**2.2. Normal vector estimation in a panoramic multilayered range image**

A normal vector can be estimated using three points in point cloud with a triangle patch or mesh generation processing. In 2D image processing, the Delaunay division is a popular algorithm. The Delaunay division can also be applied for 3D point-cloud processing with millions of points [13]. However, using the Delaunay division, it is hard to generate triangle patches for more than hundreds of millions of points without a high-speed computing environment [14, 15]. Thus, we focused on point-cloud rendering that restricts visible point-cloud data as a 2D image. A closed point detection and topology assignment can be processed as 2D image processing.

and *P4*

and *C*-*P4*

attachment to the point cloud.

of all points in point cloud.

as shown in **Figure 8**.

**2.3. Normal vector-based point clustering**

in the range image are set from point *C* with *d1*

**Figure 7.** Normal vector estimation in panoramic multilayered range image.

zontal directions. Triangulation is applied to these points as vertexes *C*-*P1*

with a clockwise topology in the image space. Moreover, parameters *d1*

in this procedure depend on the accuracy and resolution of the measurement data taken from the laser scanner or stereo camera. When the accuracy and resolution are high enough, these parameters are set as one pixel. These parameters are set to more than one pixel for low accuracy and resolution measurement data to keep a smooth condition of normal vectors on a flat surface. This procedure, which is based on 2D image processing, can provide a higher topology

Additionally, the normal vector on each triangle is estimated using the 3D coordinate values of each point. When five points consisting of a center and four vertex points exist on the same plane in 3D space, each normal vector has the same direction. When point *C* exists on the edge of the 3D space, two clusters can be classified by two directions. Moreover, when point *C* exists on the corner of the 3D space, each triangle has a different direction. Surfaces, edges, and corners in the 3D space were estimated in point-cloud data using these clues. In this research, we used the point cloud taken from a laser scanner that presents difficulties for measuring edges and corners clearly. Thus, the average value of each normal vector is used as a normal vector of point *C*. These procedures were iterated to estimate the normal vectors

Point clusters are generated from a classification result of normal vectors. The accuracy of point-cloud classification can be improved with several approaches such as the Mincut, Markov network, and fuzzy-based algorithms [16–18]. However, in this study, we focused on verifying the practicality of our point-based rendering for point-cloud clustering. Thus, we applied multilevel slicing as a simple classification algorithm to classify normal vectors,

This classification detected boundaries of point clusters with the same normal vectors. Moreover, clustered normal vectors were compared with normal vectors of neighboring

, *d2*

, *d3,* and *d4*

pixels in vertical and hori-

, *d2*

, *d3,* and *d4*

83

Point Cloud Clustering Using Panoramic Layered Range Image

http://dx.doi.org/10.5772/intechopen.76407

In our normal vector estimation, four faces in a range image are generated to estimate normal vectors of a point in point cloud, as shown in **Figure 7**. First, a point in the projected point cloud on a panoramic layered range image is defined as point *C*. Next, the projected points *P1* , *P2* , *P3* ,

**Figure 6.** LiDAR VR processing result: input point cloud (upper image) and output point cloud (bottom image).

**Figure 7.** Normal vector estimation in panoramic multilayered range image.

value of the search range. Moreover, the start value plus a defined distance parameter is assumed as the end value. The defined distance parameter is determined with the continuity of the points in the point cloud. For example, the defined parameter would be between 10 cm

Thus, the pixel-selectable averaging filter uses valid points in the range data to achieve an interpolation without reducing geometrical accuracy by a uniform smoothing effect. **Figure 6**

A normal vector can be estimated using three points in point cloud with a triangle patch or mesh generation processing. In 2D image processing, the Delaunay division is a popular algorithm. The Delaunay division can also be applied for 3D point-cloud processing with millions of points [13]. However, using the Delaunay division, it is hard to generate triangle patches for more than hundreds of millions of points without a high-speed computing environment [14, 15]. Thus, we focused on point-cloud rendering that restricts visible point-cloud data as a 2D image. A closed point detection and topology assignment can be processed as 2D image

In our normal vector estimation, four faces in a range image are generated to estimate normal vectors of a point in point cloud, as shown in **Figure 7**. First, a point in the projected point cloud

> , *P2* , *P3* ,

on a panoramic layered range image is defined as point *C*. Next, the projected points *P1*

**Figure 6.** LiDAR VR processing result: input point cloud (upper image) and output point cloud (bottom image).

and 1 m from experience, when trees and building walls are measured.

