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Now showing 1 - 4 of 4
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    Shape Analysis with Subspace Symmetries
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Berner, Alexander; Wand, Michael; Mitra, Niloy J.; Mewes, Daniel; Seidel, Hans-Peter; M. Chen and O. Deussen
    We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising.
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    Computing Correspondences in Geometric Data Sets
    (The Eurographics Association, 2011) Chang, Will; Li, Hao; Mitra, Niloy; Pauly, Mark; Rusinkiewicz, Szymon; Wand, Michael; Ralph Martin and Juan Carlos Torres
    Shape registration and, more generally speaking,computing correspondence across shapes are fundamental problems in computer graphics and vision. Problems from this area show up in many different variants such as scan registration, deformable shapematching, animation reconstruction, or finding partial symmetries of objects. Computing correspondences is a main prerequisite for higher level shape processing algorithms, such as building statistical models, non-local denoising, or inverse procedural modeling. Our tutorial addresses correspondence problems in geometric shapes. We will look at the problem from two different perspectives: In the first part of our tutorial, we will motivate the problem and explain the problem structure (formal models for shape matching), its variants (partial vs. complete matching, deformable vs. rigid, etc) and specific challenges (such as noise, incomplete data, and statistical descriptions thereof). In the second part, we will look at algorithms for solving these problems, and at applications of these. Again, we will focus on the main ideas and principles. Our overall goal is to give the attendee a "coordinate system" of the field, to convey the main problem structure and the main approaches to solve the problem, as well as open questions and research challenges. Topics covered will include rigid and deformable shape matching, local and global correspondence algorithms, as well as symmetry detection and applications.
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    Intrinsic Shape Matching by Planned Landmark Sampling
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Tevs, Art; Berner, Alexander; Wand, Michael; Ihrke, Ivo; Seidel, Hans-Peter; M. Chen and O. Deussen
    Recently, the problem of intrinsic shape matching has received a lot of attention. A number of algorithms have been proposed, among which random-sampling-based techniques have been particularly successful due to their generality and efficiency. We introduce a new sampling-based shape matching algorithm that uses a planning step to find optimized "landmark" points. These points are matched first in order to maximize the information gained and thus minimize the sampling costs. Our approach makes three main contributions: First, the new technique leads to a significant improvement in performance, which we demonstrate on a number of benchmark scenarios. Second, our technique does not require any keypoint detection. This is often a significant limitation for models that do not show sufficient surface features. Third, we examine the actual numerical degrees of freedom of the matching problem for a given piece of geometry. In contrast to previous results, our estimates take into account unprecise geodesics and potentially numerically unfavorable geometry of general topology, giving a more realistic complexity estimate.
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    Learning Line Features in 3D Geometry
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Sunkel, Martin; Jansen, Silke; Wand, Michael; Eisemann, Elmar; Seidel, Hans-Peter; M. Chen and O. Deussen
    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.