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Microtiles: Extracting Building Blocks from Correspondences
(The Eurographics Association and Blackwell Publishing Ltd., 2012) Kalojanov, Javor; Bokeloh, Martin; Wand, Michael; Guibas, Leonidas; Seidel, Hans-Peter; Slusallek, Philipp; Eitan Grinspun and Niloy Mitra
In this paper, we develop a theoretical framework for characterizing shapes by building blocks. We address two questions: First, how do shape correspondences induce building blocks? For this, we introduce a new representation for structuring partial symmetries (partial self-correspondences), which we call "microtiles". Starting from input correspondences that form point-wise equivalence relations, microtiles are obtained by grouping connected components of points that share the same set of symmetry transformations. The decomposition is unique, requires no parameters beyond the input correspondences, and encodes the partial symmetries of all subsets of the input. The second question is: What is the class of shapes that can be assembled from these building blocks? Here, we specifically consider r-similarity as correspondence model, i.e., matching of local r-neighborhoods. Our main result is that the microtiles of the partial r-symmetries of an object S can build all objects that are (r+e)-similar to S for any e>0. Again, the construction is unique. Furthermore, we give necessary conditions for a set of assembly rules for the pairwise connection of tiles. We describe a practical algorithm for computing microtile decompositions under rigid motions, a corresponding prototype implementation, and conduct a number of experiments to visualize the structural properties in practice.
Reconstruction of Deforming Geometry from Time-Varying Point Clouds
(The Eurographics Association, 2007) Wand, Michael; Jenke, Philipp; Huang, Qixing; Bokeloh, Martin; Guibas, Leonidas; Schilling, Andreas; Alexander Belyaev and Michael Garland
In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent real-time range scanning devices. Our technique reconstructs both the geometry and dense correspondences over time. Using the correspondences, holes due to occlusion are filled in from other frames. Our reconstruction technique is based on a statistical framework: The reconstruction should both match the measured data points and maximize prior probability densities that prefer smoothness, rigid deformation and smooth movements over time. The optimization procedure consists of an inner loop that optimizes the 4D shape using continuous numerical optimization and an outer loop that infers the discrete 4D topology of the data set using an iterative model assembly algorithm. We apply the technique to a variety of data sets, demonstrating that the new approach is capable of robustly retrieving animated models with correspondences from data sets suffering from significant noise, outliers and acquisition holes.
Partial Symmetry Detection in Volume Data
(The Eurographics Association, 2011) Kerber, Jens; Wand, Michael; Krüger, Jens; Seidel, Hans-Peter; Peter Eisert and Joachim Hornegger and Konrad Polthier
In this paper, we present an algorithm for detecting partial Euclidean symmetries in volume data. Our algorithm finds subsets in voxel data that map to each other approximately under translations, rotations, and reflections. We implement the search for partial symmetries efficiently and robustly using a feature-based approach: We first reduce the volume to salient line features and then create transformation candidates from matching only local configurations of these line networks. Afterwards, only a shortlist of transformation candidates need to be verified using expensive dense volume matching. We apply our technique on both synthetic test scenes as well as real CT scans and show that we can recover a large amount of partial symmetries for complexly structured volume data sets.
Building Construction Sets by Tiling Grammar Simplification
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Kalojanov, Javor; Wand, Michael; Slusallek, Philipp; Joaquim Jorge and Ming Lin
This paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as many similar variants can be reassembled. This process is formalized by tiling grammars. Our core contribution is an approach for simplifying tiling grammars such that we obtain physically manufacturable building blocks of controllable granularity while retaining variability, i.e., the ability to construct many different, related shapes. Simplification is performed by sequences of two types of elementary operations: non-local joint edge collapses in the tile graphs reduce the granularity of the decomposition and approximate replacement operations reduce redundancy. We evaluate our method on abstract graph grammars in addition to computing several physical construction sets, which are manufactured using a commodity 3D printer.
