Indoor scene reconstruction using feature sensitive primitive extraction and graph-cut

TLDR: The main idea behind the approach is a graph-cut formulation to solve an inside/outside labeling of a space partitioning of an indoor scene, which shows watertight surface meshes reconstructed from point clouds measured on multi-level buildings.

Abstract: We present a method for automatic reconstruction of permanent structures, such as walls, doors and ceilings, given a raw point cloud of an indoor scene. The main idea behind our approach is a graph-cut formulation to solve an inside/outside labeling of a space partitioning. We rst partition the space in order to align the reconstructed models with permanent structures. The horizontal structures are located through analysis of the vertical point distribution, while vertical wall structures are detected through feature preserving multi-scale line tting, followed by clustering in a Hough transform space. The nal surface is extracted through a graph-cut formulation that trades faithfulness to measurement data for geometric complexity. A series of experiments show watertight surface meshes reconstructed from point clouds measured on multi-level buildings.

Figures

Figure 8: Global clustering of wall segments. Upper left: Clustered wall segments. Upper right: Lines extracted without global clustering. Lower left: Global clustering using Hough transform leads to reduction of the number of lines. Lower right: Over-simplification induced by coarse resolution for Hough Accumulator and a high value for ǫ.

Figure 7: Multi-scale line hypothesis. Wall directions depicted by color in real data scene. Left: Excerpt of scene containing a corridor. The circular wall section is matched accurately. Middle: Some smaller segments have an unsharp diffuse fitting. Right: Segments are separated after filtering.

Figure 3: Horizontal slicing applied to a synthetic scene. Top: Input point cloud. The excerpt shown below is highlighted by a black box. Left: Distribution along vertical direction. The point cloud is split horizontally within a small range around the peaks. Ranges for horizontal structure-slices are depicted in blue, and yellow for wall-slices. Middle: Excerpt of original point cloud in side-view. Right: Side-view of excerpt colored by slice type.

Figure 9: 3D space partitioning. The 2D cell decomposition is extended in 3D through stacking and vertical extrusion. mi denote the height of the detected peak during the horizontal slicing step.

Figure 14: Reconstruction from a synthetic data set. Two views on the same reconstruction are shown, colored by the Hausdorff distance from the result to the ground truth.

Figure 15: Reconstruction of Kinect-recorded indoor scene. Upper left: Input point cloud featuring an office room. Upper & lower right: Reconstructed model. Lower left: The labeled cell decomposition exhibits a good alignment of the room with the exception of the occluded corner.

Frequently asked questions

Q1. What are the contributions in "Indoor scene reconstruction using feature sensitive primitive extraction and graph-cut" ?

The authors present a method for automatic reconstruction of permanent structures, such as walls, floors and ceilings, given a raw point cloud of an indoor scene. The main idea behind their approach is a graph-cut formulation to solve an inside/outside labeling of a space partitioning. The horizontal structures are located through analysis of the vertical point distribution, while vertical wall structures are detected through feature preserving multi-scale line fitting, followed by clustering in a Hough transform space. 

Q2. What are the future works in "Indoor scene reconstruction using feature sensitive primitive extraction and graph-cut" ?

As future work, the authors will investigate the use of non-planar primitives and non-vertical walls in order to both improve accuracy and decrease complexity by simplifying the space partitioning. The authors will also further investigate regularization through the Hough transform. 

Q3. How do the authors construct a watertight model of an indoor space?

Through global energy minimization the authors label the cells of a 3D space partitioning in order to reconstruct a watertight model consolidating missing data. 

Q4. What is the first technical contribution for the reconstruction of a cluttered indoor space?

Their first technical contribution is a multi-scale, feature-preserving approach for detecting walls as line segments, followed by global clustering in a Hough transform space in order to align the reconstructed model with the permanent structures. 

Q5. What is the way to trade data faithfulness for regularity?

As the clustering is also restricted by the choice of ǫ, a coarser resolution of the Hough Accumulator can be used as a starting point for parameterization: 2◦ · τ. α is used to trade data faithfulness for regularity in the energy minimization formulation. 

Q6. How do the authors partition the bounding box?

The authors partition the bounding box by first splitting the horizontal cross section of the bounding box into single 2D cell decomposition and stacking copies of that 2D cell decomposition vertically to yield the 3D space partitioning. 

Q7. What are the common knowledge assumptions for the reconstruction of permanent structures?

Common knowledge assumptions are piecewise planar permanent structures and Manhattan-World scenes, i.e., exactly three orthogonal directions: two for the walls and one for floors and ceilings. 

Q8. Why do larger cells receive a higher penalty from the regularization term?

Due to the different sizes of cells, larger cells receive a higher penalty from the regularization term as they have a larger surface area. 

Q9. How do the authors reconstruct a scene in a cluttered environment?

Through detecting the permanent structures in a cluttered scene the authors reconstruct a model of the indoor space with satisfactory tradeoff between accuracy and low complexity. 

Q10. What is the rationale for the ray cast from a point?

Their rationale is, that a ray cast from a point has an odd number of intersections with the geometry if the point is in empty space and an even number if it is in solid space. 

Q11. How much noise is required for clustering of the wall directions?

Compared to commercial-grade laser scanners the high level of noise requires a high tolerance value (ǫ = 6 cm) for clustering of the wall directions. 

Q12. How is the binary labeling problem solved?

The authors formulated this binary labeling problem as a global energy minimization, solved through a graph-cut algorithm (Boykov et al., 2001). 

Q13. How is the algorithmic complexity of the ray casting?

The algorithmic complexity of the ray casting is quadratic in the number of cells of the space decomposition, this number being itself related to the level of detail adjusted through a tolerant or selective line clustering.