# Feature Point Matching Method Based on Consistent Edge Structures for Infrared and Visible Images
## 2 Proposed Methods
### Feature Description Establishment  
The proposed feature description method leverages the edge length weighted edge orientation histogram to establish feature descriptions based on the global structure of images. Because edges of the global structure are similar in infrared and visible images, feature descriptions need to depict the edge information in the local neighborhood of feature points. The edge length weighted edge orientation histogram can depict the statistics of edges in the local neighborhood of feature points. The steps of establishing feature descriptions based on edge structures include feature point neighborhood partition, edge orientation substogram establishment, and histogram normalization. (1) The local neighborhood of feature points is divided into multiple sub-regions to describe the spatial distribution of edges in the neighborhoods. The size of the neighborhood is \(80\times 80\)[27]. Two-layer concentric circles are used to partition the neighborhood as HOG (Histogram of Oriented Gridients) [42]. The outer circle has a radius of r and the inner circle has a radius of r/2 where r is 40. Each circle is equally divided by \(\pi\)/9 radians into 18 sectors. Each of the two adjacent sectors of the same circle are expanded so that their overlap is \(\pi\)/36. In the case that only edge information is available, which is not as rich as gray and gradients, the neighborhood partition that contains overlapping areas can improve the description ability for feature points [43]. (2) The edge orientation is used to describe the edge information in the neighborhood. During the calculation of the edge orientation, the inconsistent short edges formed by local details are ignored and the consistent long edges formed by global structures are considered. The calculation of the edge orientation is performed by \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), \(135^{\circ}\), and non-directional (n.o.) Sobel filters, which are shown in Figure 3[28]. The edge orientation is calculated for each point \(p\) of consistent edges in the neighborhood. The edge orientation of the point \(p\) is the orientation of the Sobel filter corresponding to the maximum response value. Let symbols \(f_{i}\), \(i=1\), \(2\), \(3\), \(4\), \(5\) denote \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), \(135^{\circ}\), and n.o. Sobel filters. The orientation \(b\) of the point \(p\) can be formulated by the equation below. \[b(p)=\left\{ \begin{array}{ll}\underset{\begin{array}{c}\text{argmax}_{i} \end{array}}{\left|I(p)\ast f_{i}\right|},&e_{k}\in le\wedge p\in e_{k}\\ 0,&\text{otherwise}\end{array} \right. \tag{4}\]  
Figure 2: Example of common feature detection. (**a**) Harris corners. (**b**) Common feature points. where * stands for the convolution operation and \(\parallel\) stands for the absolute operation. (3) The edge length weighted edge orientation histogram is used to present the distribution of edges in the neighborhood of feature points. After the edge orientation of each edge pixel in the neighborhood is obtained, the histogram is calculated in each sub-region. Since the long edge has strong discrimination for infrared and visible images, the edge length is utilized in the histogram establishment. In order to enhance feature discrimination, the gradient orientation histogram is weighted by the gradient magnitude in the generation of SIFT and HOG. The length of the edge where the point is located is used as the weight in a similar manner to SIFT and HOG when the edge orientation histogram is calculated. The weight of point \(p\) on edge \(e_{i}\) is calculated by the equation below. \[w(p)=exp(min(l_{i},l_{m}))\delta(l_{i}\geq\alpha) \tag{5}\]  
where \(l_{i}\) is the length of \(e_{i}\) and \(\delta(\cdot)=\left\{ \begin{array}{c}1\text{ {\it true}}\\ 0\text{ {\it false}}\end{array} \right.\). Parameter \(l_{m}\) prevents long edges from suppressing the other edges and dominating the histogram. Parameter \(l_{m}\) is 1/2 max[H,W] where H and W are image height and width, respectively.