Learning Line Features in 3D Geometry

Feature detection in geometric datasets is a fundamental tool for solving shape matching problems such as partial symmetry detection. Traditional techniques usually employ a priori models such as crease lines that are unspecific to the actual application. Our paper examines the idea of learning geometric features. We introduce a formal model for a class of linear feature constellations based on a Markov chain model and propose a novel, efficient algorithm for detecting a large number of features simultaneously. After a short user‐guided training stage, in which one or a few example lines are sketched directly onto the input data, our algorithm automatically finds all pieces of geometry similar to the marked areas. In particular, the algorithm is able recognize larger classes of semantically similar but geometrically varying features, which is very difficult using unsupervised techniques. In a number of experiments, we apply our technique to point cloud data from 3D scanners. The algorithm is able to detect features with very low rates of false positives and negatives and to recognize broader classes of similar geometry (such as “windows” in a building scan) even from few training examples, thereby significantly improving over previous unsupervised techniques.     

Large‐Scale Integer Linear Programming for Orientation Preserving 3D Shape Matching

We study an algorithmic framework for computing an elastic orientation‐preserving matching of non‐rigid 3D shapes. We outline an Integer Linear Programming formulation whose relaxed version can be minimized globally in polynomial time. Because of the high number of optimization variables, the key algorithmic challenge lies in efficiently solving the linear program. We present a performance analysis of several Linear Programming algorithms on our problem. Furthermore, we introduce a multiresolution strategy which allows the matching of higher resolution models.     

Approximate on‐Surface Distance Computation using Quasi‐Developable Charts

There is a vast number of applications that require distance field computation over triangular meshes. State‐of‐the‐art algorithms have quadratic or sub‐quadratic worst‐case complexity, making them impractical for interactive applications. While most of the research on this subject has been focused on reducing the computation complexity of the algorithms, in this work we propose an approximate algorithm that achieves similar results working in lower resolutions of the input meshes. The creation of lower resolution meshes is the essence of our proposal. The idea is to identify regions on the input mesh that can be unfolded into planar regions with minimal area distortion (i.e. quasi‐developable charts). Once charts are computed, their interior is re‐triangulated to reduce the number of triangles, which results in a collection of simplified charts that we call a base mesh. Due to the properties of quasi‐developable regions, we are able to compute distance fields over the base mesh instead of over the input mesh. This reduces the memory footprint and data processed for distance computations, which is the bottleneck of these algorithms. We present results that are one order of magnitude faster than current exact solutions, with low approximation errors.     

Piecewise‐Planar 3D Reconstruction with Edge and Corner Regularization

This paper presents a method for the 3D reconstruction of a piecewise‐planar surface from range images, typically laser scans with millions of points. The reconstructed surface is a watertight polygonal mesh that conforms to observations at a given scale in the visible planar parts of the scene, and that is plausible in hidden parts. We formulate surface reconstruction as a discrete optimization problem based on detected and hypothesized planes. One of our major contributions, besides a treatment of data anisotropy and novel surface hypotheses, is a regularization of the reconstructed surface w.r.t. the length of edges and the number of corners. Compared to classical area‐based regularization, it better captures surface complexity and is therefore better suited for man‐made environments, such as buildings. To handle the underlying higher‐order potentials, that are problematic for MRF optimizers, we formulate minimization as a sparse mixed‐integer linear programming problem and obtain an approximate solution using a simple relaxation. Experiments show that it is fast and reaches near‐optimal solutions.     

Retargeting 3D Objects and Scenes with a General Framework

In this paper, we introduce an interactive method suitable for retargeting both 3D objects and scenes. Initially, the input object or scene is decomposed into a collection of constituent components enclosed by corresponding control bounding volumes which capture the intra‐structures of the object or semantic grouping of objects in the 3D scene. The overall retargeting is accomplished through a constrained optimization by manipulating the control bounding volumes. Without inferring the intricate dependencies between the components, we define a minimal set of constraints that maintain the spatial arrangement and connectivity between the components to regularize the valid retargeting results. The default retargeting behavior can then be easily altered by additional semantic constraints imposed by users. This strategy makes the proposed method highly flexible to process a wide variety of 3D objects and scenes under an unified framework. In addition, the proposed method achieved more general structure‐preserving pattern synthesis in both object and scene levels. We demonstrate the effectiveness of our method by applying it to several complicated 3D objects and scenes.     

