Paper4：Voxel-Based Extraction and Classification of 3-D Pole-Like Object From Mobile LIDAR Point Clo

Voxel-Based Extraction and Classification of 3-D Pole-Like Object From Mobile LIDAR Point Cloud Data

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Voxel-based extraction and classification of 3D rod-shaped targets in vehicle-mounted point clouds

Summary:

Digital mapping of road environment is an important task of road infrastructure inspection and urban planning. The automatic extraction and classification of pole-like targets can significantly reduce and improve work efficiency. Therefore, this paper proposes a voxel-based method to automatically extract and classify three-dimensional (3-D) rod-shaped objects by analyzing the spatial characteristics of objects. First, a set of linear voxels are generated as rod-shaped object candidates through voxel-based shape recognition and used as input for subsequent modules. According to the local isolation of rod-shaped features and the main direction is along the Z-axis, a cylindrical model with adaptive radius and vertical growth is used to identify voxels belonging to rod-shaped features. Finally, a number of semantic rules are derived based on the shape features and spatial topological relations, and the extracted pole-like objects are further divided into four categories (light poles, telephone poles, tree poles and others). The proposed method is evaluated using three data sets of mobile lidar point cloud data. The experimental results show that this method can effectively extract class-like targets from three samples, and the extraction rates are 85.3%, 94.1% and 92.3%, respectively. In addition, the method proposed in this article can effectively classify, especially trunk classification.

The flow chart of the proposed method is as follows:

The steps of the proposed method:

1) Generation: Generate a series of linear voxels as candidates for rod-shaped targets through voxel-based shape recognition.

2) Identification: Use a circular model with an adaptive radius to identify voxels belonging to a rod-shaped object.

3) Extraction: Extract individual rod-shaped objects based on the vertical area growth algorithm.

4) Classification: further classify the extracted rod-shaped objects according to several semantic rules.

The following is a detailed breakdown of the ABCD steps corresponding to the above 1) 2) 3) 4) steps.

A、Voxel-Based Shape Recognition

The part of the rod-shaped body presents a linear pattern, while the others (such as buildings and tree crowns) usually present flat or spherical features. Therefore, in this section, we adopt a continuous scheme for voxel-based shape recognition, including voxelization, voxel-based dimensional analysis, and MRF-based shape recognition optimization. Therefore, a set of linear voxels are generated as input to subsequent modules.

1) Voxelization: Vehicle radar contains many points, and the distribution of these points is very complicated. Therefore, in order to reduce the amount of data, we only construct 3-D voxels based on XYZ coordinates (axes) as primitives. The space is divided into regular three-dimensional grids, and each voxel is in the shape of a rectangular parallelepiped, and its geometric shape is defined by length (l), width (w) and height (h). The position of the voxel is indexed by column (i), row (j), and layer (k). According to the minimum coordinates (Xmin, Ymin, Zmin) and length (l), width (w) and height (h) of the three-dimensional voxel, the index (i, j) of each point in the point cloud can be calculated using formula (1) , k). Therefore, a large number of points are grouped together to form 3-D voxels. As shown in the figure below, multiple points are combined to form a three-dimensional voxel.

2) Voxel-Based Dimension Analysis: (Voxel-Based Dimension Analysis---line, surface, sphere)

After voxelization, we use PCA to analyze the dimensionality of the voxel, because PCA is a widely accepted method of dimensional analysis, which is widely used to infer objects in point cloud data into three shapes: linear, Plane and spherical.

Voxel dimension analysis is a program that analyzes the local shape of points within a voxel. It is well known that the size of a voxel directly determines the number of points it contains, which is likely to affect the correctness of the dimensional analysis, or we can perform dimensional analysis based on the geometric center of the query voxel and the neighborhood of its predefined radius R. In order to describe the geometric structure around p (geometric center), use the following formula to query the geometric center p and its neighborhood to get the covariance matrix $C_{p}$

$C_{p}=\frac{1}{|N|}\sum_{p_{i}\subseteq n}^{ } (p_{i}-\bar{p})(p_{i}-\bar{p})^{T}$

The above formula |N| represents the number of point neighborhoods, $\bar{p}=\frac{1}{|N|}\sum_{p_{i}\subseteq n}^{ } p_{i}$ and let $\lambda _{1}> \lambda _{2}>\lambda _{3}>0$ be $C_{p}$ the standard eigenvalue of the covariance matrix . According to the idea of literature [24], we use linear ( $a_ {1d}$ ), plane ( $a_{2d}$ ), spherical ( $a_{3d}$ ) characteristics to identify the geometric structure of points, as shown below:

