## 3 Path Feature Recognition
### Feature Extraction  
In order to classify different types of guide paths with noise points, the path features were extracted using the field scanning technique [9]. The detailed field scanning process is described as follows. 1. In the binary path image, assume the pixel value as \(f(x,y)\), where it is 1 for the path and 0 for the background. 2. Scan all pixels in row \(j\) (1\(\leq\)\(j\)\(\leq\)\(N\), \(N\) = 360) from left to right. Record the column coordinates of the first path pixel as \(h\)\(l\)\(j\), that of the last path pixel as \(h\)\(l\)\(r\)\(j\), and the number of all path pixels as \(h\)\(p\)\(j\). 3. Scan all pixels in column \(i\) (1\(\leq\)\(l\)\(\leq\)\(M\), \(M\) = 480) from top to bottom. Record the row coordinates of the first path pixel as \(v\)\(t\)\(t\), that of the last path pixel as \(v\)\(b\)\(t\), and the number of all path pixels as \(v\)\(p\)\(j\). 4. The contour features of the path can be described by means of the four-boundary contour scanning. The corresponding feature vectors are: \[ \begin{array}{l}\mathbf{H}_{l}=\left[\begin{array}{ccc}hl_{1}&\cdots&hl_{N }\end{array}\right]^{\mathrm{T}}\\ \mathbf{H}_{r}=\left[\begin{array}{ccc}hr_{1}&\cdots&hr_{N}\end{array} \right]^{\mathrm{T}}\\ \mathbf{V}_{t}=\left[\begin{array}{ccc}v\)\(t\)\(t_{1}&\cdots&vt_{M}\end{array}\right]^{\mathrm{T}}\\ \mathbf{V}_{b}=\left[\begin{array}{ccc}vb_{1}&\cdots&vb_{M}\end{array} \right]^{\mathrm{T}}\end{array} \] (1)
5. The region projections in the directions of row and column can be used for measuring the size features of the path. The feature vectors are: \[ \begin{array}{l}\mathbf{H}_{p}=\left[\begin{array}{ccc}hp_{1}&\cdots&hp_{ N}\end{array}\right]^{\mathrm{T}}\\ \mathbf{V}_{p}=\left[\begin{array}{ccc}vp_{1}&\cdots&vp_{M}\end{array} \right]^{\mathrm{T}}\end{array} \] (2)
6. Insert one of the aforementioned feature vectors behind the end of another sequentially, to constitute a total feature vector \(\mathbf{P}\) of a 3(\(M\)+\(N\)) dimension with redundant information, i.e.,: \[\mathbf{P}=\left[\mathbf{H}_{l}^{\mathrm{T}}\mathbf{H}_{r}^{\mathrm{T}} \mathbf{V}_{t}^{\mathrm{T}}\mathbf{V}_{b}^{\mathrm{T}}\mathbf{H}_{p}^{\mathrm{ T}}\mathbf{V}_{p}^{\mathrm{T}}\right]^{\mathrm{T}}\]  
Figure 6: The binary images of path pixels. (**a**) A straight path, (**b**) a straight path with highlights, (**c**) a straight path with coverings, (**d**) a curve path, (**e**) a curve path with highlights and coverings, and (**f**) a curve path with coverings. In order to search the inherent characteristics in the high-dimensional observational data, the total feature vector **P** needs to be projected to a low-dimensional space [30]. First, the total feature vector **P** is mapped from its original space to a high-dimensional space **H**, i.e., the reproducing kernel Hilbert space [31], by means of a Gaussian radial basis kernel function. Then, kernel principal component analysis (KPCA) is used to reduce the dimensionality of feature vectors in the feature space [32]. The following steps are taken for dimensionality reduction. (1) Collect \(n\) frames of path images as a training sample set for path features. Let the dimensionality of feature vectors be \(m=3(M+N)\). These \(n\) feature vectors constitute a sample matrix \(\textbf{X}_{n\times m}\). (2) An \(n\times n\) real positive definite kernel function matrix **K** is developed for clustering data in the high-dimensional space **H**. The development process is as follows. Assuming the sample matrix:  
\(\textbf{X}=\{\textbf{x}_{1},\textbf{x}_{2},\ldots,\textbf{x}_{n}\}\), \(\textbf{x}_{i}\in\textbf{R}^{m}\), where \(\textbf{R}^{m}\) is the input space, and \(m\) is the dimension of the samples, \(\textbf{x}_{i}\), \(m=3(M+N)\). (3) The nonlinear mapping of the input space is \(\varphi:\textbf{X}\rightarrow\textbf{H}\). Moreover, we assume that we are dealing with centered data, i.e., \(\sum_{i=1}^{n}\varphi(x_{i})=0\).