Hierarchical Convex Approximation of 3D Shapes for Fast Region Selection

Given a 3D solid model S represented by a tetrahedral mesh, we describe a novel algorithm to compute a hierarchy of convex polyhedra that tightly enclose S. The hierarchy can be browsed at interactive speed on a modern PC and it is useful for implementing an intuitive feature selection paradigm for 3D editing environments. Convex parts often coincide with perceptually relevant shape components and, for their identification, existing methods rely on the boundary surface only. In contrast, we show that the notion of part concavity can be expressed and implemented more intuitively and efficiently by exploiting a tetrahedrization of the shape volume. The method proposed is completely automatic, and generates a tree of convex polyhedra in which the root is the convex hull of the whole shape, and the leaves are the tetrahedra of the input mesh. The algorithm proceeds bottom‐up by hierarchically clustering tetrahedra into nearly convex aggregations, and the whole process is significantly fast. We prove that, in the average case, for a mesh of n tetrahedra O(n log² n) operations are sufficient to compute the whole tree.     

gProximity: Hierarchical GPU‐based Operations for Collision and Distance Queries

We present novel parallel algorithms for collision detection and separation distance computation for rigid and deformable models that exploit the computational capabilities of many‐core GPUs. Our approach uses thread and data parallelism to perform fast hierarchy construction, updating, and traversal using tight‐fitting bounding volumes such as oriented bounding boxes (OBB) and rectangular swept spheres (RSS). We also describe efficient algorithms to compute a linear bounding volume hierarchy (LBVH) and update them using refitting methods. Moreover, we show that tight‐fitting bounding volume hierarchies offer improved performance on GPU‐like throughput architectures. We use our algorithms to perform discrete and continuous collision detection including self‐collisions, as well as separation distance computation between non‐overlapping models. In practice, our approach (gProximity) can perform these queries in a few milliseconds on a PC with NVIDIA GTX 285 card on models composed of tens or hundreds of thousands of triangles used in cloth simulation, surgical simulation, virtual prototyping and N‐body simulation. Moreover, we observe more than an order of magnitude performance improvement over prior GPU‐based algorithms.     

Designing Quad‐dominant Meshes with Planar Faces

We study the combined problem of approximating a surface by a quad mesh (or quad‐dominant mesh) which on the one hand has planar faces, and which on the other hand is aesthetically pleasing and has evenly spaced vertices. This work is motivated by applications in freeform architecture and leads to a discussion of fields of conjugate directions in surfaces, their singularities and indices, their optimization and their interactive modeling. The actual meshing is performed by means of a level set method which is capable of handling combinatorial singularities, and which can deal with planarity, smoothness, and spacing issues.     

Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes

We present a novel technique for the efficient boundary evaluation of sweep operations applied to objects in polygonal boundary representation. These sweep operations include Minkowski addition, offsetting, and sweeping along a discrete rigid motion trajectory. Many previous methods focus on the construction of a polygonal superset (containing self‐intersections and spurious internal geometry) of the boundary of the volumes which are swept. Only few are able to determine a clean representation of the actual boundary, most of them in a discrete volumetric setting. We unify such superset constructions into a succinct common formulation and present a technique for the robust extraction of a polygonal mesh representing the outer boundary, i.e. it makes no general position assumptions and always yields a manifold, watertight mesh. It is exact for Minkowski sums and approximates swept volumes polygonally. By using plane‐based geometry in conjunction with hierarchical arrangement computations we avoid the necessity of arbitrary precision arithmetics and extensive special case handling. By restricting operations to regions containing pieces of the boundary, we significantly enhance the performance of the algorithm.     

Fast and Robust Normal Estimation for Point Clouds with Sharp Features

This paper presents a new method for estimating normals on unorganized point clouds that preserves sharp features. It is based on a robust version of the Randomized Hough Transform (RHT). We consider the filled Hough transform accumulator as an image of the discrete probability distribution of possible normals. The normals we estimate corresponds to the maximum of this distribution. We use a fixed‐size accumulator for speed, statistical exploration bounds for robustness, and randomized accumulators to prevent discretization effects. We also propose various sampling strategies to deal with anisotropy, as produced by laser scans due to differences of incidence. Our experiments show that our approach offers an ideal compromise between precision, speed, and robustness: it is at least as precise and noise‐resistant as state‐of‐the‐art methods that preserve sharp features, while being almost an order of magnitude faster. Besides, it can handle anisotropy with minor speed and precision losses.     

A Global Parity Measure for Incomplete Point Cloud Data

Shapes with complex geometric and topological features such as tunnels, neighboring sheets, and cavities are susceptible to undersampling and continue to challenge existing reconstruction techniques. In this work we introduce a new measure for point clouds to determine the likely interior and exterior regions of an object. Specifically, we adapt the concept of parity to point clouds with missing data and introduce the parity map, a global measure of parity over the volume. We first examine how parity changes over the volume with respect to missing data and develop a method for extracting topologically correct interior and exterior crusts for estimating a signed distance field and performing surface reconstruction. We evaluate our approach on real scan data representing complex shapes with missing data. Our parity measure is not only able to identify highly confident interior and exterior regions but also localizes regions of missing data. Our reconstruction results are compared to existing methods and we show that our method faithfully captures the topology and geometry of complex shapes in the presence of missing data.     

