TY - JOUR
AU - Date, Hiroaki
AB - Abstract Recently, renovations of plant equipment have been more frequent because of the shortened lifespans of the products, and as-built models from large-scale laser-scamied data is expected to streamline rebuilding processes. However, the laser-scanned data of an existing plant has an enormous amount ofpoints, captures inmcate objects, and includes a high noise level, so the manual reconstmction of a 3D model is very time-consuming and costly. Among plant equipment, piping systems account for the greatest proportion. Therefore, the purpose of this research was to propose an algorithm which could automatically recognize a piping system from the terrestrial laser- scanned data plant equipment. The straight pomon pipes, connecting parts, and connection relationship ofthe piping system can be recognized in this algorithm. Normal-based region growing and cylinder surface fitting can extract all possible locations ofpipes, including straight pipes, elbows, and junctions. Tracing the axes of a piping system enables the recognition of the positions of these elements and their connection relationship. Using only point clouds, the recognition algorithm can be performed in a fUlly automatic way. The algorithm was applied to large-scale scamied data of an oil rig and a chemical plant. Recognition rates of about 86%, 88%, and 71% were achieved straight pipes, elbows, andjunctions, respectively. Laser scanning, Object recognition, As-built model, Piping system, Point clouds 1 Introduction Recently, because of the short lifespans of plant products, renovations of plant equipment have been more frequent. However, the results of the renovations are not necessarily recorded in the plant drawings in many cases. Thus, unintended collisions between existing equipment and newly designed ones often take place in the construction stage. This causes additional costs and labor. The performance of terrestrial laser scanners has been rapidly developing, and shapes of objects in environments can be easily captured as 3D point clouds. With these laserscanned point clouds of existing plants, an as-built model of the plant equipment could be reconstmcted. Once the model is reconstmcted, the unintended works could be pre-checked on computers and avoided in the planning stage. However, the laser-scanned data of existing plants have massive point clouds, include a large amount of noise, and capture tangled objects. Therefore, recognizing each plant component from the point cloud, including the tangled objects, and constructing a 3D model of the plants are nearly impossible or very time-consuming when done in an interactive way. Thus, automation of the recognition and 3D model construction processes from point clouds need to be strongly promoted in the plant engineering field. Plants consist of many types of components. One of the more impoitant components is a piping system, which accounts for the greatest proportion and is renovated frequently. A piping system consists of various elements and their connection relationships: straight pipes, connecting parts such as junctions and elbows, and attached parts such as indicators and valves. Several studies have been proposed to recognize piping systems from laser-scanned point clouds. However, these algorithms cannot be applied to the point clouds that have already been registered and the intensity, or that can only recognize few classes of piping systems. Masuda et al. [1] proposed a method which could recognize planes and cylinders from the scanned data ofplants. However, it required the combination of a scanned point and reflected intensity from a scanner. Rabbaini et al. [2] proposed a method that reconstructed a 3D primitive model from the combination of a point cloud and a photograph taken from the same location. However, the method needed a pair of point cloud data and a photo shot from the scanner position. Piping systems often occupy a broad area of plants, and multiple scans and their registration are inevitable to obtain a point cloud covering the whole shape of the system. Therefore, it is probable that these algorithms cannot be applied to a registered point cloud generated from multiple scans. Aurelien et al. [3] proposed a method which fits an optimized cylinder model to the scanned points using