TopoLAP: Topology Recovery for Building Reconstruction by Deducing the Relationships between Linear and Planar Primitives
Abstract
:1. Introduction
- Structural contour extraction from point clouds, taking full advantages of the characteristics of topological and textural information.
- Topology recovery for the incomplete planar primitives based on the relationship between the linear and planar primitives, which generates a complete set of candidate planes to describe the building.
- An optimized pipeline to reconstruct polyhedral models efficiently with high fitness to point clouds and high correctness of planar primitives.
2. Related Works
2.1. Linear Primitive Extraction and Generalization
2.2. Planar Primitive-Based Building Reconstruction
2.3. Topology Repair towards the Incomplete Dataset
3. Overview
4. Structural Planar Contour Extraction
4.1. Linear Feature Detection
Algorithm 1. Boundary line contouring | ||
Input: Concave hull point string ; Boundary lines and the endpoints | ||
Output: Looped boundary line strings ; | ||
1 for each do | ||
2 | if then | |
3 | Status() = UNUSED | |
4 | end | |
5 end 6 for each do | ||
7 8 9 | closest to closest to for each Status() = UNUSED, do | |
10 | add to the final endpoint set | |
11 12 | end for each do | |
13 14 | add to | |
15 | end | |
16 end |
4.2. Contour Optimization
4.2.1. Hypothesis Generation
4.2.2. Energy Formulation
5. Plane Deduction Based on the Relationships between Linear and Planar Primitives
5.1. Geometry Primitive Candidates
5.2. Plane Detection from Lines and Validation Criterion
5.2.1. Line-and-Plane (LaP) Group
5.2.2. Line-and-Line (LaL) Unit
- Connected junction. Border Lines are considered as connected and snapped together if they satisfy that two lines intersect, and the sum of the distance from the intersection point to the closer end point of each segment is less than a distance threshold. (a) If three or more border lines are connected as a triple junction, check if the extended line of the outward borders meets an existing plane candidate. Connect the intersection points on the plane if found, otherwise, connect the two outward endpoints of the triple junction as the contour to enclose the unit. (b) If only two border lines connected, check if there are planes intersect with the junction. Take the connections of intersection points as contour segments if planes are found. If no plane is around (refer to the third subfigure in Figure 9b), find inner edges from and points from UA inside the angle between the two segments. When more than candidates are found, close the group polygon by convex hull; otherwise, add parallel segments to but leave this LaP group pending in the candidate pools. (c) For the junction that the segments are intersected but the endpoints are not connected, interrupt the segments by the intersection point and divide the group into 4 areas, each of which forms as the type (b). Examine each sub-part as (b) and confirm that with the largest sum of candidates the final LaP group.
- Parallel pair. Border lines that are confirmed as parallel pair are valid only if more than candidates can be attached to the LaP. Then the borders are connected similarly to the triple junction as illustrated in Figure 9a.
- Scattering lines. LaP group where no connected junction or parallel pair can be detected is treated as a group of scattering lines (Figure 9e) and is validated simply by the number of lines and points attached to it, i.e., abandon the group to which less than candidates can be attached.
5.3. Deduction Iterations
- Planes are detected from based on RANSAC and new LaP groups are formed.
- For each , the LaL Unit is identified and evaluated according to each unit pattern. Once the LaL Unit is validated, assemble the lines of as a new plane and assign lines and points candidates that are -close to this plane, retrieving from and respectively, to .
- Subsequently, the structural contour of the plane is extracted based on the algorithm proposed in Section 4 and the contour segments are added into if available.
- Back to start and repeat steps 1–3. The next iteration starts with the increased until no more LaP group can be detected and/or no more LaL units can be validated.