However, the performance of dimensionality analysis is easily affected by the predefined radius R. For example, if the predefined radius R is too small, the geometric structure of the point may be estimated incorrectly, and when the predefined radius R is large, it may be affected by noise. Therefore, this paper uses the entropy function [26] to adaptively determine the predefined radius R to infer the geometric structure of the point, as follows:

Let $R_ {min}$ and $R_{max}$ be the minimum and maximum radius respectively. The $R_{add}$ entropy function is $E_{f}(V_{p}^{R})$ minimized by iteratively increasing the predefined radius R. The geometric center of the query p, predefined radius R, eigenvalues $\ lambda _ {1}, \ lambda _ {2}, \ lambda _ {3}$ and corresponding eigenvectors $v_ {1}$ , $v_ {2}$ and $v_ {3}$ are stored. Then calculate $a_ {1d}$ , $a_{2d}$ , $a_{3d}$ and (see Table I).

Local shape inference based on the covariance matrix of eigenvalues

When $a_ {1d}$ there is a maximum value, the point set in the voxel has a linear shape, and its main direction is the direction of the feature vector v1, which is aligned with the direction of the linear object. When the $a_{2d}$ value is the largest, the point cloud in the voxel presents a planar shape, and its main direction is the direction of the feature vector v3, that is, the normal direction of the plane. Finally, when $a_{3d}$ the value of is the largest, the point cloud within the voxel is spherical and has no dominant direction. Figure 3 shows the result of voxel-based shape recognition. (Refer to the literature [24] explains why $a_ {1d}$ , $a_{2d}$ , $a_{3d}$ may represent a linear planar spherical reasons)

用MRF模型优化的是PCA的结果（we used the MRF model to optimize the results of PCA since some pole-like parts might belong to other ground objects, especially buildings and tree branches）

3) MRF-Based Shape Recognition Optimization: (Optimization is linear)

As shown in Figure 4, the linear voxels identified in Section II-A2 (the previous step) may be linear parts of branches or buildings, rather than rod-like objects, because of the complexity and incompleteness, occlusion and noise. In addition, we also observed that, unlike rod-shaped objects, most of other ground objects (such as buildings and tree crowns) are flat and spherical.

Some typical linear voxel illustrations are not part of a rod-shaped object

In order to solve this problem in Figure 4, the MRF model is usually used to model context information to obtain locally continuous and global optimal results. Therefore, in this section, our goal is to optimize the shape recognition results by introducing context information for subsequent detection and classification modules, and represent the optimization problem as a binary labeling problem (that is, linear and non-linear voxels).

(Find linear but not rod-shaped, then use the MRF model to optimize)

The Markov model ( introduced in [27] ) is a weighted undirected graph $G=<V,E>$ , where V represents a set of nodes corresponding to a voxel, and E represents a set of undirected edges between adjacent nodes. Herein, the weighting no further comprises additional terminal to FIGS two $V_ {s}$ and $V_{t}$ , corresponding to the linear and nonlinear type. For a point cloud D, use to $\zeta$ denote a set of voxels $\zeta =\left \{ \zeta _{1},\zeta _{2},...,\zeta _{N} \right \}$ , use Ω to denote a set of tags $\Omega =\left \{ linear,nonlinear \right \}$ , and let L denote all the possibilities of the voxel tag structure (configuration and shape (conﬁgurations) are not known) $L=\left \{ l=(l_{\zeta 1},l_{\zeta 2},...,,l_{\zeta N})|l_{\zeta i}\in \Omega ,i=1,2,...,N \right \}$ . Hence the node set $V=\left \{ V_{\zeta i}|i=1,2,...,N \right \}\cup \left \{ V_{s} ,V_{t}\right \}$ and edge set $\left \{\left \{V _{u},V_{v} \right \} , \left \{ V _{u},V_{s} \right \},\left \{ V _{u},V_{t} \right \}\right \},u,v\in \left \{ \zeta _{i} |i=1...N\right \}$ . In the field of computer vision, finding the optimal label configuration $L^{*}$ can naturally be expressed as the energy function minimization, as shown below:

The data item Endata(L) measures the inconsistency between L and the observed data, and the smoothing item Esmooth(L) measures the degree of non-segmental smoothing of L and $\lambda$ represents the weight parameter.

