A Reliability-Based Multi-Algorithm Fusion Technique in Detecting Changes in Land Cover

2.1. Definitions of Reliability and Evaluation Indicators

Reliability is defined as the probability that an item can perform its intended function for a specified interval under given conditions [26,27]. In a similar manner, change-detection reliability can be defined as the probability of an algorithm or method to detect changes from specified satellite images under given conditions. Thus, this work proposes measuring the reliability of a change-detection algorithm using the following quantized indicators to evaluate the reliability of a change-detection algorithm:

• Integrality (R) refers to the probability of an algorithm or method to correctly detect changes from specified satellite imagery data under the given conditions. Let N_{correctly_dc} be the number of changed pixels correctly detected by the algorithm and N_{actual_c} be the number of actual changed pixels in the specified images, we then obtain:

  $$R=\raisebox{1ex}{$N_{\mathit{correctly}\_\mathit{dc}}$}\!\left/ \!\raisebox{-1ex}{$N_{\mathit{actual}\_c}$}\right..$$

  (1)
  In practice, N_{correctly_dc} ≤ N_{actual_c} is always satisfied; thus, the value of R must be in [0, 1].

• Correctness (O) refers to the probability of correctly detecting changed pixels in all detected changed pixels. Let N_{detected_change_pixel} be the number of detected change pixels by the algorithm, then, the correctness of a change-detection algorithm is defined as:

  $$O=\raisebox{1ex}{$N_{\mathit{correctly}\_\mathit{dc}}$}\!\left/ \!\raisebox{-1ex}{$N_{\text{det}\mathit{ected}\_\mathit{change}\_\mathit{pixel}}$}\right.$$

  (2)

• Error detection rate (E) refers to the probability of incorrectly detecting changed pixels by an algorithm in the overall pixels of an image. Let N_{incorrectly_dc} be the number of incorrectly detected pixels, then, the error detection rate is defined as:

  $$E=\raisebox{1ex}{$N_{\mathit{incorrectly}\_\mathit{dc}}$}\!\left/ \!\raisebox{-1ex}{$N_{\mathit{overall}\_p}$}\right.$$

  (3)

• Consistency ( C ) refers to the ability of an algorithm to maintain its performance in detecting changes when applied to different areas under the given conditions. Let r₁ ={R, O, E} and r₂ ={R, O, E} represent the vector consisting of reliability indicators obtained at two different sample areas, regardless of whether the land cover classes are the same or different. Then, the consistency of a change-detection algorithm is defined as:

  $$C=1-d({\mathbf{r}}_1,{\mathbf{r}}_2)$$

  (4)
  where d(r₁, r₂) is the Euclidean distance between vectors r₁ and r₂.

Evidently, the values of R, O, E and C are within the range of [0, 1]. Larger R, O and C values lead to a higher reliability of the algorithm. By contrast, smaller E values lead to a higher reliability of the algorithm.

2.2. Proposed Reliability-Based Fuzzy Comprehensive Change-Detection Technique

Unlike traditional individual change-detection methods, the purpose of the proposed fusion method is to solve problems, such as threshold selection, accuracy and reliability of change-detection results and to generate a robust change-detection algorithm that suits different image data sources, study areas and research purposes. These goals are challenging problems faced by most individual change-detection algorithms. Furthermore, uncertainties widely exist in the entire change-detection procedure, such as difference in geometry, radiometry and resolution between two-date images, as well as the performance of the change-detection method. These uncertainties make fuzziness a common issue or basic characteristic in change-detection. In other words, using a certain threshold to decide whether a pixel is changed or unchanged based on a change-detection algorithm result is difficult. However, we can conclude the possibility of change. Therefore, overcoming these limitations in most individual change-detection algorithms requires introducing a fuzzy comprehensive evaluation combined with a reliability-based weight to solve the fuzziness issue in change decision. The following procedure shows the specific steps of the proposed change-detection method.

• Evaluation indicator (EI). Consider a pixel, I_i, in t₁ image, in the fuzzy comprehensive evaluation technique to evaluate whether the considered pixel is changed or unchanged. Several indicators should be set. Taking into account the purpose of this study, results computed using selected individual candidate change-detection algorithms are considered to evaluate whether a pixel is changed. Suppose that x = [x_i]_{1 ×n} represents selected individual candidate algorithms used to compare the given pixel I_i, with its corresponding pixel in the t₂ image to decide if change has occurred, then, the evaluation indicator set is defined as:

  $$\mathbf{U}={[u_{x_1},u_{x_2},\cdots ,u_{x_n}]}^T.$$

  (5)

• Evaluation grade (EG). The ultimate objective of the case is to determine if object, x, has changed; thus, changed, half-changed, unchanged, and so on, may be considered as assessment grades to create an evaluation grade, which is set as follows:

  $$\mathbf{G}={[g_1,g_2,\cdots ,g_J]}^T,$$

  (6)
  where g_J represents the change grade.

