# Deep Fusion Feature Based Object Detection Method for High Resolution Optical Remote Sensing Images
## 4 Size-Scalable Candidate Region Proposal Algorithm
### pBING Algorithm with Multiple Weak Feature Scoring  
In practice, we found that the ambiguous objects were missed by the original BING algorithm. The possible reason for this phenomenon is that only a simple NG feature is used in the algorithm, and in order to speed up the calculation, the NG feature serves as the BING feature. Thus, some information would be lost in the process, which further reduces the distinguishing degree of the feature. However, in order to preserve the time and space complexity advantages of the BING algorithm, we are not able to use too complex features such as SIFT and HOG features due to the parallel optimization strategy of the algorithm. Thanks to the AdaBoost algorithm [28] that inspired us: integrating multiple weak classifiers is used to obtain a strong classifier. Therefore, we improved the BING algorithm by integrating multiple weak feature scoring models. We improved the first stage of the candidate window scoring model, and the second stage of score correction was same as the original algorithm. For convenience, we name the improved BING algorithm as the pBING algorithm. Figure 2 shows the flowchart of the pBING algorithm, and the shaded part is our improvement. For each training sample, we extract multiple weak feature channels and train a scoring model for each weak feature channel; in the detection process, we integrate the score of multiple weak feature scoring models as the final score of the candidate window, in which a simple linear weighting method is adopted, and the weights are determined by the accuracy of each model. Each scoring model still uses an efficient linear SVM algorithm. The score of each candidate window in each scoring model is: \(s_{kl}=\langle w_{k},g_{kl}\rangle\), where \(s_{kl}\) denotes the score of model \(k\) for window \(l\), \(w_{k}\) denotes the parameter of model \(k\), and \(g_{kl}\) denotes the feature \(k\) of window \(l\). The final window score for the first stage is as follows:  
The NG feature map used in the BING algorithm captures the edge intensity information of the original image by computing the gradient magnitude of each pixel, but this feature is simple and susceptible to noise. In this paper, the NG feature map is replaced by the Sobel feature map with better edge information capture. At the same time, the local binary pattern (LBP) feature map and the difference of Gaussians (DoG) feature map are introduced. The Sobel feature map uses 3 \(\times\) 3 Sobel operators to convolute the original image to obtain the horizontal and vertical direction of the approximate gradient, as shown in Formula (8). Then, it computes the gradient amplitude through Formula (9). \[ \begin{split} G_{x}=\begin{bmatrix}-1&0&+1\\ -2&0&+2\\ -1&0&+1\end{bmatrix}\ \otimes A\\ G_{y}=\begin{bmatrix}+1&+2&+1\\ 0&0&0\\ -1&-2&-1\end{bmatrix}\ \otimes A\\ G=\sqrt{G_{x}^{2}+G_{y}^{2}}\end{split}  \tag{8}\]  
where \(A\) represents the original image matrix, \(G_{x}\) and \(G_{y}\) represent the horizontal and vertical gradient of the image, respectively, and \(G\) represents the gradient magnitude matrix, which is the obtained feature map. \(\otimes\) represents the convolution operation. LBP can be used to describe the local texture features, often used for face classification, pedestrian detection [29], and so on. We can get the LBP feature map by computing the LBP code for each pixel point. In order to simplify the calculation, we use the simplest 3 \(\times\) 3 LBP operator to calculate in the gray image. The DoG feature map is obtained by subtracting two different degrees of blurred images from the original image. The blurred image is obtained by the Gaussian kernel convolution of different standard deviation parameters on the gray image. Two Gaussian blurred image subtractions can increase the  
Figure 2: pBING algorithm flowchart. visibility of edges and other details, and the DoG algorithm does not enhance noise because Gaussian blur suppresses high-frequency noise.