Automatically discovering high-level facade structures in unorganized 3D point clouds of urban scenes is crucial for applications like digitalization of real cities. However, this problem is challenging due to poor-quality input data, contaminated with severe missing areas, noise and outliers. This work introduces the concept of adaptive partitioning to automatically derive a flexible and hierarchical representation of 3D urban facades. Our key observation is that urban facades are largely governed by concatenated and/or interlaced grids. Hence, unlike previous automatic facade analysis works which are typically restricted to globally rectilinear grids, we propose to automatically partition the facade in an adaptive manner, in which the splitting direction, the number and location of splitting planes are all adaptively determined. Such an adaptive partition operation is performed recursively to generate a hierarchical representation of the facade. We show that the concept of adaptive partitioning is also applicable to flexible and robust analysis of image facades. We evaluate our method on a dozen of LiDAR scans of various complexity and styles, and the image facades from the eTRIMS database and the Ecole Centrale Paris database. A series of applications that benefit from our approach are also demonstrated.

In this paper, we develop a novel blind source separation (BSS) method for nonnegative and correlated data, particularly for the nearly degenerate data. The motivation lies in nuclear magnetic resonance (NMR) spectroscopy, where a multiple mixture NMR spectra are recorded to identify chemical compounds with similar structures (degeneracy).

We propose a new framework to reconstruct building details by automatically assembling 3D templates on coarse textured building models. In a preprocessing step, we generate an initial coarse model to approximate a point cloud computed using Structure from Motion and Multi View Stereo, and we model a set of 3D templates of facade details. Next, we optimize the initial coarse model to enforce consistency between geometry and appearance (texture images). Then, building details are reconstructed by assembling templates on the textured faces of the coarse model. The 3D templates are automatically chosen and located by our optimization-based template assembly algorithm that balances image matching and structural regularity. In the results, we demonstrate how our framework can enrich the details of coarse models using various data sets.

In geometric modeling and processing, computer graphics and computer vision, smooth surfaces are approximated by discrete triangular meshes reconstructed from sample points on the surfaces. A fundamental problem is to design rigorous algorithms to guarantee the geometric approximation accuracy by controlling the sampling density. This paper gives explicit formulae to the bounds of Hausdorff distance, normal distance and Riemannian metric distortion between the smooth surface and the discrete mesh in terms of principle curvature and the radii of geodesic circum-circle of the triangles. These formulae can be directly applied to design sampling density for data acquisitions and surface reconstructions. Furthermore, we prove that the meshes induced from the Delaunay triangulations of the dense samples on a smooth surface are convergent to the smooth surface under both Hausdorff distance and normal

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