an a priori CAD model of plants. However, 3D cylinder models, which have similar radii and axis directions, have to be placed near the points on pipes manually. Johnson et al. [4] proposed a method which matches a 3D CAD model in a database to a point cloud using a spin image. However, it is difficult to prepare an exact 3D model of straight pipes because their lengths are not fixed. Namatame et al. [5] proposed a method which recognized points on pipes under the assumption of Manhattan World Grammar. However, the algorithm could only recognize the straight poffion of a piping system. Recently, Lee et al. [6] proposed a method which recognized straight pipes, elbows, andjunctions from points on a piping system using the voronoi diagram. However, in their algorithm, the input point cloud only included the pipes themselves, and did not include any unwanted parts, such as flanges or valves, or supporting members, thus sacrificing generality. Belton et al. [7] and Rabbani et al. [8] proposed methods that classified and partitioned the scanned points of plants into those on planar surfaces and on cylindrical surfaces using covariance analysis and using a combination of normal-based region growing and plane fitting. However, points on elbows and junctions and the connectivity of the piping systems were not identified. Vosselman et al. [9] proposed a method using 3D Hough transforms for recognition. However, only straight pipes are recognized in the piping system. El-Harawany et al. [10] proposed a method that identified cylinders from scanned points of pole-like objects on a road side using a combination of eigen- based segmentation, linear feature extraction, and cylinder fitting. However, if applied to scanned points of plants, only straight pipes could be extracted from them. Marshall et al. [11] proposed a non-linear least-square-based method where scanned points of general obj ects are segmented into spheres, cylinders, cones, and tori. However, the method dealt only with the point clouds of relatively simple-shaped objects, so it could not work well when applied to the tangled objects in plants. Therefore, the purpose of this research was to propose a new algorithm that could automatically recognize piping elements consisting of straight pipes and connecting parts and their connection relationships only from raw laser- scanned point clouds of a whole plant, which includes point clouds other than the piping system. The algorithm was tested for large-scale laser-scanned point clouds of a real plant, and the recognition accuracy of the straight pipes and connecting parts were verified. We have already proposed a similar recognition algorithm of piping systems, but it had some problems [12]. In the process of extracting points on straight pipes, a delicate parameter setting of the searching radius was needed. The parameter should be set in relation to a pipe radius on which the point lies. Therefore, if there is a great distinction among the radii of pipes in the plant, then most of the pipes cannot be extracted. Moreover, the algorithm could not extract some points around non-straight pipes such as supporting materials, attached parts, and junction parts on a straight pipe. Therefore, if tangled pipes are concentrated in a small area, these pipes would not be recognized. To solve these problems, this paper introduces a normal-based region growing which automates the extraction of points on a piping system and segmentation of points into each pipe. By introducing the algorithm, almost all points of pipes can be extracted without calculating the normal tensor. With this method, great improvement was achieved in the recognition rates of straight pipes, junctions, and elbows than with previous methods [12]. 2 Algorithm overview As shown in Figure 1, the proposed recognition algorithm consists of three processes. First, the normal vector of every scanned point is estimated using grid cells and quadratic polynomial surface fitting. Next, the points on each pipe are extracted using normal-based region growing, and their radii and positions are estimated by cylindrical surface fitting. Finally, the connection relationships among the extracted pipes are recognized by tracing and interpolating axes of the recognized pipes. Figure 1 Open in new tabDownload slide The overview of the proposed piping system recognition algorithm. 