5.4. Watertight Polyhedral Model Reconstruction based on Optimized PolyFit
6. Experimental Results and Discussion
6.1. Data Overview
6.2. Building Reconstruction Results
6.3. Performance Analysis of the Linear Primitives
6.4. Limitations
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Input Planar Segments | Reference Image | Output Models | |
---|---|---|---|
Dublin1 | |||
Dublin2 | |||
Dublin3 | |||
Dublin4 | |||
Ningbo | |||
MVS |
Bld. | Input Data | Model Reconstruction | ||||
---|---|---|---|---|---|---|
#Points/av. Spacing 1 | #Images/H/Gsd 2 | #Planes/#Segments 3 | #Deduced/#Model Planes 4 | Runtime (s) | ||
Dublin1 | 1.1M/0.11 | 115/300/3.4 | 103/65 | 125/109 | 35.5 | |
Dublin2 | 695K/0.09 | 118/300/3.4 | 26/19 | 30/22 | 20.3 | |
Dublin3 | 266K/0.07 | 41/300/3.4 | 23/14 | 29/25 | 25.6 | |
Dublin4 | 158K/0.11 | 49/300/3.4 | 24/26 | 35/16 | 18.8 | |
Ningbo | 17K/0.64 | 99/900/4.8 | 15/14 | 25/14 | 15.9 | |
MVS | 237K/0.24 | 50/300/3.8 | 20/10 | 28/23 | 23.6 |
Parameter | Value | Representation | ||
---|---|---|---|---|
Dublin | Ningbo | MVS | ||
0.1 m | 1 m | 1 m | Distance threshold in plane segmentation | |
1000 | 200 | 1000 | Min points number to support a plane segment | |
Max square of circumradius of facets in α-shape mesh | ||||
2m | Max distance to intersect two planes | |||
0.5 m | 2 m | 2 m | Buffer threshold to support a line | |
10 | Smooth scalar in contour optimization | |||
5 | The min number of the sum of lines and points to support a new LaP group. |
2.5D-DC 1 | LoD2 | PolyFit | TopoLAP | ||||||
---|---|---|---|---|---|---|---|---|---|
Dublin4 | |||||||||
0.060 | 0.187 | 0.222 | 0.429 | 0.343 | 0.583 | 0.238 | 0.442 | ||
6.56 × 10−3 | 0.093 | 4.23 × 10−3 | 0.069 | 1.86 × 10−3 | 0.01 | 1.53 × 10−3 | 0.024 | ||
#Planes | 11,138 | 124 | 17 | 16 | |||||
86.6% | 91.3% | 76.9% | 82.3% | 76.5% | 76.5% | 93.7% | 93.7% | ||
Ningbo | |||||||||
0.446 | 0.885 | 0.209 | 0.517 | 0.535 | 0.946 | 0.392 | 0.761 | ||
830 × 10−3 | 0.918 | 59 × 10−3 | 0.638 | 6.69 × 10−3 | 0.224 | 6.12 × 10−3 | 0.169 | ||
#Planes | 1121 | 342 | 12 | 14 | |||||
62.3% | 67.4% | 73.6% | 82.1% | 66.7% | 66.7% | 92.8% | 100.0% |
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Liu, X.; Zhang, Y.; Ling, X.; Wan, Y.; Liu, L.; Li, Q. TopoLAP: Topology Recovery for Building Reconstruction by Deducing the Relationships between Linear and Planar Primitives. Remote Sens. 2019, 11, 1372. https://doi.org/10.3390/rs11111372
Liu X, Zhang Y, Ling X, Wan Y, Liu L, Li Q. TopoLAP: Topology Recovery for Building Reconstruction by Deducing the Relationships between Linear and Planar Primitives. Remote Sensing. 2019; 11(11):1372. https://doi.org/10.3390/rs11111372
Chicago/Turabian StyleLiu, Xinyi, Yongjun Zhang, Xiao Ling, Yi Wan, Linyu Liu, and Qian Li. 2019. "TopoLAP: Topology Recovery for Building Reconstruction by Deducing the Relationships between Linear and Planar Primitives" Remote Sensing 11, no. 11: 1372. https://doi.org/10.3390/rs11111372