# Tire Defect Detection via 3D Laser Scanning Technology
## 2 Materials and Methods
### Normal-Based 3D Rendering  
In this section, we elaborate on the normal-based rendering strategy for processing and extracting raw 3D surface data. By introducing point normals into the obtained feature map, we can estimate the surface orientations and search irregular bulge-like areas that contain rich information for subsequent detection. Then, in the rendering process, we combine the captured 3D information (normal and depth) and project it onto 2D planes for joint inputs from different domains. * **Surface normal estimation** The raw data captured by laser scanners are presented as depth information of parallel scanning lines. Intuitively, the obtained depth image (as shown in Figure 3c) is not ideal for defect detection because of the insignificant depth difference in local areas and inevitable noise. We first estimate geometric properties based on surface normals to extract accurate 3D surface characteristics from raw scans. In 3D geometry, a normal is one of the most  
Figure 2: Overview of the proposed architecture for tire defect detection. (**a**) shows our mechanical environment where a laser scanner is installed to capture 3D point clouds on tire surfaces. (**b**) denotes the training phase of our method, which combines a normal-based 3D rendering process and a 2D detection model. (**c**) shows the testing phase where our method predicts results based on rendered images. fundamental properties that can effectively reflect the surface orientation of local regions. A surface normal at a point is a vector perpendicular to the surface around that point, as is shown in Figure 3a. Many different normal estimation techniques exist in the literature. Among them, one of the simplest methods is based on estimating the normal of a plane tangent to the surface. Given a point cloud patch \(\mathcal{P}\in\mathbb{R}^{N\times 3}\), we consider the neighboring points of each point \(p\in\mathcal{P}\). We firstly employ an efficient Kd-tree to query neighboring points \(\mathcal{K}=\{p_{k}|k\in\mathcal{N}(p)\}\) (\(p\) is included). Then, we use the least-square plane fitting estimation algorithm [13] to calculate the tangent plane \(t\) located at \(p\). Following a previous study [13], the tangent plane \(t\) is represented by \(p\) and a normal vector \(n\). We set \(c\) as an approximation of the centroid of neighboring points. For estimating the normal vector \(n\), we must analyze the \(3\times 3\) covariance matrix \(A\), which is written as  
\[A=\frac{1}{\|\mathcal{K}\|}\sum_{p_{k}\in\mathcal{K}}\left(p_{k}-c\right) \left(p_{k}-c\right)^{T} \tag{1}\]  
where \(c\) is the centroid of neighboring points calculated by the mean of coordinates. By calculating the eigenvalues \(v_{j}\) and eigenvectors \(u_{j}\) (\(j=0,1,2\)) of \(A\), we can obtain the smallest eigenvalue termed as \(v_{l}=\min_{j\in\{0,1,2\}}v_{j}\), and the corresponding eigenvector \(u_{l}\) is the approximation of \(n\). * **Projecting 3D point clouds into 2D features** On the basis of the above two steps (i.e., preprocessing and normal estimation), we obtain the accurate depth information and surface geometric properties of each point in the local patches. Because of the difficulty of annotating 3D data and the heavy computational cost of neighbor searching in the 3D space, directly applying 3D detection models on raw point cloud data for inspecting tire defects is challenging [14; 15; 16]. To ease this problem, we intend to convert depth and normal information into regular 2D feature maps using a 3D projection strategy. * **Depth images** We first convert 3D point cloud data into regular grids according to camera parameters and scanning resolutions. The raw scan of a tire sample consists of several parallel scanning lines, each of which captures accurate depth values of different positions with a fixed resolution (see Figure 3). Therefore, we align the depth vectors and pad possible failure values with zero, which yields a regular 2D map with regard to the original scanning resolutions.