3 Estimating normal vectors In order to reduce computational costs of normal vectors for a huge set of scanned points, a grid whose cell has a width lg is placed to cover the whole scanned space. Each grid cell keeps scanned points inside the cell. In the algorithm, lg is recommended to be set as one third of the smallest pipe radius rmin to be dealt with in the piping system. Next, in order to estimate the normal vectors of all scanned points, for each grid cell i, the covariance matrix Ci is first calculated by equation (1). Ci=1|{pj}|∑j=1|{pj}|(pj−bi)T(pj−bi)(1) where {pj} is a set of position vectors of the points inside the cell i and its one-neighboring 26 grid cells, and bi is an average position vector of {pj} The eigenvalues λ1λ2λ3(λ1≥λ2≥λ3≥0) and corresponding eigenvectors e1 ⁠, e2 ⁠, e3 are obtained by an eigenvalue analysis of Ci ⁠. If lσ is sufficiently smaller than the radius of the pipe, the points {pj} are approximately distributed on a plane, and the eigen- vectors e1 and e2 indicate the principal axes placed on the plane. Therefore, the vector e3 approximates the normal vectors at all points {pj} ⁠. Thus, e3 is adopted as an initial normal vector ni′ ⁠. Next, a local orthogonal coordinate system u-v-w whose origin is placed at bi with u//e1 ⁠, u//e2 ⁠, and w//ni′ is selected. Then, {pj} are projected onto the plane u-v. An explicit quadratic polynomial surface w=h(u,v) of equation (2) is then fitted to {pj} using the least squares method. w=h(u,v)=aou2+a1u2+a2uv+a3u+a4v+a5(2) Finally, {pj} are projected onto the surface to obtain their projected points {pj′} ⁠, and the normal vector of w=h(u,v) at every projected point pi′ in the original coordinate frame (x,y,z) is estimated as a normal vector ni of pi ⁠. 4 Recognizing pipes in a piping system 4.1 Extracting points on a piping system In order to extract points on a piping system from all scanned points P, a normal-based region growing was developed. First, the normal-based region growing is applied. In the region growing, a seed point ps∈P is chosen from P at random. Then, the points {pi|pi∈P,pi∈N(ps,r1),||ns⋅ni||>τn} are extracted and added to a region, where N(ps,r1) is a set of neighboring scanned points contained in the sphere of the radius r1 centered at ps ⁠. The threshold τn was set to 0.97 based on our experiments. Each of the added points is then chosen as a new seed point, and the other points satisfying the same condition are progressively added to the region. These steps are iterated until any points satisfying the condition exist in the neighborhood ofthe seed points. After the region-growing process, a covariance matrix is calculated for all points in every region {pj} ⁠, and eigenvalues λ^1,λ^2,λ^3(λ^1≥λ^2≥λ^3≥0) and corresponding eigenvectors e^1,e^2,e^3 are obtained. An oriented bounding box which aligns to the vectors e^1,e^2,e^3 is fit to the points {pn} ⁠. As shown in Figure 2(a) and Figure 2(b), if the scanned points exist on straight pipes, the regions take the shape of thin strips placed along the pipe axis, and the vector e^1 approximates the axis direction of the pipe. If the points exist on elbows or junctions, the region takes the concatenated shape thin straight strips and thin circular strips. In contrast, if the points exist on wide planar surfaces such as floors or walls, the region takes the shape of a broad width. Figure 2 Open in new tabDownload slide Recognizing pipes of a piping system: (a) normal-base region growing, (b) oriented bounding box, (c) median of ranges of projected points, (d) integrated region. Then, as shown in Figure 2(c), several numbers of dividing planes whose normal vectors are equal to e^1 are placed at regular intervals, and the points in {pn} are projected onto the nearest plane. Moreover, on each plane, the set of the projected points is further projected onto the line parallel to e^2 ⁠, and the range of the projected points on the line is evaluated. If the median value of the ranges d^ satisfy d^<τw ⁠, where τw is a threshold, the regions are classified as points on the piping system, such as straight pipes, elbows, and junctions. Otherwise, they are classified as points on the other components, such as planar surfaces. As for the threshold, τw was set as 2.0 ⋅rmaxsincos-1(τn) from