Symmetry Detection Using Feature Lines

In this paper, we describe a new algorithm for detecting structural redundancy in geometric data sets. Our algorithm computes rigid symmetries, i.e., subsets of a surface model that reoccur several times within the model differing only by translation, rotation or mirroring. Our algorithm is based on matching locally coherent constellations of feature lines on the object surfaces. In comparison to previous work, the new algorithm is able to detect a large number of symmetric parts without restrictions to regular patterns or nested hierarchies. In addition, working on relevant features only leads to a strong reduction in memory and processing costs such that very large data sets can be handled. We apply the algorithm to a number of real world 3D scanner data sets, demonstrating high recognition rates for general patterns of symmetry.     

Creating Fluid Animation from a Single Image using Video Database

We present a method for synthesizing fluid animation from a single image, using a fluid video database. The user inputs a target painting or photograph of a fluid scene along with its alpha matte that extracts the fluid region of interest in the scene. Our approach allows the user to generate a fluid animation from the input image and to enter a few additional commands about fluid orientation or speed. Employing the database of fluid examples, the core algorithm in our method then automatically assigns fluid videos for each part of the target image. Our method can therefore deal with various paintings and photographs of a river, waterfall, fire, and smoke. The resulting animations demonstrate that our method is more powerful and efficient than our prior work.     

SimSelect: Similarity‐based selection for 3D surfaces

Surface selection is one of the fundamental interactions in shape modeling. In the case of complex models, this task is often tedious for at least two reasons: firstly the local geometry of a given region may be hard to manually select and needs great accuracy; secondly the selection process may have to be repeated a large number of times for similar regions requiring similar subsequent editing. We propose SimSelect, a new system for interactive selection on 3D surfaces addressing these two issues. We cope with the accuracy issue by classifying selections in different types, namely components, parts and patches for which we independently optimize the selection process. Second, we address the repetitiveness issue by introducing an expansion process based on shape recognition which automatically retrieves potential selections similar to the user‐defined one. As a result, our system provides the user with a compact set of simple interaction primitives providing a smooth select‐and‐edit workflow.     

Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh

We develop a novel isotropic remeshing method based on constrained centroidal Delaunay mesh (CCDM), a generalization of centroidal patch triangulation from 2D to mesh surface. Our method starts with resampling an input mesh with a vertex distribution according to a user‐defined density function. The initial remeshing result is then progressively optimized by alternatively recovering the Delaunay mesh and moving each vertex to the centroid of its 1‐ring neighborhood. The key to making such simple iterations work is an efficient optimization framework that combines both local and global optimization methods. Our method is parameterization‐free, thus avoiding the metric distortion introduced by parameterization, and generating more well‐shaped triangles. Our method guarantees that the topology of surface is preserved without requiring geodesic information. We conduct various experiments to demonstrate the simplicity, efficacy, and robustness of the presented method.     

Automatic Correction of Saturated Regions in Photographs using Cross‐Channel Correlation

Incorrectly setting the camera's exposure can have a significant negative effect on a photograph. Over‐exposing photographs causes pixels to exhibit unpleasant artifacts due to saturation of the sensor. Saturation removal typically involves user intervention to adjust the color values, which is tedious and time‐consuming. This paper discusses how saturation can be automatically removed without compromising the essential details of the image. Our method is based on a smoothness prior: neighboring pixels have similar channel ratios and color values. We demonstrate that high quality saturation‐free photos can be obtained from a simple but effective approach.     

Scales and Scale‐like Structures

We present a method for generating scales and scale‐like structures on a polygonal mesh through surface replacement. As input, we require a triangular mesh that will be covered with scales and one or more proxy‐models to be used as the scale's shape. A user begins scale generation by drawing a lateral line on the model to control the distribution and orientation of scales on the surface. We then create a vector field over the surface to control an anisotropic Voronoi tessellation, which represents the region occupied by each scale. Next we replace these regions by cutting the proxy model to match the boundary of the Voronoi region and deform the cut model onto the surface. The result is a fully connected 2‐manifold that is suitable for subsequent post‐processing applications like surface subdivision.     

Variational 3D Shape Segmentation for Bounding Volume Computation

We propose a variational approach to computing an optimal segmentation of a 3D shape for computing a union of tight bounding volumes. Based on an affine invariant measure of e-tightness, the resemblance to ellipsoid, a novel functional is formulated that governs an optimization process to obtain a partition with multiple components. Refinement of segmentation is driven by application-specific error measures, so that the final bounding volume meets pre-specified user requirement. We present examples to demonstrate the effectiveness of our method and show that it works well for computing ellipsoidal bounding volumes as well as oriented bounding boxes.