# Image Copy-Move Forgery Detection Based on Fused Features and Density Clustering
## 4 The Proposed Scheme
### Removing Mismatched Pairs  
Matching point pairs were obtained in the previous step, but many of them contain errors. At this point, an effective method is needed to eliminate the mismatched pairs in order to improve the accuracy of forgery detection and localization. Currently, the k-means clustering algorithm or the hierarchical clustering algorithm are commonly used to eliminate mismatches, but the problem is that they only consider the positional information of the matching point pairs and ignore the constraints between the point pairs. The number  
Figure 2: Flowchart of method proposed in this paper.  
of clusters needs to be set before clustering. [PERSON] et al. [36] proposed a density-based clustering algorithm, DBSCAN, which considers clusters as sets of maximum density-connected points and partitions the dense areas accordingly. DBSCAN does not require the extraction or setting of clustering parameters and can handle clusters of any shape even in the presence of noise. Therefore, in this paper, DBSCAN is used for feature clustering to eliminate mismatched pairs.  
DBSCAN requires setting two important parameters, Eps and MinPts, respectively denoting the radius of density and the threshold of core points, which is the minimum number of points required to form a cluster. In this paper, Eps and MinPts are represented as \(\tau\) and \(M\), respectively. In DBSCAN, point sets are defined based on the following three categories, as shown in Figure 3:  
1. Core point: If point \(X_{i}\) has at least \(M\) points in its neighborhood, then \(X_{i}\) is a core point. We can define the sets of all core points as \(P_{c}\) and the set of non-core points as \(P_{nc}\).
2. Boundary point: If \(X_{i}\) satisfies \(X_{i}\in P_{nc}\) and is in the \(\tau\) neighborhood of a core point, then \(X_{i}\) is a boundary point. Boundary points can be located within the \(\tau\) neighborhood of one or more core points at the same time.
3. Outlier: This is neither a core point nor a boundary point.  
The relationships between points are classified into three types: density direct, density reachable, and density connected, as shown in Figure 3. The main process of the DBSCAN algorithm is to classify the input points into different categories, iteratively search for density-reachable objects of core points, form a new cluster, and then produce the final clustering result through density connectivity. Figure 3 illustrates the relationships between points, where density reachable is a transitive relationship but not symmetric. Two boundary points in the same cluster may not be density reachable to each other because the core point condition may not be satisfied for both of them. However, there must be at least one core point within a cluster from which all points are density reachable. In Figure 3c, both boundary points are density reachable. Therefore, we introduce the concept of density connectedness, which encompasses this relationship between boundary points. The steps to transition from density  
The goal of DBSCAN is transformed into generating clustering identification array \(m_{i}\), where \(i=1,2,\ldots,n\) and \(k\) is the number of all non-negative values in the \(\left\{m_{i}\right\}_{i=1}^{n}\) types (negative values represent outliers). The outliers in clustering identification array \(m_{i}\) are mismatched points. Finally, removing outliers produces an accurate matching sequence.