a simple geometric relation, where rmax is the radius of the largest pipe in the measured environment. For parts of regions on elbows or junctions, the vector e^1 is not coincident with the axes vectors ofthe pipes. Therefore, to modify the segmentation, a line is fitted to each region using RANSAC. The number of sampling in the RANSAC is set as 50, and the outlier threshold to the distance between a point in the region and the fitted line is set as d^/2.0 ⁠. Finally, the points whose distance to the fitted line was less than the outlier threshold were chosen and segmented as one region. The remaining points will be segmented iteratively using the above region-growing process. 4.2 Grouping points on a pipe segment In order to integrate the segmented regions into a new single region which belong to a same pipe, the constraint region-growing is further applied to points on the piping system. First, as shown in Figure 2(d), a covariance matrix E is calculated for the set of points in a region, and the eigenvector q^1 corresponding to the largest eigenvalue of E is assigned to all scanned points in the region. Next, a seed point ps is chosen from the points on a piping system at random. Then, the other points pi which satisfy ‖q^1,s⋅q^1,i‖>τq contained in neighboring points N(ps,r1) centered at ps are added into the region. τq was set to be 0.95 based on our experiments. Each of the added points is next chosen as a new seed point. The above steps are iterated until any points satisfying the condition appear in the neighborhood ofthe seed points. 4.3 Extracting the pipe parameters After grouping points on the pipe segments, a cylinder is fitted to each pipe region, and the axis of the pipe and its radius are estimated. As shown in Figure 3, for each region, normal vectors of the grouped points are first proj ected to a unit sphere surface. Then, a plane is fitted to the projected normal vectors using RANSAC, and the normal vector of the plane is determined as an initial axis vector of the cylinder vinit ⁠. The number of sampling in the RANSAC is set as 50, and the outlier threshold to the inner product normal vectors is set as 0.01. Then, all points in the region are proj ected onto the fitted plane, and a circle is fitted to the projected points by the Least Median of Squares (LMedS) [13]. Figure 3 Open in new tabDownload slide Initial cylinder fitting. The number of sampling in the LMedS is set as 50. The center point and the radius of the circle are determined as the point on the axis sinit and the initial radius rinit of the cylinder. Next, a cylinder is precisely fitted onto the points by the Levenberg-Marquardt method [14]. In this method, parameters of a cylinder model are expressed as seven variables (α,β,γ,a,b,c,r) ⁠, where (α,β,γ) is the unit axis vector of the cylinder, (a,b,c) is the point coordinates on the axis, and r is the cylinder radius. Finally, an objective function of the cylinder fitting is expressed as equations (3), (4), and (5). 1N∑i=0N−1(fi−r)2→min(3) fi=m2+n2+o2(4) m=γ(yj−b)−β(zi−c)n=α(zi−c)−γ(xi−a)o=β(xi−a)−α(yi−b)(5) where (xi,yi,zi) is a position vector of the grouped point. Then, based on the obtained radii r from equation (3), outlier points which satisfy (r<rmin)V(r>rmax) are removed from the points on the piping system. If the grouped points cover a small angle of the cylinder surface, the parameters of a fitted cylinder can contain aberrant values. In order to confirm whether the fitted cylinder is reliable or not, as shown in Figure 4, the cylinder surface is equiangularly divided into regions by angle θ ⁠, and scanned points are projected onto the corresponding divided cylindrical regions. If a number of regions m which contain the projected points do not satisfy mθ>τθ ⁠, the points are removed from the points on pipes, where θ is π/36 and τθ is π/2 ⁠. Figure 4 Open in new tabDownload slide Point coverage of cylinder. 