kappa, is −1~1; if the detection result is completely correct, the K value will be equal to 1; if K is equal to 0, the detection result will be all sprouts or all non-sprouts. If the K value is smaller than 0, the detected result will be worse than the stochastic prediction.

3.2. Sparse Enhancement-Based Weighted Background Suppression Target Detection Results

The RPCA kernel used in this section was the OPRMF kernel and RPCA is used to separate the original image (O) into a low rank image (L) and a sparse image (S), as shown in Figure 8. In addition, the RGB band in grey scale is shown in Figure 8. In terms of the preprocessing mode in this section, the L image and S image are separated by RPCA. The detected sprout characteristic falls in the characteristics of S; therefore, the preprocessing in this section uses a linear combination to put S back into the original image to enhance the target properties, known as sparse enhancement, which renders the target more visible. This experiment uses the WBS of ED and SID for weighted adjustments.

3.2.1. Global WBS Target Detection Results

The first purpose of this paper was to use weights to suppress the background and improve the accuracy of the original target detection. Therefore, this section tested a number of target detection algorithms for background suppression, as based on global R and global K, including ACE, WBS-ACE, SE-WBS-ACE, TCIMF, WBS-TCIMF, SE-WBS-TCIMF, CEM, WBS-CEM, and SE-WBS-CEM. Two kinds of w_i were compared in this study: The Euclidean distance-based weight and the SID based weight, and background suppression was changed using different weights. In order to calculate the efficiency of different algorithms, the ground truth, as mentioned in Section 3.1, as well as the experimental results in this section, were used for evaluation of the ROC curve. As mentioned in Section 3.1.1, the ROC curve can be used to evaluate the effect of an algorithm, and the performance of the algorithm can be known from the area under the receiver operating characteristic curve (AUC) of the ROC curve. In addition, two computing modes for WBS (ED and SID) were compared in the experiment. All the results were normalized into 0–255 by thresholding using (14), as shown in

Table 2. Detection results of global target detection methods.

Detection	AUC	PD	PF	ACC	Kappa	Threshold	Computing Time (s)
Traditional ACE	0.9417	0.8827	0.1099	0.8897	0.3389	15	5.82
WBS-ACE (SID)	0.9384	0.8727	0.1029	0.8962	0.3517	27	8.02
WBS-ACE (ED)	0.9375	0.8697	0.1113	0.8880	0.3313	8	6.59
SE-WBS-ACE (SID)	0.9499	0.8905	0.0722	0.9264	0.4484	86	8.28
SE-WBS-ACE (ED)	0.9658	0.9154	0.0887	0.9115	0.4058	171	6.68
Traditional TCIMF	0.95737	0.8903	0.1076	0.8924	0.3472	42	0.72
WBS-TCIMF (SID)	0.9450	0.8692	0.1136	0.8858	0.3261	34	2.40
WBS-TCIMF (ED)	0.9583	0.8906	0.1082	0.8917	0.3458	88	0.83
SE-WBSTCIMF (SID)	0.9708	0.9055	0.0803	0.9192	0.4275	127	2.37
SE-WBS-TCIMF (ED)	0.9691	0.8963	0.0749	0.9241	0.4417	145	0.82
Traditional CEM	0.9606	0.8915	0.1022	0.8976	0.3604	136	0.04
WBS-CEM (SID)	0.9595	0.8897	0.1032	0.8965	0.3574	134	2.11
WBS-CEM (ED)	0.9613	0.8882	0.1006	0.8990	0.3632	133	0.55
SE-WBS-CEM (SID)	0.9703	0.9057	0.0816	0.9179	0.4235	112	2.13
SE-WBS-CEM (ED)	0.9713	0.9029	0.0738	0.9254	0.4483	112	0.57
Sparse WCEM [33]	0.9710	0.9067	0.0800	0.9194	0.4288	133	9.48

. Figure 9 and Figure 10 show the comparison of AUC and Kappa.

Figure 11, Figure 12 and Figure 13 show the resulting images of ACE, TCIMF, and CEM with WBS and SE-WBS (the red points represent correctly hit targets, the blue points represent false alarms, and the yellow points represent missed targets). According to the preliminary experiment, the accuracy of almost all the algorithms with SE-WBS was increased, the improvement effect on SE-WBS-ACE was relatively significant, and the SE-WBS-CEM had higher AUC and kappa, which were quite close to the results of sparse weighted CEM [33]. Therefore, the proposed sparsity enhancement concept could be used in all global target detection algorithms with improved results, as compared with the case without sparsity enhancement. According to the experimental results shown in Table 2, among the different global target detection algorithms, the accuracy rates of the WBS of SID and the WBS of ED were increased. According to the comparison between the two methods, for ACE, the WBS of ED had an especially good AUC effect, while SID had a higher kappa effect. Regarding TCIMF and CEM, the SID and ED were almost the same.

