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  • 1. Chambers, E. W.
    et al.
    Vejdemo-Johansson, Mikael
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP. University of Minnesota, United States; Jozef Stefan Institute, Slovenia.
    Computing Minimum Area Homologies2015In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 34, no 6, p. 13-21Article in journal (Refereed)
    Abstract [en]

    Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algorithms for curves on surfaces with provable guarantees on the quality of the measure. In this paper, we present a similarity measure for any two cycles that are homologous, where we calculate the minimum area of any homology (or connected bounding chain) between the two cycles. The minimum area homology exists for broader classes of cycles than previous measures which are based on homotopy. It is also much easier to compute than previously defined measures, yielding an efficient implementation that is based on linear algebra tools. We demonstrate our algorithm on a range of inputs, showing examples which highlight the feasibility of this similarity measure.

  • 2. Günther, D.
    et al.
    Seidel, H. -P
    Weinkauf, Tino
    Max Planck Institute for Informatics, Germany .
    Extraction of Dominant Extremal Structures in Volumetric Data using Separatrix Persistence2012In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 31, no 8, p. 2554-2566Article in journal (Refereed)
    Abstract [en]

    Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood. These features are important in many applications, e.g., computer tomography, fluid dynamics, cell biology. We present a novel topological method to extract these features using discrete Morse theory. In particular, we extend the notion of Separatrix Persistence from 2D to 3D, which gives us a robust estimation of the feature strength for extremal lines and surfaces. Not only does it allow us to determine the most important (parts of) extremal lines and surfaces, it also serves as a robust filtering measure of noise-induced structures. Our purely combinatorial method does not require derivatives or any other numerical computations.

  • 3. Jacobson, A.
    et al.
    Weinkauf, Tino
    MPI Informatik, Germany.
    Sorkine, O.
    Smooth Shape-Aware Functions with Controlled Extrema2012In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 31, no 5, p. 1577-1586Article in journal (Refereed)
    Abstract [en]

    Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior of the solved domain occur. However, these functions are only C0 at the constrained points, which often causes smoothness problems. For this reason, many applications optimize higher-order Laplacian energies such as biharmonic or triharmonic. Their minimizers exhibit increasing orders of continuity but also increasing oscillation, immediately releasing the maximum principle. In this work, we identify characteristic artifacts caused by spurious local extrema, and provide a framework for minimizing quadratic energies on manifolds while constraining the solution to obey the maximum principle in the solved region. Our framework allows the user to specify locations and values of desired local maxima and minima, while preventing any other local extrema. We demonstrate our method on the smoothness energies corresponding to popular polyharmonic functions and show its usefulness for fast handle-based shape deformation, controllable color diffusion, and topologically-constrained data smoothing.

  • 4.
    Ruhland, Kerstin
    et al.
    Trinity College Dublin.
    Peters, Christopher E.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Andrist, Sean
    University of Wisconsin–Madison.
    Badler, Jeremy B.
    Université catholique de Louvain.
    Badler, Norman I.
    University of Pennsylvania.
    Gleicher, Michael
    University of Wisconsin–Madison.
    Mutlu, Bilge
    University of Wisconsin–Madison.
    McDonnell, Rachel
    Trinity College Dublin.
    A Review of Eye Gaze in Virtual Agents, Social Robotics and HCI: Behaviour Generation, User Interaction and Perception2015In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 34, no 6, p. 299-326Article, review/survey (Refereed)
    Abstract [en]

    A person's emotions and state of mind are apparent in their face and eyes. As a Latin proverb states: ‘The face is the portrait of the mind; the eyes, its informers’. This presents a significant challenge for Computer Graphics researchers who generate artificial entities that aim to replicate the movement and appearance of the human eye, which is so important in human–human interactions. This review article provides an overview of the efforts made on tackling this demanding task. As with many topics in computer graphics, a cross-disciplinary approach is required to fully understand the workings of the eye in the transmission of information to the user. We begin with a discussion of the movement of the eyeballs, eyelids and the head from a physiological perspective and how these movements can be modelled, rendered and animated in computer graphics applications. Furthermore, we present recent research from psychology and sociology that seeks to understand higher level behaviours, such as attention and eye gaze, during the expression of emotion or during conversation. We discuss how these findings are synthesized in computer graphics and can be utilized in the domains of Human–Robot Interaction and Human–Computer Interaction for allowing humans to interact with virtual agents and other artificial entities. We conclude with a summary of guidelines for animating the eye and head from the perspective of a character animator.

  • 5.
    Saikia, Himangshu
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Weinkauf, Tino
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Global Feature Tracking and Similarity Estimation in Time-Dependent Scalar Fields2017In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 36, no 3, p. 1-11Article in journal (Refereed)
    Abstract [en]

    We present an algorithm for tracking regions in time-dependent scalar fields that uses global knowledge from all time steps for determining the tracks. The regions are defined using merge trees, thereby representing a hierarchical segmentation of the data in each time step. The similarity of regions of two consecutive time steps is measured using their volumetric overlap and a histogram difference. The main ingredient of our method is a directed acyclic graph that records all relevant similarity information as follows: the regions of all time steps are the nodes of the graph, the edges represent possible short feature tracks between consecutive time steps, and the edge weights are given by the similarity of the connected regions. We compute a feature track as the global solution of a shortest path problem in the graph. We use these results to steer the - to the best of our knowledge - first algorithm for spatio-temporal feature similarity estimation. Our algorithm works for 2D and 3D time-dependent scalar fields. We compare our results to previous work, showcase its robustness to noise, and exemplify its utility using several real-world data sets.

