# Dual-Dense Convolution Network for Change Detection of High-Resolution Panchromatic Imagery
## 3 Change Detection with the Proposed Dual-Dense Convolutional Neural Network
### Dual-Dense Convolutional Neural Network for Change Detection  
In order to achieve accurate change detection without a perfect registration, this paper proposes a dual-dense convolutional network (dual-DCN) with two deep convolutional networks, as shown in Figure 4. This proposed network identifies the change areas by measuring the dissimilarity distance of two inputs at the last stage for use of all the information of the two input images. Two branch networks, \(N^{1}\) and \(N^{2}\), handle two input images acquired at different time instances, respectively. The proposed network is based on CNN, thus, it can robustly conduct a pixel-wise change detection by inspecting the neighboring pixels. A pair of images is cropped into two patches (\(40\times 40\)) by sliding in the raster scan order and two cropped patches (\(I^{1}\) and \(I^{2}\)) are fed into the proposed network. The center pixel of the cropped patch is identified as changed or unchanged with the presence of a single dissimilar value between the cropped two patches. The Siamese network proposed by Reference [24] extracts features from an image pair. The pair of the convolutional networks is used to capture similarity characteristics by sharing the weights of the two network paths. However, the shared weights of Siamese network reduce the parameters optimized during training for fast convergence. However, it is known to be frequently overfitted. Thus, the proposed network does not employ the shared weights to provide more flexible optimization than a restricted Siamese network. The parameters of each network branch of the proposed algorithm can be independently optimized in order to avoid early overfitted convergence. In addition, the proposed network employs dense connection [27] in the convolutional layers by reusing all the preceding feature-maps, in order to enhance representation capability of the feature-maps, as shown in Figure 4. The preceding feature maps are directly connected to all of the subsequent layers. The traditional CNN connects the output of the (\(l-1\))th layer as input to the \(l\)th [28]. In the proposed dual-DCN model, the \(l\)th layer receives all of the preceding feature-maps. The feature map of the \(l\)th layer at the \(r\)th dense block and the \(i\)th network can be computed by  
\[F^{i}_{l,d_{r}}=H^{i}_{l-1,d_{r}}\Big{(}\left[F^{i}_{0,d_{r}}F^{i}_{1,d_{r}}, \ldots,F^{i}_{l-1,d_{r}}\right]\Big{)},r=0,1;i=1,2 \tag{1}\]  
where \(\left[F^{i}_{0,d_{r}},F^{i}_{1,d_{r}},\ldots,F^{i}_{l-1,d_{r}}\right]\) indicates concatenation of the feature-maps of all of the previous layers, layer 0,..., layer (\(l-1\)). Each dense block is a group of convolution layers with the dense connectivity to avoid variant sizes of the feature maps. \(H(\cdot)\) plays a role in batch normalization (BN) [29], \(3\times 3\) convolution, and ReLU. The BN is used to normalize parameters change of the preceding layers. The ReLU is used by thresholding at zero following \(3\times 3\) convolution. The convergence of the stochastic gradient descent algorithm can be accelerated. \(G\) including \(3\times 3\) convolution followed by ReLU is employed before a dense block in order to generate the feature-map \(F_{0}\). In the proposed architecture, each dense block contains three \(H(\cdot)\), including 64 feature maps of each layer. After a dense block is performed, a down-sampling operation is applied to produce variety scales with \(2\times 2\) maximum pooling. Furthermore, the feature maps at the last convolutional layer are vectorized and fed into the fully-connected layer consisting of 64 neurons and 0.5 drop-out. The probability output, \(O^{i}\), at the last stage is computed by the sigmoid function. Furthermore, Euclidean distance (\(D\)) is employed in order to measure the dissimilarity between \(I^{1}\) and \(I^{2}\) computed by  
\[D=O^{1}-O^{2}_{2}\]  
Figure 4: The proposed dual-DCN architecture for change detection.