Geometric model fitting is a fundamental task in computer graphics and computer vision. However, most geometric model fitting methods are unable to fit an arbitrary geometric model (e.g. a surface with holes) to incomplete data, due to that the similarity metrics used in these methods are unable to measure the rigid partial similarity between arbitrary models. This paper hence proposes a novel rigid geometric similarity metric, which is able to measure both the full similarity and the partial similarity between arbitrary geometric models. The proposed metric enables us to perform partial procedural geometric model fitting (PPGMF). The task of PPGMF is to search a procedural geometric model space for the model rigidly similar to a query of non-complete point set. Models in the procedural model space are generated according to a set of parametric modeling rules. A typical query is a point cloud. PPGMF is very useful as it can be used to fit arbitrary geometric models to non-complete (incomplete, over-complete or hybrid-complete) point cloud data. For example, most laser scanning data is non-complete due to occlusion. Our PPGMF method uses Markov chain Monte Carlo technique to optimize the proposed similarity metric over the model space. To accelerate the optimization process, the method also employs a novel coarse-to-fine model dividing strategy to reject dissimilar models in advance. Our method has been demonstrated on a variety of geometric models and non-complete data. Experimental results show that the PPGMF method based on the proposed metric is able to fit non-complete data, while the method based on other metrics is unable. It is also shown that our method can be accelerated by several times via early rejection.
Given a noisy and incomplete point set, we introduce a method that simultaneously recovers a set of locally fitted primitives along with their global mutual relations. We operate under the assumption that the data corresponds to a man-made engineering object consisting of basic primitives, possibly repeated and globally aligned under common relations. We introduce an algorithm to directly couple the local and global aspects of the problem. The local fit of the model is determined by how well the inferred model agrees to the observed data, while the global relations are iteratively learned and enforced through a constrained optimization. Starting with a set of initial RANSAC based locally fitted primitives, relations across the primitives such as orientation, placement, and equality are progressively learned and conformed to. In each stage, a set of feasible relations are extracted among the candidate relations, and then aligned to, while best fitting to the input data. The global coupling corrects the primitives obtained in the local RANSAC stage, and brings them to precise global alignment. We test the robustness of our algorithm on a range of synthesized and scanned data, with varying amounts of noise, outliers, and non-uniform sampling, and validate the results against ground truth, where available. LiDAR scanning has become a prevalent technique for digitalizing large-scale outdoor scenes. However, the raw LiDAR data often contain imperfections, e.g., missing large regions, anisotropy of sampling density, and contamination of noise and outliers, which are the major obstacles that hinder its more ambitious and higher level applications in digital city modeling. Observing that 3D urban scenes can be locally described with several low dimensional subspaces, we propose to locally classify the neighborhoods of the scans to model the substructures of the scenes. The key enabler is the adaptive kernel-scale scoring, filtering and clustering of substructures, making it possible to recover the local structures at all points simultaneously, even in the presence of severe data imperfections. Integrating the local analyses leads to robust shape detection from raw LiDAR data. On this basis, we develop several urban scene applications and verify them on a number of LiDAR scans with various complexities and styles, which demonstrates the effectiveness and robustness of our methods. Abstract This paper presents an automatic method for reconstruction of building facade models from terrestrial laser scanning data. Important facade elements such as walls and roofs are distinguished as features. Knowledge about the features’ sizes, positions, orientations, and topology is then introduced to recognize these features in a segmented laser point cloud. An outline polygon of each feature is generated by least squares fitting, convex hull fitting or concave polygon fitting, according to the size of the feature. Knowledge is used again to hypothesise the occluded parts from the directly extracted feature polygons. Finally, a polyhedron building model is combined from extracted feature polygons and hypothesised parts. The reconstruction method is tested with two data sets containing various building shapes. Urban models are key to navigation, architecture and entertainment. Apart from visualizing facades, a number of tedious tasks remain largely manual (e.g. compression, generating new facade designs and structurally comparing facades for classification, retrieval and clustering). We propose a novel procedural modelling method to automatically learn a grammar from a set of facades, generate new facade instances and compare facades. To deal with the difficulty of grammatical inference, we reformulate the problem. Instead of inferring a compromising, one-size-fits-all, single grammar for all tasks, we infer a model whose successive refinements are production rules tailored for each task. We demonstrate our automatic rule inference on datasets of two different architectural styles. Our method supercedes manual expert work and cuts the time required to build a procedural model of a facade from several days to a few milliseconds. We present a complete system to semantically decompose and reconstruct 3D models from point clouds. Different than previous urban modeling approaches, our system is designed for residential scenes, which consist of mainly low-rise buildings that do not exhibit the regularity and repetitiveness as high-rise buildings in downtown areas. Our system first automatically labels the input into distinctive categories using supervised learning techniques. Based on the semantic labels, objects in different categories are reconstructed with domain-specific knowledge. In particular, we present a novel building modeling scheme that aims to decompose and fit the building point cloud into basic blocks that are block-wise symmetric and convex. This building representation and its reconstruction algorithm are flexible, efficient, and robust to missing data. We demonstrate the effectiveness of our system on various datasets and compare our building modeling scheme with other state-of-the-art reconstruction algorithms to show its advantage in terms