Rhaleb Zayer, Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany
Room: 208, Phone: +49 681 9325-408, Fax: +49 681 9325-499, Email: zayer@mpi-sb.mpg.de
Research Overview
Linear Angle Based Parameterization
In the field of mesh parameterization, the impact of angular and boundary distortion on parameterization quality
have brought forward the need for robust and efficient free boundary angle preserving methods. One of the
most prominent approaches in this direction is the Angle Based Flattening (ABF) which directly formulates the
problem as a constrained nonlinear optimization in terms of angles. Since the original formulation of the ABF, a
steady research effort has been dedicated to improving its efficiency. As for any well posed numerical problem,
the solution is generally an approximation of the underlying mathematical equations. The economy and accuracy
of the solution are to a great extent affected by the kind of approximation used. In this work we reformulate the
problem based on the notion of error of estimation. A careful manipulation of the resulting equations yields for the
first time a linear version of angle based parameterization. The error induced by this linearization is quadratic
in terms of the error in angles and the validity of the approximation is further supported by numerical results.
Besides performance speedup, the simplicity of the current setup makes re-implementation and reproduction of
our results straightforward.
Rhaleb Zayer, Bruno Lévy, and Hans-Peter Seidel.
Linear Angle Based Parameterization.
ACM/Eurographics Symposium on Geometry Processing (2007).
Video-Driven Animation of Human Body Scans
We present a versatile, fast and simple framework to generate animations of scanned human characters from input multiview video sequences. Our method is purely
mesh-based and requires only a minimum of manual interaction. The proposed algorithm implicitly generates realistic body deformations and can easily transfer motions between human subjects of completely different shape and proportions. We feature a working prototype system that demonstrates that our method can generate convincing lifelike character animations from marker-less optical motion capture data.
Edilson de Aguiar, Rhaleb Zayer, Christian Theobalt, Marcus Magnor, and Hans-Peter Seidel
Video-Driven Animation of Huamn Body Scans
3DTV-Conference, Kos Island, Greece, 2007
Curvilinear Spherical Parameterization
We present an efficient approach for solving the spherical parameterization problem. The essence of the approach is to look for a solution in the curvilinear coordinate system, without requiring the additional spherical constraints usually needed in cartesian formulations. This setup allows us to take full advantage of some existing techniques originally developed for planar parameterization. Our results substantiate the efficiency of the method and confirm its robustness. Meshes of non-trivial geometry with tens of thousands of triangles are processed in a few seconds, always yielding bijective maps.
Rhaleb Zayer, Christian Rössl, Zachi Karni, and Hans-Peter Seidel.
Curvilinear Spherical Parameterization.
Shape Modeling International (SMI), Matsushima, Japan, 2006.
Harmonic Guidance for Surface Deformation
We present an interactive method for applying deformations to a surface mesh while preserving its global shape and local properties. Two surface editing scenarios are discussed, which conceptually differ in the specification of deformations: Either interpolation constraints are imposed explicitly, e.g., by dragging a subset of vertices, or, deformation of a reference surface is mimicked. The contribution of this paper is a novel approach for interpolation of local deformations over the manifold and for efficiently establishing correspondence to a reference surface from only few pairs of markers. As a general tool for both scenarios, a harmonic field is constructed to guide the interpolation of constraints and to find correspondence required for deformation transfer. We show that our approach fits nicely in a unified mathematical framework, where the same type of linear operator is applied in all phases, and how this approach can be used to create an intuitive and interactive editing tool.
Rhaleb Zayer, Christian Rössl, Zachi Karni, and Hans-Peter Seidel.
Harmonic Guidance for Surface Deformation.
EUROGRAPHICS 2005, Dublin, Ireland
Mesh Segmentation Driven by Gaussian Curvature
In this paper we propose a new segmentation method for the generation of charts that can be flattened efficiently. The integrated Gaussian curvature is used to measure the developability of a chart and a robust and simple scheme is proposed to integrate the Gaussian curvature. The segmentation approach evenly distributes Gaussian curvature over the charts and automatically ensures disc-like topology of each chart. For numerical stability, we use area on the Gauss map to represent Gaussian curvature. Resulting parameterization shows that charts generated in this way have less distortion compared to charts generated by other methods.
Hitoshi Yamauchi, Stefan Gumhold, Rhaleb Zayer, and Hans-Peter Seidel.
Mesh Segmentation Driven by Gaussian Curvature.
The Visual Computer 21 (8-10): 649-658, 2005
Setting the Boundary Free: A Composite Approach to Surface Parameterization
In the last decade, surface mesh parameterization has emerged as a standard technique in computer graphics. The ever increasing need for processing large and highly detailed data sets fosters the development of efficient parameterization techniques that can capture the geometry of the input meshes and produce low distortion planar maps. We present a set of novel techniques allowing for low distortion parameterization. In particular, we address one of the major shortcomings of linear methods by allowing the parametric representation to evolve freely on the plane without any fixed boundary vertices.
Rhaleb Zayer, Christian Rössl, and Hans-Peter Seidel.
Setting the Boundary Free: A Composite Approach to Surface Parameterization.
Symposium on Geometry Processing, Vienna, Austria, 2005
Discrete Tensorial Quasi-Harmonic Maps
We introduce new linear operators for surface parameterization. Given an initial mapping from the parametric plane onto a surface mesh, we establish a secondary map of the plane onto itself that mimics the initial one. The resulting low-distortion parameterization is smooth as it stems from solving a quasi-harmonic equation. Our parameterization method is robust and independent of (the quality of) the initial map. In fact, for most cases the methods converges from a simple projection on the least squares plane even for complex models.
Rhaleb Zayer, Christian Rössl, and Hans-Peter Seidel.
Discrete Tensorial Quasi-Harmonic Maps.
Shape Modeling International 2005 (SMI 2005), Cambridge, MA, U.S.A, 2005
Polygonal decomposition of the 1-ring neighborhood of the Catmull-Clark scheme
We propose a polygonal decomposition of the 1-ring neighborhood of a quadrilateral mesh, which is suitable for the study of the Catmull-Clark subdivision scheme. The initial configuration consists of 2n planar 2n-gons and under the Catmull-Clark subdivision they transform into 4n planar n-gons coming in pairs of coplanar polygons and quadruples of parallel polygons. We calculate the eigenvalues and eigenvectors of the transformations of these configurations showing their relation with the tangent plane and the curvature properties of the subdivision surface. Using direct computations on circulant-block matrices we show how the same eigenvalues can be analytically deduced from the subdivision matrix.
Ioannis Ivrissimtzis, Rhaleb Zayer, and Hans-Peter Seidel
Polygonal decomposition of the 1-ring neighborhood of the Catmull-Clark scheme
In: Shape Modeling International 2004 (SMI 2004), Genoa, Italy, 2004, 101-109
Variations of angle based flattening
Angle Based Flattening is a robust parameterization technique allowing a free boundary. The numerical optimization associated with the approach yields a challenging problem. We discuss several approaches to effectively reduce the computational effort involved and propose appropriate numerical solvers. We propose a simple but effective transformation of the problem which reduces the computational cost and simplifies the implementation. We also show that fast convergence can be achieved by finding approximate solutions which yield a low angular distortion.
Rhaleb Zayer, Christian Rössl, and Hans-Peter Seidel
Variations of angle based flattening
In: Advances in Multiresolution for Geometric Modelling, 2004, 187-199