• One-way evaluation matrix. Let a_i,j be the possibility of a change that occurred over a pixel, which is computed by comparing x with its corresponding pixel in the t₂ image using the individual candidate change-detection algorithm, i; thus, the one-way evaluation matrix A of this case is given by:

  $${\mathbf{A}}_{n\times J}={\left[\begin{array}{cccc}{a}_{1,1},& a_{1,2},& \cdots ,& a_{1,J}\\ a_{2,1},& a_{2,2},& \cdots ,& a_{2,J}\\ \cdots & ,& \cdots & \\ a_{n,1},& a_{n,2},& \cdots ,& a_{n,J}\end{array}\right]}_{n\times J}$$

  (7)

• Reliability-based fuzzy comprehensive evaluation. The purpose of the proposed change-detection approach is to improve the reliability and accuracy of the obtained change map. For this purpose, this study proposes a reliability-weighted fuzzy comprehensive evaluation approach to use the advantages of different individual candidate change-detection algorithms employed in comparing two-date images. Let w = [w_i]_{1 ×n} be the weight of selected individual candidate algorithms determined by the aforementioned reliability factors through a fuzzy transformation between w and one-way evaluation matrix A, we obtain a fuzzy evaluation set, s, as:

  $$\mathbf{s}=\mathbf{w}\circ \mathbf{A}=[w_1,w_2,\cdots ,w_n]\circ \left[\begin{array}{cccc}{a}_{1,1},& a_{1,2},& \cdots ,& a_{1,J}\\ a_{2,1},& a_{2,2},& \cdots ,& a_{2,J}\\ \cdots & ,& \cdots & \\ a_{n,1},& a_{n,2},& \cdots ,& a_{n,J}\end{array}\right]={[s_1,s_2,\cdots ,s_J]}_{1\times J}$$

  (8)
  where s_J represents the membership grade. We can then conclude that a change occurred over a pixel according to the principle of maximum membership.

2.3. Accuracy Assessment Methods

Selecting a proper method to assess the accuracy of results obtained by different methods is a key procedure of change-detection. Almutairi [28] stated that the results of the accuracy analysis can be summarized by an overall accuracy percentage and a kappa statistic. In this study, the overall accuracy and kappa coefficient [29,30] were introduced to the study. Here, overall accuracy is defined to be the percentage of pixels correctly detected. Let p_a be the proportion of agreement, p_e be the chance agreement, and the kappa coefficient is defined as the proportion of agreement among raters after chance agreement has been removed [30], which can be expressed as:

3.1. Area and Data

The following sections quantitatively analyze a specific application of the proposed multi-algorithm integrated approach and its potential effects on land cover change-detection. In this study, two ortho-rectified 2.5 m SPOT 5 spatial resolution satellite images were obtained in order to generate a land cover map of WuQin district in Tianjin, China for the years 2009 (t₁ image, Figure 2(a)) and 2010 (t₂ image, Figure 2(b)). Reference data is always a problem for accuracy assessment of land cover change-detection; inaccurate reference data will lead to improper assessment result. To assess the accuracy of different methods in land cover change-detection, we prepared a man-made change map (Figure 3) as reference data for the accuracy assessment. Since change of land cover is the main focus of this study, so, in the manual interpretation, areas where land cover classes are different in two-date images have been labeled as change areas (e.g., Figure 4).

3.2. Case of Individual Algorithms

In this study, we selected two typical change-detection algorithms to participate in testing the validity of the proposed reliability-based multi-algorithm fusion technique. The following descriptions introduce these two algorithms and the obtained change maps after using them.

CVA is a typical algorithm in algebra-based change-detection method. It is a multivariate change-detection technique that processes the full dimension (spectral + temporal) of the image data and produces two outputs: change magnitude and change direction [31]. The central idea of CVA, which was given by Malila (1980), states that given multi-date pairs of spectral measurements, one computes spectral change vectors and compares their magnitudes to a specified threshold criterion. The decision that a change has occurred is made when that threshold is exceeded [3].The major advantage of the CVA algorithm is its capability to analyze change concurrently in all data layers as opposed to selected bands [31]. In this case, we first generated change vector map using RGB (red, green, blue) features of corresponding pixels in the t₁ and t₂ image. Then, pixels with a magnitude of change vector exceeding the given threshold (here, it is 1.2-times the average of all change vectors) would be determined as change pixels. Here, we considered the average of the 1.2-times repetition of the change magnitude as the threshold. After applying the standardized CVA algorithm presented in [1] to the two-date imagery shown in Figure 2(a,b), we obtained the change map shown in Figure 5(a).

PCA-based change-detection, which captures maximum variances in a finite number of orthogonal components based on an eigenvector analysis of the data correlation matrix has been used in change-detection for many years and has become one of the most popular techniques, because of its simplicity and capability in enhancing information on change [32]. A standardized PCA of regional-to-continental scale time series using wide-angle sensors proved to be a powerful technique in separating changes taking place at different time frequencies [31]. Thus, the authors recommended the PCA approach as a candidate algorithm, because it identifies change in a more consistent and interpretable manner. The central idea of the principal components is usually calculated using a variance-covariance matrix. The standardization of the covariance matrix into a correlation matrix achieved by division with the appropriate standard deviation reduces all variables to equal importance as measured by scale. As a result, the dimensionality of a data set consisting of a large number of interrelated variables is also reduced, while retaining as much as possible of the variation present in the data set [32,33]. In this case, the PCA transformation algorithm was initially implemented on two-date images to obtain transformed images using ENVI software. Subsequently, the image difference was implemented between the two-date transformed images to obtain the change map shown in Figure 5(b). In the change map generation, we considered 1.2-times the average difference in whole images as the threshold in transformed image difference.

3.3. Reliability-Based Multi-Algorithm Fusion

The fusion of multiple change-detection algorithms to generate a highly reliable and accurate method for detecting changes is the central idea of the proposed approach. The reliability of each individual algorithm is the basis of the fusion. Thus, the proposed approach must first assess the reliability of each candidate algorithm. The next step is to combine the selected candidate algorithms based on reliability to generate a new, more reliable change-detection approach.