3.2.2. Local WBS Target Detection Results

This paper proposes the innovative algorithms of WBS and SE-WBS, as based on the local CEM algorithm proposed by [30]. The concept of WBS was added to various algorithms to observe whether or not the background suppression was better, and the original image was further enhanced by sparse enhancement, in order to obtain better detection results. In the following experiments, the subset CEM image size is set as 200 × 260 and the default window size of SW CEM and ASW CEM is 151 × 151, which are the same as [30]. Sparse weighted CEM, as proposed by [33], and the results of WBS and SE-WBS, as proposed in this paper, were used for comparison and data analysis, in order to determine how much efficiency could be increased by WBS and SE-WBS. The data of various algorithms are shown in

Table 3. Detection results of local target detection methods.

Detection	AUC	PD	PF	ACC	Kappa	Threshold	Computing Time (s)
Subset CEM	0.9685	0.9099	0.0874	0.9125	0.4074	129	0.06
Subset WBS-CEM (SID)	0.9718	0.9152	0.0798	0.9201	0.4333	89	2.10
Subset WBS-CEM (ED)	0.9725	0.9177	0.0827	0.9173	0.4248	119	0.58
Subset SE-WBS-CEM (SID)	0.9741	0.9157	0.0700	0.9294	0.4671	146	2.11
Subset SE-WBS-CEM (ED)	0.9749	0.9159	0.0681	0.9313	0.4744	145	0.59
SW CEM	0.9694	0.9151	0.0811	0.9188	0.4289	99	339.25
SW WBS-CEM (SID)	0.9735	0.9192	0.0727	0.9270	0.4591	98	614.72
SW WBS-CEM (ED)	0.9749	0.9204	0.0729	0.9269	0.4588	82	598.23
SW SE-WBS-CEM (SID)	0.9749	0.9245	0.0705	0.9293	0.4693	172	568.1
SW SE-WBS-CEM (ED)	0.9766	0.9241	0.0681	0.9316	0.4778	142	563.7
ASW CEM	0.9704	0.9257	0.0753	0.9248	0.4526	99	411.24
ASW WBS-CEM (SID)	0.9747	0.9251	0.0658	0.9338	0.4872	98	500.68
ASW WBS-CEM (ED)	0.9781	0.9325	0.0673	0.9327	0.4847	82	506.79
ASW SE-WBS-CEM (SID)	0.9757	0.9278	0.0600	0.9395	0.5121	172	502.94
ASW SE-WBS-CEM (ED)	0.9796	0.9324	0.0616	0.9382	0.5076	142	503.21
Sparse WCEM [33]	0.9710	0.9067	0.0801	0.9194	0.4286	133	9.48

. Figure 14 and Figure 15 show the comparison of AUC and kappa.

The main algorithms of subsets CEM, SW CEM, and ASW CEM were weighted (WBS) and compared with the SE-WBS mentioned in this paper, and the data are shown in the above tables. The calculated data of SE-WBS-CEM, as proposed in this paper, had universally better Area Under Curve (AUC) and kappa values than [33] and were highly improved, as compared with the original method without SE-WBS. Figure 16, Figure 17 and Figure 18 show subsets CEM, SW CEM, and ASW CEM. Figure 18h shows the resulting image of sparse Weighted CEM [33]. Figure 16, Figure 17 and Figure 18 show that the local CEM with the concept of the WBS of ED had higher accuracy (the red points represent correctly hit targets, the blue points represent false alarms, and the yellow points represent missed targets).

3.3. Computing Time

This study calculated the computing time in seconds using MATLAB. The computer environment used for the experiments was a 64-bit Windows operating system with an Intel i7-4710, a 2.5 Ghz CPU, and 16 GB of memory (RAM). Regarding global target detection, as shown in Table 2, the times for the traditional ACE, TCIMF, and CEM had the shortest time. However, the proposed SE-WBS-ACE (ED), SE-WBS-TCIMF(ED), and SE-WBS-CEM(ED) also required less than one second and were very close to the traditional times; in addition, they were much faster than [33] and provide better performance. Regarding local target detection, as shown in Table 3, since SW CEM must recalculate the inverse of the correlation matrix with the fixed window, it required the longest time. As AWS CEM can adjust the window size, the required computing time is the second longest. However, the proposed subset SE-WBS-CEM (ED) provides reasonable improvement with no computing time penalty. Moreover, it can be applied in real-time causal processing [54], as time is an issue in some applications. On the contrary, if time is not the main consideration, while ASW SE-WBS-CEM (ED) can provide the best detection performance, it does have a time penalty.

4. Discussion

The two important functions of a target detection algorithm are suppressing the background and enhancing the target object, in order for the contrast between the target object and background to be enhanced. This paper used the concept of WBS and emphasized the importance of background suppression. References [22,26,30] mentioned using R⁻¹ or K⁻¹ to suppress the background to contain more pixels of the "non-target object" in the calculation of R⁻¹ or K⁻¹, which better suppresses the background. On the contrary, if R⁻¹ or K⁻¹ contains the desired target object, the target object will be suppressed at the same time and the detection result will be degraded. Therefore, this paper used the concept of WBS to reduce the effect of similar target objects on R⁻¹ or K⁻¹ in order to reduce the P^F, i.e., the misrecognition rate. This point is shown in Table 2 and Table 3, especially the subsets CEM, SW CEM, and ASW CEM of the local CEM, where P^F was highly reduced after WBS was applied. The results indicate that ED performed slightly better than SID in WBS, which may be because only RGB bands were used in this experimental image, while SID could have better performance in a hyperspectral image.

