34-Issue 2

Permanent URI for this collection

https://diglib.eg.org/handle/10.2312/12150

Browse

Browsing 34-Issue 2 by Subject "Computational Geometry and Object Modeling"

Now showing 1 - 7 of 7
  • Thumbnail Image
    Item
    Approximating the Generalized Voronoi Diagram of Closely Spaced Objects
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Edwards, John; Daniel, Eric; Pascucci, Valerio; Bajaj, Chandrajit; Olga Sorkine-Hornung and Michael Wimmer
    We present an algorithm to compute an approximation of the generalized Voronoi diagram (GVD) on arbitrary collections of 2D or 3D geometric objects. In particular, we focus on datasets with closely spaced objects; GVD approximation is expensive and sometimes intractable on these datasets using previous algorithms. With our approach, the GVD can be computed using commodity hardware even on datasets with many, extremely tightly packed objects. Our approach is to subdivide the space with an octree that is represented with an adjacency structure. We then use a novel adaptive distance transform to compute the distance function on octree vertices. The computed distance field is sampled more densely in areas of close object spacing, enabling robust and parallelizable GVD surface generation. We demonstrate our method on a variety of data and show example applications of the GVD in 2D and 3D.
  • Thumbnail Image
    Item
    Composition-Aware Scene Optimization for Product Images
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Liu, Tianqiang; McCann, Jim; Li, Wilmot; Funkhouser, Thomas; Olga Sorkine-Hornung and Michael Wimmer
    Increasingly, companies are creating product advertisements and catalog images using computer renderings of 3D scenes. A common goal for these companies is to create aesthetically appealing compositions that highlight objects of interest within the context of a scene. Unfortunately, this goal is challenging, not only due to the need to balance the trade-off among aesthetic principles and design constraints, but also because of the huge search space induced by possible camera parameters, object placement, material choices, etc. Previous methods have investigated only optimization of camera parameters. In this paper, we develop a tool that starts from an initial scene description and a set of high-level constraints provided by a stylist and then automatically generates an optimized scene whose 2D composition is improved. It does so by locally adjusting the 3D object transformations, surface materials, and camera parameters. The value of this tool is demonstrated in a variety of applications motivated by product catalogs, including rough layout refinement, detail image creation, home planning, cultural customization, and text inlay placement. Results of a perceptual study indicate that our system produces images preferable for product advertisement compared to a more traditional camera-only optimization.
  • Thumbnail Image
    Item
    Designing Camera Networks by Convex Quadratic Programming
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Ghanem, Bernard; Cao, Yuanhao; Wonka, Peter; Olga Sorkine-Hornung and Michael Wimmer
    In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
  • Thumbnail Image
    Item
    Layer-Based Procedural Design of Façades
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Ilcík, Martin; Musialski, Przemyslaw; Auzinger, Thomas; Wimmer, Michael; Olga Sorkine-Hornung and Michael Wimmer
    We present a novel procedural framework for interactively modeling building façades. Common procedural approaches, such as shape grammars, assume that building façades are organized in a tree structure, while in practice this is often not the case. Consequently, the complexity of their layout description becomes unmanageable for interactive editing. In contrast, we obtain a façade by composing multiple overlapping layers, where each layer contains a single rectilinear grid of façade elements described by two simple generator patterns. This way, the design process becomes more intuitive and the editing effort for complex layouts is significantly reduced. To achieve this, we present a method for the automated merging of different layers in the form of a mixed discrete and continuous optimization problem. Finally, we provide several modeling examples and a comparison to shape grammars in order to highlight the advantages of our method when designing realistic building façades.
  • Thumbnail Image
    Item
    Optimal Spline Approximation via l0-Minimization
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Brandt, Christopher; Seidel, Hans-Peter; Hildebrandt, Klaus; Olga Sorkine-Hornung and Michael Wimmer
    Splines are part of the standard toolbox for the approximation of functions and curves in Rd. Still, the problem of finding the spline that best approximates an input function or curve is ill-posed, since in general this yields a ''spline'' with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be formulated as an 0-regularized quadratic problem. This gives us a notion of optimal approximating splines that depend on one parameter, which weights the approximation error against the number of segments. We detail this concept for different types of splines including B-splines and composite Bézier curves. Based on the latest development in the field of sparse approximation, we devise a solver for the resulting minimization problems and show applications to spline approximation of planar and space curves and to spline conversion of motion capture data.
  • Thumbnail Image
    Item
    Template Assembly for Detailed Urban Reconstruction
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Nan, Liangliang; Jiang, Caigui; Ghanem, Bernard; Wonka, Peter; Olga Sorkine-Hornung and Michael Wimmer
    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.
  • Thumbnail Image
    Item
    Woodification: User-Controlled Cambial Growth Modeling
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Kratt, Julian; Spicker, Marc; Guayaquil, Alejandro; Fiser, Marek; Pirk, Sören; Deussen, Oliver; Hart, John C.; Benes, Bedrich; Olga Sorkine-Hornung and Michael Wimmer
    We present a botanical simulation of secondary (cambial) tree growth coupled to a physical cracking simulation of its bark. Whereas level set growth would use a fixed resolution voxel grid, our system extends the deformable simplicial complex (DSC), supporting new biological growth functions robustly on any surface polygonal mesh with adaptive subdivision, collision detection and topological control.We extend the DSC with temporally coherent texturing, and surface cracking with a user-controllable biological model coupled to the stresses introduced by the cambial growth model.