5 Estimating axes and recognizing elements of a piping system 5.1 Tracing the axes of a pipeline In the result of Section 4.2, points on elbows have been divided into several regions, and a number of cylinders are fitted to an elbow. Thus, it is difficult to estimate the true axes of elbows using the fitted cylinder axes. In order to correct the axes of these parts, axes of the piping system are traced using regions of a pipe and their pipe parameter. As shown in Figure 5, for each pipe region, a sphere is first centered at a midpoint of axis segment si ⁠, where the radius of the sphere is set as 1.2 times the fitted cylinder radius r. Then, on both sides of si ⁠, points on the piping system {pk} nearly existing on the sphere are collected, and a set of offset points {pk′} is generated as pk′=pk+rnk ⁠, where nk is a normal vector towards the inside of the pipe. Then, an average point of these offset points d is determined as an axis point ofthe pipe. These processes are repeated until points on the piping system exist on the sphere, and an axis point sequence [d1,d2,…,dn] is obtained for each region of the pipe. Figure 5 Open in new tabDownload slide Tracing axes of a piping system. However, in this method, as shown in Figure 6(a), when an axis point reaches junction, only the axis point on either of the branches can be traced, and an untraced axis necessarily remains. Therefore, non-traced axes can remain. In order to recognize these untraced axes, as shown in Figure 6(b), each region is traced once again but limited to trace only the points of their own region in the trace. After re-tracing the axes, as shown in Figure 6(c), a part of the obtained axis point sequence is duplicated. To delete these duplicated axis points, as shown in Figure 6(d), for each axis point d, if other axis points obtained in the other steps exist in the vicinity of an axis point d within the distance r, these axis points are erased, as shown in Figure 6(e). Figure 6 Open in new tabDownload slide Tracing the axis points: (a) tracing points of all region, (b) tracing points of own region, (c) combining the two results, (d) erasing the duplicated points, (e) obtaining axis point sequences. 5.2 Continuous arc–line fitting After recognizing the axis point sequence ofthe piping system, lines and arcs are altematively fit to the points using a previous algorithm [15]. As shown in Figure 7, a plane Q passing three points di ⁠, di+i ⁠, dj+1(i+1<j) is first defmed, and the axis points in the sequence [di,…,dj+1] are projected onto the plane, and the projected point sub-sequence [d′i,…,d′j+1] is obtained. Next, lines l1=di′di+1′¯ ⁠, l2=dj′dj+1′¯ and their intersection point L are calculated. Then, for each projected point dk′∈{di+1′,,dj′} ⁠, a circle C ⁠, which is tangent to l1 ⁠, l2 and dk′ ⁠, is calculated as follows. Figure 7 Open in new tabDownload slide Arc-line fitting to an axis point sequence. A tangent point M1 between C and l1 satisfies equation (6): R=‖c-dk′‖=‖c-M1‖(6) where c is a center point of C and r is a radius of C ⁠. Using the geometric relations of c=L+λt and M1+di′+〈c-di′,v〉v ⁠, where t is a directional vector of the bisector line of l1 and l2 ⁠, the equation (6) can be rewritten as equations (7) and (8). (‖w‖2−‖t‖2)λ2+2{(w⋅y)−(t⋅z)}λ+(‖y‖2−‖z‖2)=0(7) w=t−(t⋅v)vy=L−di′−{(L−di′)⋅v}vz=L−M(8) where v is a directional vector of l1 ⁠. The largest solution of the quadratic equation (7) gives the center point of c and the radius r of C ⁠. From the solution, a line segment l′=dι′M1¯ and an arc segment a′=M1M2¯ are obtained. If any segment does not reach the last axis point dn ⁠, the tangent point M2 between C and l2 is inserted as a new axis point, and a new line and arc segment are fitted onto the remaining axis points [M2,dj+1′,…,dn′] ⁠. However, arc segments with very large radii are sometimes fit to axis points of straight pipes. To correct these results, if consecutive line-arc-line segments are nearly collinear, the three segments are replaced with one line segment. 5.3 Complementing line segments on the same straight pipe First, pairs of nearly collinear axis segments li=eιeι′¯ and lj=eJeJ′¯ ⁠, which satisfy |ui⋅uj|>τinner and |ui⋅eij|> τinner ⁠, are selected, where e and e′ are edge points of the axis segment, u is a unit direction vector ofthe line segment, and eij is a unit vector of a line connecting the two edge points ei and ej ⁠. The threshold τinner was set to be 0.98. If the distance between ei and ej is less than τl ⁠, the two segments li and lj are replaced with a new line segment lk=eι′eJ′¯ ⁠. Moreover, if any arc segment is connected with ei or ej ⁠, a junction may be falsely recognized as an arc segment. In this case, the arc segment is removed. 