  • 6. Wang, Z.
    et al.
    Esturo, J. M.
    Seidel, H. -P
    Weinkauf, Tino
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Max Planck Institute for Informatics, Germany .
    Stream Line-Based Pattern Search in Flows2016In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659Article in journal (Refereed)
    Abstract [en]

    We propose a method that allows users to define flow features in form of patterns represented as sparse sets of stream line segments. Our approach finds similar occurrences in the same or other time steps. Related approaches define patterns using dense, local stencils or support only single segments. Our patterns are defined sparsely and can have a significant extent, i.e., they are integration-based and not local. This allows for a greater flexibility in defining features of interest. Similarity is measured using intrinsic curve properties only, which enables invariance to location, orientation, and scale. Our method starts with splitting stream lines using globally consistent segmentation criteria. It strives to maintain the visually apparent features of the flow as a collection of stream line segments. Most importantly, it provides similar segmentations for similar flow structures. For user-defined patterns of curve segments, our algorithm finds similar ones that are invariant to similarity transformations. We showcase the utility of our method using different 2D and 3D flow fields.

  • 7.
    Weinkauf, Tino
    et al.
    Courant Institute, New York University, USA.
    Gingold, Y.
    Sorkine, O.
    Topology-based Smoothing of 2D Scalar Fields with C1-Continuity2010In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 29, no 3, p. 1221-1230Article in journal (Refereed)
    Abstract [en]

    Data sets coming from simulations or sampling of real-world phenomena often contain noise that hinders their processing and analysis. Automatic filtering and denoising can be challenging: when the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features; in addition, the filtering process itself may introduce artificial features into the data set that were not originally present. In this paper, we propose a smoothing method for 2D scalar fields that gives the user explicit control over the data features. We define features as critical points of the given scalar function, and the topological structure they induce (i.e., the Morse-Smale complex). Feature significance is rated according to topological persistence. Our method allows filtering out spurious features that arise due to noise by means of topological simplification, providing the user with a simple interface that defines the significance threshold, coupled with immediate visual feedback of the remaining data features. In contrast to previous work, our smoothing method guarantees a C1-continuous output scalar field with the exact specified features and topological structures.

  • 8.
    Weinkauf, Tino
    et al.
    Courant Institute, New York University, USA.
    Günther, D.
    Separatrix Persistence: Extraction of Salient Edges on Surfaces Using Topological Methods2009In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 28, no 5, p. 1519-1528Article in journal (Refereed)
    Abstract [en]

    Salient edges are perceptually prominent features of a surface. Most previous extraction schemes utilize the notion of ridges and valleys for their detection, thereby requiring curvature derivatives which are rather sensitive to noise. We introduce a novel method for salient edge extraction which does not depend on curvature derivatives. It is based on a topological analysis of the principal curvatures and salient edges of the surface are identified as parts of separatrices of the topological skeleton. Previous topological approaches obtain results including non-salient edges due to inherent properties of the underlying algorithms. We extend the profound theory by introducing the novel concept of separatrix persistence, which is a smooth measure along a separatrix and allows to keep its most salient parts only. We compare our results with other methods for salient edge extraction.

  • 9.
    Weinkauf, Tino
    et al.
    Max Planck Institute for Informatics, Germany.
    Hege, H. -C
    Theisel, H.
    Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields2012In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 31, no 2, p. 825-834Article in journal (Refereed)
    Abstract [en]

    We present the first general scheme to describe all four types of characteristic curves of flow fields – stream, path, streak, and time lines – as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter-free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.

  • 10.
    Weinkauf, Tino
    et al.
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Theisel, H.
    Hege, H. -C
    Seidel, H. -P
    Topological Construction and Visualization of Higher Order 3D Vector Fields2006In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 23, no 3, p. 469-478Article in journal (Refereed)
    Abstract [en]

    We present the first algorithm for constructing 3D vector fields based on their topological skeleton. The skeleton itself is modeled by interactively moving a number of control polygons. Then a piecewise linear vector field is automatically constructed which has the same topological skeleton as modeled before. This approach is based on a complete segmentation of the areas around critical points into sectors of different flow behavior. Based on this, we present the first approach to visualizing higher order critical points of 3D vector fields.

  • 11.
    Weinkauf, Tino
    et al.
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Theisel, H.
    Hege, H. -C
    Seidel, H. -P
    Topological Structures in Two-Parameter-Dependent 2D Vector Fields2006In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 25, no 3, p. 607-616Article in journal (Refereed)
    Abstract [en]

    In this paper we extract and visualize the topological skeleton of two-parameter-dependent vector fields. This kind of vector data depends on two parameter dimensions, for instance physical time and a scale parameter. We show that two important classes of local bifurcations – fold and Hopf bifurcations – build line structures for which we present an approach to extract them. Furthermore we show that new kinds of structurally stable local bifurcations exist for this data, namely fold-fold and Hopf-fold bifurcations. We present a complete classification of them. We apply our topological extraction method to analyze a number of two-parameter-dependent vector fields with different physical interpretations of the two additional dimensions.

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