of both quality and speed. Recent advances in scanning technologies, in particular devices that extract depth through active sensing, allow fast scanning of urban scenes. Such rapid acquisition incurs imperfections: large regions remain missing, significant variation in sampling density is common, and the data is often corrupted with noise and outliers. However, buildings often exhibit large scale repetitions and self-similarities. Detecting, extracting, and utilizing such large scale repetitions provide powerful means to consolidate the imperfect data. Our key observation is that the same geometry, when scanned multiple times over reoccurrences of instances, allow application of a simple yet effective non-local filtering. The multiplicity of the geometry is fused together and projected to a base-geometry defined by clustering corresponding surfaces. Denoising is applied by separating the process into off-plane and in-plane phases. We show that the consolidation of the reoccurrences provides robust denoising and allow reliable completion of missing parts. We present evaluation results of the algorithm on several LiDAR scans of buildings of varying complexity and styles. Line segment detection in images is already a well-investigated topic, although it has received considerably less attention in 3D point clouds. Benefiting from current LiDAR devices, large-scale point clouds are becoming increasingly common. Most human-made objects have flat surfaces. Line segments that occur where pairs of planes intersect give important information regarding the geometric content of point clouds, which is especially useful for automatic building reconstruction and segmentation. This paper proposes a novel method that is capable of accurately extracting plane intersection line segments from large-scale raw scan points. The 3D line-support region, namely, a point set near a straight linear structure, is extracted simultaneously. The 3D line-support region is fitted by our Line-Segment-Half-Planes (LSHP) structure, which provides a geometric constraint for a line segment, making the line segment more reliable and accurate. We demonstrate our method on the point clouds of large-scale, complex, real-world scenes acquired by LiDAR devices. We also demonstrate the application of 3D line-support regions and their LSHP structures on urban scene abstraction. We present a novel and robust method for modeling cities from 3D-point data. Our algorithm provides a more complete description than existing approaches by reconstructing simultaneously buildings, trees and topologically complex grounds. A major contribution of our work is the original way of modeling buildings which guarantees a high generalization level while having semantized and compact representations. Geometric 3D-primitives such as planes, cylinders, spheres or cones describe regular roof sections, and are combined with mesh-patches that represent irregular roof components. The various urban components interact through a non-convex energy minimization problem in which they are propagated under arrangement constraints over a planimetric map. Our approach is experimentally validated on complex buildings and large urban scenes of millions of points, and is compared to state-of-the-art methods. With the proliferation of acquisition devices, gathering massive volumes of 3D data is now easy. Processing such large masses of pointclouds, however, remains a challenge. This is particularly a problem for raw scans with missing data, noise, and varying sampling density. In this work, we present a simple, scalable, yet powerful data reconstruction algorithm. We focus on reconstruction of man-made scenes as regular arrangements of planes (RAP), thereby selecting both local plane-based approximations along with their global inter-plane relations. We propose a novel selection formulation to directly balance between data fitting and the simplicity of the resulting arrangement of extracted planes. The main technical contribution is a formulation that allows less-dominant orientations to still retain their internal regularity, and not become overwhelmed and regularized by the dominant scene orientations. We evaluate our approach on a variety of complex 2D and 3D pointclouds, and demonstrate the advantages over existing alternative methods. We propose a complete framework for the automatic modeling from point cloud data. Initially, the point cloud data are preprocessed into manageable datasets, which are then separated into clusters using a novel two-step, unsupervised clustering algorithm. The boundaries extracted for each cluster are then simplified and refined using a fast energy minimization process. Finally, three-dimensional models are generated based on the roof outlines. The proposed framework has been extensively tested, and the results are reported. We introduce an interactive tool which enables a user to quickly assemble an architectural model directly over a 3D point cloud acquired from large-scale scanning of an urban scene. The user loosely defines and manipulates simple building blocks, which we call SmartBoxes, over the point samples. These boxes quickly snap to their proper locations to conform to common architectural structures. The key idea is that the building blocks are smart in the sense that their locations and sizes are automatically adjusted on-the-fly to fit well to the point data, while at the same time respecting contextual relations with nearby similar blocks. SmartBoxes are assembled through a discrete optimization to balance between two snapping forces defined respectively by a data-fitting term and a contextual term, which together assist the user in reconstructing the architectural model from a sparse and noisy point cloud. We show that a combination of the user's interactive guidance and high-level knowledge about the semantics of the underlying model, together with the snapping forces, allows the reconstruction of structures which are partially or even completely missing from the input. People learning new concepts can often generalize successfully from just a single example, yet machine learning algorithms typically require tens or hundreds of examples to perform with similar accuracy. People can also use learned concepts in richer ways than conventional algorithms—for action, imagination, and explanation. We present a computational model that captures these human learning abilities for a large class of simple visual concepts: handwritten characters from the world’s alphabets. The model represents concepts as simple programs that best explain observed examples under a Bayesian criterion. On a challenging one-shot classification task, the model achieves human-level performance while outperforming recent deep learning approaches. We also present several “visual Turing tests” probing the model’s creative generalization abilities, which in many cases are indistinguishable from human behavior.