The form of the data item is usually defined as:

Among them , the degree of fit between the $D_{u}(l_{u})$ quantitative measurement label $l_ {u}$ and the observation data is calculated using formula (7). $a_ {1d}$ The larger the value, the $D_{u}(l_{u})$ smaller the data item :

In order to generate a locally continuous and globally optimal label structure (how to translate configuration and shape (conﬁgurations) is not known), the smooth term Esmooth(L) is usually defined as:

Where R represents the 26 neighborhood system,

$\rho$ Expressed as the expected value of the adjacent distance (Reference [28]). As defined in formula (8), the penalty term for neighboring voxels with the same label is zero. For adjacent voxels with different labels, the smaller the distance between them, the larger the smoothness penalty. Therefore, the smooth term Ensmooth(L) encodes the extent to which the adjacent voxels belong to the same label (the smooth term Ensmooth(L) encodes the extent to which the adjacent voxels belong to the same label). Table II lists the definition of the weights of the edges in the weighted undirected graph. Finally, the $\ alpha - \ beta$ energy function (5) is minimized by the exchange algorithm (Reference [29]). Because it approximately minimizes the energy function of any finite label set, it not only proves the increase in computational efficiency, but also obtains the global optimal solution.

B. Identifying Voxels of Pole-Like Objects Using a Circular Model With an Adaptive Radius（识别杆状）

(Because part A already has labels linear, surface, and sphere, so this step is identification)

According to the steps described in Section II-A, each voxel is labeled as linear, flat, or spherical type. It is worth noting that rod-shaped objects are usually independent and isolated, and their main directions are approximately parallel to the z-axis. Independent rod-shaped voxels are arranged linearly in the vertical direction, and there are no flat or spherical voxels in the horizontal direction. In contrast, other ground objects, such as tree canopies, low vegetation, and building facades, may have multiple continuous voxels in the horizontal direction, and most of these voxels are flat or spherical. Therefore, we follow the slicing strategy (reference [7]) and use a circular model with an adaptive radius (reference [13]) to identify voxels belonging to rod-shaped objects.

As shown in Figure 6(a), we first slice the non-ground points according to the selected interval (such as the size of the voxel in this article) . After slicing, cluster the linear voxels generated in Section II with their neighboring linear voxels in the same slice (reference [30]) is to cluster the connected linear voxels in the same slice . ) Then, the cluster points are projected onto the relevant slice plane, as shown in Figure 6(b).

In fact, in the lidar point cloud data, these individual rod-shaped objects should be slender point clusters with empty spaces around them. Therefore, we established a circular model with adaptive radius composed of two concentric circles. As shown in Figure 6(b), suppose the geometric center p of the query cluster is the center of two concentric circles, and the maximum horizontal distance between the geometric center p and any point in the query cluster is $d_{max}$ the search radius of the inner circle, let $d_{max}+r$ Is the search radius of the outer circle, and r is the threshold to control the search radius. In theory, if the query cluster is part of a rod-shaped object, then the number of points in the outer circle (Nmax) and the number of points in the inner circle (Nmin) are equal. Considering that there may be scenes in which there are some non-rod-shaped objects (such as street signs), if they are satisfied $N_{max}-N_{min}< N_{threshold}$ , we mark the query cluster as rod-shaped; (where Nthreshold is the threshold for controlling the number of non-rod-shaped object points) .

Figure 7 is an example of a circular model for detecting different ground objects. The telegraph pole is mainly composed of linear voxels. The voxel has no nonlinear voxels in the vertical direction (that is, the voxels in this direction are linear). In the horizontal direction, the surroundings are almost empty space, while the canopy of street trees It is relatively complex with building structures, mostly flat or spherical voxels in the vertical and horizontal directions.

Therefore, the circular model was used to identify the linear voxels belonging to the rod-like objects, the vertical area growth algorithm was used to individualize the rod-like objects, and the same rod-like objects were matched and merged (Thus, the circle model was used to recognize the linear voxels belonging to the pole-like objects and the vertical region growing algorithm was conducted to individualize the pole-like objects for matching and merging the same pole-like objects)

C. Pole-Like Object Extraction Based on Vertical Region Growing (Pole-Like Object Extraction Based on Vertical Region Growing)

For each slice, the voxels belonging to the rod-shaped object are identified, and they will be used as the seed voxels for detecting a single rod-shaped object.