**2.2. Normal vector estimation in a panoramic multilayered range image**

shows an example of processing result.

82 Recent Applications in Data Clustering

processing.

and *P4* in the range image are set from point *C* with *d1* , *d2* , *d3,* and *d4* pixels in vertical and horizontal directions. Triangulation is applied to these points as vertexes *C*-*P1* -*P2* , *C*-*P2* -*P3* , *C*-*P3* -*P4,* and *C*-*P4* -*P1* with a clockwise topology in the image space. Moreover, parameters *d1* , *d2* , *d3,* and *d4* in this procedure depend on the accuracy and resolution of the measurement data taken from the laser scanner or stereo camera. When the accuracy and resolution are high enough, these parameters are set as one pixel. These parameters are set to more than one pixel for low accuracy and resolution measurement data to keep a smooth condition of normal vectors on a flat surface. This procedure, which is based on 2D image processing, can provide a higher topology attachment to the point cloud.

Additionally, the normal vector on each triangle is estimated using the 3D coordinate values of each point. When five points consisting of a center and four vertex points exist on the same plane in 3D space, each normal vector has the same direction. When point *C* exists on the edge of the 3D space, two clusters can be classified by two directions. Moreover, when point *C* exists on the corner of the 3D space, each triangle has a different direction. Surfaces, edges, and corners in the 3D space were estimated in point-cloud data using these clues. In this research, we used the point cloud taken from a laser scanner that presents difficulties for measuring edges and corners clearly. Thus, the average value of each normal vector is used as a normal vector of point *C*. These procedures were iterated to estimate the normal vectors of all points in point cloud.

#### **2.3. Normal vector-based point clustering**

Point clusters are generated from a classification result of normal vectors. The accuracy of point-cloud classification can be improved with several approaches such as the Mincut, Markov network, and fuzzy-based algorithms [16–18]. However, in this study, we focused on verifying the practicality of our point-based rendering for point-cloud clustering. Thus, we applied multilevel slicing as a simple classification algorithm to classify normal vectors, as shown in **Figure 8**.

This classification detected boundaries of point clusters with the same normal vectors. Moreover, clustered normal vectors were compared with normal vectors of neighboring

and point-cloud clustering results are shown in **Figure 10**. The results show that building features such as ceilings, beams, window shades, pillars, benches, and floors are classi-

Point Cloud Clustering Using Panoramic Layered Range Image

http://dx.doi.org/10.5772/intechopen.76407

85

We selected a bridge as a study area in the outdoor environment. We acquired 25.9 million points using a terrestrial laser scanner (GLS-2000, TOPCON) from four viewpoints. Rendered point cloud, depth range image, and point-cloud clustering results are shown in **Figure 11**. The results show that vertical planes, horizontal planes, and natural features are classified clearly. The processing time for the clustering was 6.1 s (Intel Core i7-6567U

**Figure 10.** Point-cloud clustering result: rendered point cloud (left image), filtered point cloud (center image), and

fied clearly.

**Figure 9.** Indoor MMSs.

3.30 GHz, MATLAB).

clustered point cloud (right image).

**3.2. Experiment 2: terrestrial laser scanner data (1)**

**Figure 8.** Normal vector-based point clustering.

planes to be integrated into a larger plane or deleted as a small segment. When a specified plane is extracted, the direction of a normal vector and the cluster number are available as initial value inputs. The point-cloud clustering methodology for extracting the intersection of planes as ridge lines requires appropriate initial values such as curvature, fitting accuracy and distances to closed points [19]. However, our approach can extract boundaries from a point cloud without these parameters.


**6.1 Kinetic models**

The uptake of hydrogen and release of hydrogen in hydrogen storage systems is made of adsorption, penetration through the surface, internal diffusion and chemical reaction [56]. **Figure 5** below show the detailed steps of these processes:

The two possible reaction modes for hydrogenation and dehydrogenation reactions are geometrical contraction and nucleation growth. These reaction routes are supported by theoretical and experimental research [57]. Hydrogen storage

**Figure 5.** *Hydrogenation and dehydrogenation steps (Adapted from [58]).*

kinetic models are thereby segregated according to these reaction routes. These models are founded on isothermal fitting and non-isothermal calculation analysis methods [58]. These methods help determine kinetic parameters and reaction modes this subsequently leads to a better understanding of the kinetic mechanism.