Hierarchical 3D line restoration based on angular proximity in structured environments

We present a method based on a hierarchical clustering to restore the 3D lines of structured environments. In previous approaches, the restoration of noisy 3D lines is a challenging problem because it is difficult to define a suitable similarity measure discriminative to other lines. Our motivation to overcome the difficulty is that most structured scenes consist of sets of parallel 3D lines with the same angular proximity, which provides a hierarchical similarity measure for structured 3D lines. Accordingly, our restoration method works in a manner that clustering is hierarchically performed on angular and distance levels. The 3D line restoration is then achieved by finding the center of each cluster. The framework also makes the clustered 3D lines align along the associated angular directions. We compare the proposed algorithm with methods using no knowledge of the angular information, and demonstrate its effectiveness through real-world experiments.