As shown in Figure 8, some components in the rod-shaped object may not be rod-shaped. For a single rod-like object, this section carries out the vertical region growth algorithm in a columnar structure ( reference [10] ) to match and merge the rod-like voxels, that is, the same rod-like object. Therefore, all independent pole-like objects will be extracted. As shown in Figure 9, the specific process of the vertical area growth algorithm is as follows:

1) The vertical growth starts from one of the voxels belonging to the rod-like object, creating the first single rod-like object.

2) Growing vertically from the seed voxel in the columnar structure, the nearest voxel belonging to the pole-like object is added to the query segmentation object.

3) This growth will continue until the distance between the query segment object and the next closest voxel belonging to the pole-like object exceeds the threshold of 0.5 m. The threshold is determined by the minimum distance between any two rod-shaped objects in the experimental scene.

4) Repeat the previous steps until all voxels belonging to the pole-like object are traversed. Therefore, each set of points represents an independent pole-like object.

The broken pole-like objects were reconstructed by the RANSAC-based method to obtain whole individual pole-like objects by reconstructing the broken pole-like objects using the ransac-based method to obtain whole individual pole-like objects.

Due to the presence of non-rod-shaped parts inside the rod-shaped object, individual rod-like objects extracted only by the vertical region growth algorithm may not have vertical continuity [Figure 9(b)]. For these broken rod-shaped objects (that is, they are not continuous in the vertical direction), we use a random sampling agreement (RANSAC) algorithm (Reference [31]) to fit the query single rod-shaped object to a 3-D line, Because it uses the initial data to satisfy as few fitting conditions as possible, and then uses a consistent method to expand the data set, it has strong robustness to noise. Then add these points in the fractured part and their distance from the three-dimensional fitting line less than the maximum radius to the query independent rod-shaped object to obtain a complete rod-like object [see fig 9(c)].

D. Pole-Like Object Classiﬁcation Based on Semantic Rules (Pole-Like Object Classiﬁcation Based on Semantic Rules)

The road environment may be composed of various pole-like objects, such as lamp posts, road signs, traffic lights, telephone poles, and tree trunks. These different types of rod-shaped objects usually exhibit different morphological characteristics and spatial topological relationships. Therefore, after identifying all independent polar objects in Section II-C, several semantic rules can be obtained from the morphological characteristics of the object and its spatial relationship with other objects. These rules are used to classify these The extracted rod-shaped objects fall into four categories, namely tree trunks, telephone poles, street lamps, and others (for example, street signs).

Height (Reference [32]) is an important feature of rod-shaped objects, which usually varies from one type to another. This can be used as a standard for classifying different rod-like objects. For example, the height of pole-like objects such as lamp posts, road signs, traffic lights, and telephone poles usually have clear specifications, while the height of tree trunks varies with the age and type of trees. Telegraph poles are the highest goal to ensure the safety of power lines and reliable power distribution.

As shown in Figure 10, different rod-shaped objects present different two-dimensional (2-D) projection point distributions, and the red 2-D grid is the position of a single rod-shaped object extracted in Part II-C.

For example, the trunk should be connected to the canopy, and the canopy can be used to identify the trunk. More specifically, we cumulatively query the number of two-dimensional grids containing points in 24 adjacent regions of the red grid. If the number of two-dimensional grids containing points exceeds the threshold, the query rod-shaped object is marked as a tree trunk. Therefore, tree trunks are different from other types of rod-shaped objects. In the following classification procedure, the poles, lamp posts and others are classified according to their height information. The height of electric poles and lamp posts in specific areas can generally be consulted with the municipal department. In our experiments, the standard height ( $N_{h}$ ) of each rod-like object can be calculated. If $N_{h}> h_{utility}$ , the query pole-like object is marked as a telephone pole. If $N_{h}> h_{lamp}$ , the query pole-like object is marked as a street light. If these two conditions are not met, the queried rod-shaped object is marked as others.

III. EXPERIMENTATION AND ANALYSIS (experiment and analysis)

Paper4：Voxel-Based Extraction and Classification of 3-D Pole-Like Object From Mobile LIDAR Point Clo

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