Rhaleb Zayer

Mesh segmentation driven by Gaussian curvature

Mesh parameterization is a fundamental problem in computer graphics as it allows for texture mapping and facilitates many mesh processing tasks. Although there exists a variety of good parameterization methods for meshes that are topologically equivalent to a disk, the segmentation into nicely parameterizable charts of higher genus meshes has been studied less. 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 a disklike topology of each chart. For numerical stability, we use an area on the Gauss map to represent Gaussian curvature. The resulting parameterization shows that charts generated in this way have less distortion compared to charts generated by other methods.

Normal based estimation of the curvature tensor for triangular meshes

We introduce a new technique for estimating the curvature tensor of a triangular mesh. The input of the algorithm is only a single triangle equipped with its (exact or estimated) vertex normals. This way we get a smooth junction of the curvature tensor inside each triangle of the mesh. We show that the error of the new method is comparable with the error of a cubic fitting approach if the incorporated normals are estimated. If the exact normals of the underlying surface are available at the vertices, the error drops significantly. We demonstrate the applicability of the new estimation at a rather complex data set.

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.

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. Our method consists of several simple steps, each solving a linear problem. Our results exhibit a fair balance between high-quality and computational efficiency.

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 from 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.

Feature sensitive bas relief generation

Among all forms of sculpture, bas-relief is arguably the closest to painting. Although inherently a two dimensional sculpture, a bas-relief suggests a visual spatial extension of the scene in depth through the combination of composition, perspective, and shading. Most recently, there have been significant results on digital bas-relief generation but many of the existing techniques may wash out high level surface detail during the compression process. The primary goal of this work is to address the problem of fine features by tailoring a filtering technique that achieves good compression without compromising the quality of surface details. As a secondary application we explore the generation of artistic relief which mimic cubism in painting and we show how it could be used for generating Picasso like portraits.

Variations on Angle Based Flattening

Angle Based Flattening is a robust parameterization technique allowing a free boundary. The numerical optimisation 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.

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.

Globally homogeneous, locally adaptive sparse matrix-vector multiplication on the GPU

The rising popularity of the graphics processing unit (GPU) across various numerical computing applications triggered a breakneck race to optimize key numerical kernels and in particular, the sparse matrix-vector product (SpMV). Despite great strides, most existing GPU-SpMV approaches trade off one aspect of performance against another. They either require preprocessing, exhibit inconsistent behavior, lead to execution divergence, suffer load imbalance or induce detrimental memory access patterns. In this paper, we present an uncompromising approach for SpMV on the GPU. Our approach requires no separate preprocessing or knowledge of the matrix structure and works directly on the standard compressed sparse rows (CSR) data format. From a global perspective, it exhibits a homogeneous behavior reflected in efficient memory access patterns and steady per-thread workload. From a local perspective, it avoids heterogeneous execution paths by adapting its behavior to the work load at hand, it uses an efficient encoding to keep temporary data requirements for on-chip memory low, and leads to divergence-free execution. We evaluate our approach on more than 2500 matrices comparing to vendor provided, and state-of-the-art SpMV implementations. Our approach not only significantly outperforms approaches directly operating on the CSR format ( 20% average performance increase), but also outperforms approaches that preprocess the matrix even when preprocessing time is discarded. Additionally, the same strategies lead to significant performance increase when adapted for transpose SpMV.

A GPU-Adapted Structure for Unstructured Grids

A key advantage of working with structured grids (e.g., images) is the ability to directly tap into the powerful machinery of linear algebra. This is not much so for unstructured grids where intermediate bookkeeping data structures stand in the way. On modern high performance computing hardware, the conventional wisdom behind these intermediate structures is further challenged by costly memory access, and more importantly by prohibitive memory resources on environments such as graphics hardware. In this paper, we bypass this problem by introducing a sparse matrix representation for unstructured grids which not only reduces the memory storage requirements but also cuts down on the bulk of data movement from global storage to the compute units. In order to take full advantage of the proposed representation, we augment ordinary matrix multiplication by means of action maps, local maps which encode the desired interaction between grid vertices. In this way, geometric computations and topological modifications translate into concise linear algebra operations. In our algorithmic formulation, we capitalize on the nature of sparse matrix‐vector multiplication which allows avoiding explicit transpose computation and storage. Furthermore, we develop an efficient vectorization to the demanding assembly process of standard graph and finite element matrices.