5.4 Complementing line segments on the junction After the complement of line segments on the same straight pipe, junctions that connected three pipes are identified. As shown in Figure 8, first, a pair of line segments li=eιeι′¯ ⁠, lj=eJeJ′¯ ⁠, which satisfy |qi⋅qj|<τskew and |ei′-ei|>|qi-ei| ⁠, are selected, where qi and qj are position vectors of the intersection points of the common perpendicular line oftwo lines Li and Lj ⁠, which respectively passed through edge points ei and ej ⁠, and are collinear to line axis segment li and lj ⁠. τskew is a threshold for the skew distance between Li and Lj ⁠. Then, if the segment pair gives a distance less than the pipe radius of line segment ri ⁠, a new edge point en is placed at qi ⁠. Also the segments li and lj are replaced with the new segments lk=eneι′¯ ⁠, ll= eneι¯ and lm=eneJ′¯ ⁠. After the complement, the segments lk ⁠, ll ⁠, and lm are respectively divided into two segments at a place of distance r′ from qi ⁠, where r′ is set as 1.1 times that of ri ⁠. The newly divided segments which connected qi are determined as ajunction segment. Figure 8 Open in new tabDownload slide Interpolation of junctions. 5.5 Complementing arc segments on the elbow If some points on the elbow are missing due to occlusions, the axis of the elbow cannot be traced completely. In that case, an arc segment is inserted between a pair of line segments using the following steps. First, a pair of line segments li=eιeι′¯ ⁠, lj=eJeJ′¯ ⁠, which satisfy |qi⋅qj|<τskew and both distances between ei and qi ⁠, which are less than τl ⁠, are selected. Then, a plane passing ei ⁠, ei′ ⁠, and ej′ is defined, and ej is projected onto the plane. A circle Ci ⁠, which is tangent to two lines Li ⁠, Lj ⁠, and e′ ⁠, and the other circle Cj ⁠, which is tangent to Li ⁠, Lj ⁠, and e^j ⁠, are calculated. Li and Lj are lines passing li and lj ⁠, and e^j is the projected edge point from ej ⁠. By comparing the radii Ri of Ci to Rj for Cj ⁠, the larger value is adopted as the maximum value of radius RM ⁠. Next, as shown in Figure 9, the radius of the tangential circle C is changed step by step between 0 and RM ⁠, and for each step, line-arc-line segments ln,i=aιeι′¯ ⁠, an=aιaJ¯ ⁠, and ln,j=aJeJ′¯ are calculated. Then, two cylinder surfaces and a part of a toms surface whose axes coincide with the three segments are considered, and the distance error between scanned points and the surfaces are calculated. Finally, a combination of the segments that has the least distance error is selected. Figure 9 Open in new tabDownload slide Interpolation of elbows. 5.6 Removing isolated axis segments After recognizing the axes of the piping system, some nonpipe objects, such as supporting materials, are still misclassified into the piping system. To remove them, based on the connectivity, if a segment does not connect any other segments and the length of the segment is less than a threshold τiso ⁠, the segment is removed from the points of the piping system. 6 Results 6.1 Experimental results As one of the recognition experiments, as shown in Figure 10, a large point cloud was scanned from a real oil rig by a terrestrial laser scanner (Cyra Technologies CYRAX2500). It has 4,524,324 points. The thresholds used were rmax=0.20 ⁠, rmin=0.03 ⁠, r1=0.05 ⁠, τ1=0.30 ⁠, and τiso=0.3m ⁠. Other necessary parameter values were taken as the ones recommended in sections 3, 4 and 5. Figure 10 Open in new tabDownload slide The original scanned points (upper) and the recognition result of the piping system (lower) of an oil rig. The total recognition process took 1234.8 sec on a PC (Xeon E55202. 2.27GHz), which included kd-tree construction (20.8 sec.), creating grid cells (2.7 sec.), estimating the normal vector (28.6 sec.), extracting points on a piping system (837.1 sec.), estimating pipes on a piping system (319.5 sec.), estimating parameters of pipes (13.9 sec.), and recognizing the connection relationship (6.2 sec.). The recognition results of the straight pipes, elbows, and junctions in the piping system are shown in Figure 10. The green cylinder expresses a straight pipe, the red toms expresses an elbow, and the blue cylinders express a junction. The recognition accuracies of the straight pipes and the connecting parts are also summarized in Table 1. The tme classes of the elements were counted by observation