We present a method for organizing a heterogeneous collection of 3D shapes for overview and exploration. Instead of relying on quantitative distances, which may become unreliable between dissimilar shapes, we introduce aqualitativeanalysis which utilizes multiple distance measures but only in cases where the measures can be reliably compared. Our analysis is based on the notion ofquartets, each defined by two pairs of shapes, where the shapes in each pair are close to each other, but far apart from the shapes in the other pair. Combining the information from many quartets computed across a shape collection using several distance measures, we create a hierarchical structure we callcategorization treeof the shape collection. This tree satisfies the topological (qualitative) constraints imposed by the quartets creating an effective organization of the shapes. We present categorization trees computed on various collections of shapes and compare them to ground truth data from human categorization. We further introduce the concept ofdegree of separationchart for every shape in the collection and show the effectiveness of using it for interactive shapes exploration.

This paper presents a technique that allows quick conversion of acquired low-quality data from consumer-level scanning devices to high-quality 3D models with labeled semantic parts and meanwhile their assembly reasonably close to the underlying geometry. This is achieved by a novel structure recovery approach that is essentially local to global and bottom up, enabling the creation of new structures by assembling existing labeled parts with respect to the acquired data. We demonstrate that using only a small-scale shape repository, our part assembly approach is able to faithfully recover a variety of high-level structures from only a single-view scan of man-made objects acquired by the Kinect system, containing a highly noisy, incomplete 3D point cloud and a corresponding RGB image.

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.

Paper architectures are 3D paper buildings created by folding and cutting. The creation process of paper architecture is often labor-intensive and highly skill-demanding, even with the aid of existing computer-aided design tools. We propose an automatic algorithm for generating paper architectures given a user-specified 3D model. The algorithm is grounded on geometric formulation of planar layout for paper architectures that can be popped-up in a rigid and stable manner, and sufficient conditions for a 3D surface to be popped-up from such a planar layout. Based on these conditions, our algorithm computes a class of paper architectures containing two sets of parallel patches that approximate the input geometry while guaranteed to be physically realizable. The method is demonstrated on a number of architectural examples, and physically engineered results are presented.