Symmetry in Shapes - Theory and Practice
(The Eurographics Association, 2013) Mitra, Niloy; Ovsjanikov, Maksim; Pauly, Mark; Wand, Michael; Ceylan, Duygu; Diego Gutierrez and Karol Myszkowski
Part I: What is symmetry? Part II: Extrinsic symmetry detection Part III: Intrinsic symmetries Part IV: Representations and applications Conclusions, wrap-up
Symmetry in 3D Geometry: Extraction and Applications
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Mitra, Niloy J.; Pauly, Mark; Wand, Michael; Ceylan, Duygu; Holly Rushmeier and Oliver Deussen
The concept of symmetry has received significant attention in computer graphics and computer vision research in recent years. Numerous methods have been proposed to find, extract, encode and exploit geometric symmetries and high‐level structural information for a wide variety of geometry processing tasks. This report surveys and classifies recent developments in symmetry detection. We focus on elucidating the key similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general. We discuss a variety of applications in computer graphics and geometry processing that benefit from symmetry information for more effective processing. An analysis of the strengths and limitations of existing algorithms highlights the plenitude of opportunities for future research both in terms of theory and applications.The concept of symmetry has received significant attention in computer graphics and computer vision research in recent years. Numerous methods have been proposed to find, extract, encode, and exploit geometric symmetries and high‐level structural information for a wide variety of geometry processing tasks. This report surveys and classifies recent developments in symmetry detection. We focus on elucidating the key similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general.
Mutable Elastic Models for Sculpting Structured Shapes
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Milliez, Antoine; Wand, Michael; Cani, Marie-Paule; Seidel, Hans-Peter; I. Navazo, P. Poulin
In this paper, we propose a new paradigm for free-form shape deformation. Standard deformable models minimize an energy measuring the distance to a single target shape. We propose a new, ''mutable'' elastic model. It represents complex geometry by a collection of parts and measures the distance of each part measures to a larger set of alternative rest configurations. By detecting and reacting to local switches between best-matching rest states, we build a 3D sculpting system: It takes a structured shape consisting of parts and replacement rules as input. The shape can subsequently be elongated, compressed, bent, cut, and merged within a constraints-based free-form editing interface, where alternative rest-states model to such changes. In practical experiments, we show that the approach yields a surprisingly intuitive and easy to implement interface for interactively designing objects described by such discrete shape grammars, for which direct shape control mechanisms were typically lacking.
Meshless Modeling of Deformable Shapes and their Motion
(The Eurographics Association, 2008) Adams, Bart; Ovsjanikov, Maks; Wand, Michael; Seidel, Hans-Peter; Guibas, Leonidas J.; Markus Gross and Doug James
We present a new framework for interactive shape deformation modeling and key frame interpolation based on a meshless finite element formulation. Starting from a coarse nodal sampling of an object's volume, we formulate rigidity and volume preservation constraints that are enforced to yield realistic shape deformations at interactive frame rates. Additionally, by specifying key frame poses of the deforming shape and optimizing the nodal displacements while targeting smooth interpolated motion, our algorithm extends to a motion planning framework for deformable objects. This allows reconstructing smooth and plausible deformable shape trajectories in the presence of possibly moving obstacles. The presented results illustrate that our framework can handle complex shapes at interactive rates and hence is a valuable tool for animators to realistically and efficiently model and interpolate deforming 3D shapes.
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.
Dynamic Geometry Processing
(The Eurographics Association, 2012) Chang, Will; Li, Hao; Mitra, Niloy; Pauly, Mark; Wand, Michael; Renato Pajarola and Michela Spagnuolo
Throughout the last few years, acquisition and processing of dynamic geometry has already received quite an amount of attention in the computer vision and graphics research community. Recently, the topic has gained a significant boost due to the availability of commodity devices for dynamic geometry acquisition: The introduction of the Microsoft ''Kinect'' device made this kind of technology broadly available, being very well received by both researchers and end-users, and even more development in this direction can probably be expected for the near future. The tutorial on ''Dynamic Geometry Processing'' considers the problem of processing such dynamic range data effectively and efficiently. The tutorial introduces basic processing techniques for analyzing and matching range data. It introduces models for correspondence estimation and presents the according basic algorithmic building blocks. Furthermore, it discusses the current state-of-the-art by looking at example approaches for processing and real-time tracking of dynamic data. In addition, the tutorial will also identify and discuss future challenges in the field, aiming at inspiring future work in this exciting area of research.

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