of the point cloud data. The recognition rate ofthe straight pipe was about 90%, that of the elbows was 92%, and that ofjunctions was 87%. Compared to the recognition rate of our former study [12], the recognition rate of straight pipes, elbows, and junctions were all improved greatly. The reason for this improvement was considered to be that by introducing the step of recognizing pipes in a piping system, almost all parts of pipes could be exhaustively extracted and recognized. Table 1 Accuracy of the piping system recognition of an oil rig. Open in new tab Table 1 Accuracy of the piping system recognition of an oil rig. Open in new tab As a second example of recognition shown in Figure 11, a large point cloud was scanned from a chemical plant by a terrestrial laser scanner. It had 98,624,221 points. The thresholds used were rmax=1.25 ⁠, rmin=0.05 ⁠, r1=0.03 ⁠, τ1=0.70 ⁠, and τiso=0.30m ⁠. The other parameter values were taken as the ones recommended in sections 3, 4, and 5. Figure 11 Open in new tabDownload slide The original scanned points (upper) and the recognition result of the piping system (lower) of a chemical plant. The total recognition process took 33821.5 sec., which included kd-tree construction (751.1 sec.), creating grid cells (20.6 sec.), estimating the normal vector (618.1 sec.), extracting points on a piping system (20051.2 sec.), estimating pipes on a piping system (7952.9 sec.), estimating parameters of pipes (4332.2 sec.), and recognizing the connection relationship (4.6 sec.). The recognition results of the straight pipes, elbows, and junctions in the piping system are shown in Figure 11. The recognition accuracies of the straight pipes and the connecting parts are also summarized in Table 2. The true classes of the elements were given by the ground truth CAD data of the plant, which had been manually modeled by a skilled operator. The recognition rate of the straight pipe was about 86%, that of elbows was 88%, and that ofjunctions was 71%. Table 2 Accuracy of the piping system recognition of a chemical plant. Open in new tab Table 2 Accuracy of the piping system recognition of a chemical plant. Open in new tab 6.2 Guideline of the parameters In recognition of the piping system, five threshold values used are rmax ⁠, rmin ⁠, r1 ⁠, τ1 and τiso ⁠. Selection criteria of these thresholds are classified into the logical criteria and trial-and-error criteria: rmax and rmin are the maximum and minimum thresholds for the radius of recognized pipes. rmax should be set a bit larger from the maximum radius of the pipes in the scanned environment, and rmin should be set a bit lower than their minimum radius. These parameters can be set based on the estimated maximum or minimum pipe radius obtained from observing the scanned points ofthe piping system. r1 is the radius of the local search area used in region growing. r1 should be set so that the search area includes at least one neighboring point. In our experiments, r1 was set to include about 10 points in the search area on a pipe which had the lowest density point. τ1 is the threshold for the maximum distance between the endpoints of two proximal axis segments to be connected. Also, its appropriate value should be selected with trial and error. τiso is the threshold for the maximum length of an isolated axis segment to be removed. To examine the effects of changing τ1 and τiso ⁠, the results for the partial point clouds (440,033 points) of the oil rig are compared and shown in Figures 12 and 13 with changing τ1 and τiso ⁠. The thresholds used were rmax=0.20 ⁠, rmin=0.03 and r1=0.05m ⁠, and τ1 and τiso were changed to 0.10, 0.30, and 1.50 m. The recognition rates of the straight pipes and the connecting parts are also summarized in Tables 3 and 4. Table 3 Accuracy of the piping system recognition of an oil rig. Open in new tab Table 3 Accuracy of the piping system recognition of an oil rig. Open in new tab Table 4 Accuracy of the piping system recognition of an oil rig. Open in new tab Table 4 Accuracy of the piping system recognition of an oil rig. Open in new tab As shown in Figure 12 and Table 3, if τ1 is selected to be much smaller than the connected pipe radius (τ1=0.10m) ⁠, most junction parts are mis-recognized as elbow parts. To avoid these situations, it is better to set τ1 to about at