Another contribution of this paper is that the NGL was enhanced by using the characteristic of the sparse matrix. As the number of nonzero elements of a sparse matrix is much smaller than the number of zero elements and the distribution of these nonzero elements is irregular, this characteristic is similar to the signal of NGL in the image. Therefore, the enhancement method of superposing the sparse matrix on the original image was proposed, and the signal of NGL could be enhanced by a simple addition principle, in order to increase the detection rate. This method is simpler and better than the method of substituting the weight of sparsity in the equation of CEM, as proposed in [33]. As shown in Figure 11, Figure 12 and Figure 13 and Figure 16, Figure 17 and Figure 18, the proposed SE-WBS-CEM has outstanding performance in various data. The SE-WBS technique not only enhances the NGL, it also enhances background suppression, which reduces false alarms. As shown in Figure 18a–f, many false alarms were removed by ASW SE-WBS-CEM in the upper left region, while the sparse WCEM [33] generated many false alarms (marked blue in the upper left and lower right regions). As sparse WCEM only enhances NGL but does not suppress the background, there will be misrecognitions. The new method of SE-WBS, as proposed in this paper, uses WBS to suppress the background. On the other hand, the signal of NGL can be enhanced by SE; in other words, WBS could reduce false alarms, while SE could increase detection power, and this combination has good effect. Taking a general view, SE-WBS has good effect on ACE, TCIMF, CEM, subsets CEM, SW CEM, and ASW-CEM, and the experimental results prove that this method is practical.

It is also worthy of note that only one image scene is used in this study; thus, collecting more data images in the same area every year will definitely occur in future work. However, the best that can currently be done for target detection is to generate the desired target information before collecting more data. Unlike [55,56], which used lab data with in-scene calibration to improve target detection in hyperspectral images, this study only has RBG bands images, which have very limited spectral information. In this case, OSGP, as proposed in [30], was applied in this study to generate the optimal desired targets, which can provide stable and consistent results. Figure 19 compares global and local versions of CEM algorithms with/without using OSGP; the ones with OSGP all have some reasonable improvement, as compared to those without OSGP.

Another point worthy of note is that target detection can be divided into two types. One is passive target detection, which is generally used in surveillance applications where there are no particular targets. Anomaly detection is the best example for this type, as it looks for unexpected targets that cannot be known by prior knowledge [22]. Passive target detection also can be found in some literature using global and local versions of anomaly detection [31,57]. The other type is active target detection, which requires some prior knowledge about the targets of interest. This type of detection can be found in reconnaissance applications. This study sought specified targets of interest, namely, NGL, and in this case, the application of active target detection algorithms was more appropriate. Moreover, [5] proved that using anomaly detection algorithms in NGL detection causes serious false alarm problems, and the results are not acceptable. Therefore, based on the above reasons, this study did not apply anomaly detection methods for NGL detection. The adaptive sliding window (ASW) approach in [30] uses similar local and global concepts in CEM, which apply different window sizes to detect small targets to provide better NGL detection. This paper further proposed weighted background suppression and sparse enhancement techniques to reduce false alarms and enhance target signals.

In contrast to the proposed sparse enhancement based weighted background suppression (SE-WBS) technique, the dual-window method recently published in [58] has demonstrated to be able to capture different levels of local spectral information and characterize anomaly targets. The ability of the dual-window and some other multiple-window approaches [30,59,60] in minimizing background contamination and improving the efficiency of target detection would be an interesting topic. A detail comparison of the methods will be explored and presented in the short future.

5. Conclusions

In target detection algorithms, some studies have indicated the importance of background suppression. This paper proposed weighted background suppression to improve the interference of the target of interest with background suppression. The main concept of WBS is to use different weights for each pixel when calculating R and K. The new nonparametric R and K matrix was redefined for background suppression. Moreover, SD and ED weighted methods were proposed in this paper. According to validation by different algorithms, this method could be extended into other related target detection algorithms to increase accuracy and detection performance.

Another important contribution of this paper is the development of a new image enhancement method for enhancing target information, which includes a new algorithm for NGL. As the characteristic of a sparse matrix is similar to NGL, this paper used simple addition to enhance the NGL signal. Finally, according to overall analysis, through the staged evolution from how to better adjust WBS to how to use SE, SE-WBS was found to considerably enhance various algorithms. The experimental results show the advantages of SE-WBS over other related algorithms. The detection effect of the original algorithms was greatly improved, proving this process has good effect on NGL. The ASW SE-WBS-CEM had the best performance, and the experimental results prove the importance and usage value of the SE-WBS technique proposed in this paper.

The future work of this study is to keep collecting more UAV images around the same areas in different seasons every year, as such quantitative results will play a crucial role in the accumulation of forest biomass/carbon storage, healthier forests, climate change, and environmental monitoring. However, the limitation of the UAV images is that only RGB bands were used, which is the major challenge of detecting NGL in very limited spectral information using target detection methods. The use of a hyperspectral UAV to collect data in the future will allow better results to be obtained.