least 3–4 times the size of the connected pipe radius. In contrast, if τ1 becomes larger than that (τ1=1.50m) ⁠, some false pairs of segments are connected. It is difficult to find a maximum range of τ1 because it greatly depends on the range of the occluded regions and the structure of the piping system. Therefore, so far, τ1 has been set with trial and error. Figure 12 Open in new tabDownload slide A part of the original scanned points (left) and the recognition results of the piping system (right) of an oil rig. On the other hand, as shown in Figure 13 and Table 4, if τiso is selected to be too small (τ1=0.10m) ⁠, some nonpipe objects still remain as pipes. In contrast, if τiso becomes too large (τ1=1.50m) ⁠, some isolated straight pipes disappear. Unfortunately, it is difficult to find the optimal value of τiso in an a priori manner, because it greatly depends on the structure of the piping system. Therefore, so far, τiso is set with trial and error manner. However, as shown in the recognition results of the experiment, the setting of τiso is not necessarily strict. τiso can be set to any value less than the length where straight pipes can be distinguish from non-pipe objects. The results of the experiment showed that τiso did not affect the recognition rates of the piping system much, if this condition is satisfied. Figure 13 Open in new tabDownload slide A part of the original scanned points (left) and the recognition results of the piping system (right) of an oil rig. 6.3 Discussion In these results, the lowest recognition rates of the straight pipes, elbows, junctions were about 86%, 88%, and 71% respectively. The recognition rates of the related work [6] were 97%, 100%, and 86%. However, their input point clouds only consisted of a cloud on the pipes, and the amount, density, and complexity of the piping objects were much smaller than ours. On the other hand [16, 17], the recognition rates of the cylindrical surface of industrial tools and commodities range from 75% to 90%. Considering the complexity of the input point clouds, our recognition rates were considered to be appropriate. If there is any pipe with a large radius, the range of the pipe radius to be recognized increases. Therefore, non-pipe objects which are misrecognized as pipes increase. These mis-recognized objects can be connected to other true pipes in the step of complementing segments of straight, junction, and elbow paits. Therefore, the accuracy ofthe piping system recognition becomes worse. For this reason, the accuracy of the recognition of the chemical plant became lower than that ofthe oil rig in our results. Also, in both of these results, false positive recognition in straight pipes, junctions, and elbows was not uncommon. This was because the paitial shape of some non-pipe obj ects, such as H-beams, had a similar shape to that of a cylinder, and those parts were misrecognized as pipes. These two problems can be reduced by cross-sectional analysis. This is left for future work. 7 Conclusions A new algorithm was proposed that could automatically recognize a piping system from registered laser-scanned points of a plant. Normal-based region growing allows one to exhaustively extract the points on a piping system and to segment the points of each pipe. Cylinder fitting could extract only the point, including straight pipes, elbows, and junctions. Tracing axes, fitting arc-line segments, and the complementing of segments could recognize the position of straight pipes, elbows, and junctions and their connection relationship. 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In: Proceedings of IEEE International Conference on Robotics and Automation ; 2007 Apr 10–14 ; Roma, Italy ; p. 1086 – 1091 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Society of CAD/CAM Engineers & Techno-Press This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) Society of CAD/CAM Engineers & Techno-Press
TI - As-built modeling of piping system from terrestrial laser-scanned point clouds using normal-based region growing
JF - Journal of Computational Design and Engineering
DO - 10.7315/jcde.2014.002
DA - 2014-01-01
UR - https://www.deepdyve.com/lp/oxford-university-press/as-built-modeling-of-piping-system-from-terrestrial-laser-scanned-L97bPoYIDA
SP - 13
EP - 26
VL - 1
IS - 1
DP - DeepDyve
ER -