Geometric signal processing on polygonal meshes

2004

In this paper we present an efficient voxelization algorithm for complex polygonal models by exploiting newest programmable graphics hardware. We first convert the model into three discrete voxel spaces according to its surface orientation. The resultant voxels are encoded as 2D textures and stored in three intermediate sheet buffers called directional sheet buffers. These buffers are finally synthesized into one worksheet, which records the volumetric representation of the target. The whole algorithm traverses the geometric model only once and is accomplished entirely in GPU (graphics processing unit), achieving real-time frame rate for models with up to 2 million triangles. The algorithm is simple to implement and can be integrated easily into diverse applications such as volume based modelling, transparent rendering and collision detection.

Proceedings Computer Animation '98 (Cat. No.98EX169), 1998

Smoothing techniques are essential in providing high quality renderings out of polygonal objects that are described with a minimal amount of geometrical information. In order to remove the "polygonal" aspect of rough polygonal meshes, several techniques are available, such as shading or interpolation techniques.

We present a new image based method of reconstructing and rendering models from a set of calibrated input images. First an improved hardware accelerated voxel carving method is used to obtain the voxels corresponding to the volume occupied by the model. Then a new method of real-time multitextured mesh is proposed in order to obtain realistic renders of the recovered models. This representation uses a polygonal relaxed surface mesh obtained from the final set of voxels and overlapping projective texture maps to achieve photo-realistic appearances.

IEEE Sixth International Symposium on Multimedia Software Engineering, 2004

High resolution 3D range scanning as well as isosurface extraction have introduced densely and uniformly sampled models that are difficult to render at an interactive rate. To remove excessive details and produce meshes of various resolutions for different kinds of applications, the study of fast and high quality polygonal mesh simplification algorithms has become important. In this paper, we propose a new linear time algorithm that can achieve fast and high quality mesh simplification. In the new algorithm, we pipeline the cost computation, optimization, and edge collapse, and use a small constantsized Replacement Selection min-heap instead of a large greedy queue to effectively reduce the runtime complexity to linear complexity. Compared to previous works, our new algorithm has at least three advantages. First, the new algorithm is runtime efficient. Second, the new algorithm is memory efficient. Third, the algorithm is capable of generating competitive high quality outputs.

Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, loss-less, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.

2003

Surface models containing billions of polygons are becoming more frequent in computer graphics. Mesh simplification is necessary for displaying such surfaces at interactive rates. We describe a novel method for simplifying polyhedral meshes while producing multiple levels of detail for progressive transmission and interactive exploration. Unlike previous work on mesh simplification, our method is not restricted to triangle meshes. We propose a highly efficient edge-collapsing algorithm for meshes composed of non-planar multi-sided polygons based on a simple edge-selection strategy.

Proceedings Geometric Modeling and Processing 2000. Theory and Applications, 2000

A computer graphics object reconstructed from real-world data often contains undesirable noise and small-scale oscillations. An important problem is how to remove the noise and oscillations while preserving desirable geometric features of the object. This paper develops methods for polyhedral surface smoothing and denoising with simultaneous increasing mesh regularity. We also propose an adaptive smoothing method allowing to reduce possible oversmoothing. Roughly speaking, our smoothing schemes consist of moving every vertex in the direction defined by the Laplacian flow with speed equal to a properly chosen function of the mean curvature at the vertex.

2002

Implicit surfaces are used for a number of tasks in computer graphics, including modeling soft or organic objects, morphing, collision detection, and constructive solid geometry. Although operating on implicit surfaces is usually straightforward, creating them is not. We introduce a practical method for creating implicit surfaces from polygonal models that produces high-quality results for complex surfaces. Whereas much previous work in implicit surfaces has been done with primitives such as "blobbies," we use implicit surfaces based on a variational interpolation technique (the three-dimensional generalization of thin-plate interpolation). Given a polygonal mesh, we convert the data to a volumetric representation to use as a guide for creating the implicit surface iteratively. We begin by seeding the surface with a number of constraint points through which the surface must pass. Iteratively, additional constraints are added; the resulting surfaces are evaluated, and the errors guide the placement of subsequent constraints. We have applied our method successfully to a variety of polygonal meshes and consider it to be robust.

International Journal for Numerical Methods in Engineering, 2005

In this paper we propose a new algorithm for accurate correction of surface noises of polygonal meshes. It consists of three basic components: (a) feature-preserving pre-smoothing; (b) partitioning of feature and non-feature regions; (c) second-order predictor for non-feature regions and median filter for feature regions. The unique contributions of our approach include (a) an idea of partitioning an input surface into feature and non-feature regions so that different smoothing algorithms, which are best suited for either feature or non-feature regions can be, respectively, applied; (b) a secondorder predictor that provides higher smoothing accuracy and better convergence on smoothly curved surfaces. In comparison with several existing algorithms, our algorithm is evaluated quantitatively in terms of surface normal and vertex distance error metrics. Numerical experiments indicate the effectiveness of our approach in the aspects of convergence and accuracy.

Journal of Computing and Information Technology, 2011

Problem statement: Displaced subdivision representation possesses a number of attractive features for efficient and convenient processing tasks like editing, geometry compression, animation, scalability and adaptive rendering of polygonal models. In this representation, a detailed surface model was built as a scalar-valued displacement map over a smooth domain surface. The construction of the smooth domain surface from a polygonal model was a challenging task in the conversion process. Approach: For building the smooth domain surface, we proposed an efficient algorithm that was based on √3-subdivision scheme, memory efficient simplification and a linear time optimization technique. Results: At some fixed level of detail, the vertex and triangle complexity of the displaced surface generated by the proposed algorithm was far less and so it resulted in better compression ratios and transmission speed. Conclusion: The proposed algorithm created surfaces of better quality, computationally more efficient and occupied less memory as compared to the original algorithm by Lee.

Terrain simplification generates multi-resolution models, from which, traditionally, irregular or semi-regular tri-angulations are extracted to render a terrain at a suitable level of detail. Recent terrain simplification techniques use GPU-friendly regular grids and apply the filtering and sub-sampling paradigm to generate multiple resolu-tions. However, such approximations only sparsely adapt the terrain surface due to the smoothing and uniform sampling. Consequently, considerably more triangles have to be rendered in order to guarantee a certain error threshold. In this paper we present a novel feature-sensitive simplification technique. Our approach follows the afore-mentioned paradigm. The key idea is to maintain the regularity and, at the same time, to recomputed the vertex positions regarding a specific metric, the quadric error metric (QEM). Compared to previous methods we apply the paradigm to the grid of vertex-associated quadrics, fromwhich the vertices for the new resolu...

ACM Transactions on Multimedia Computing, Communications, and Applications, 2018

With the increasing accessibility of the mobile head-mounted displays (HMDs), mobile virtual reality (VR) systems are finding applications in various areas. However, mobile HMDs are highly constrained with limited graphics processing units (GPUs) and low processing power and onboard memory. Hence, VR developers must be cognizant of the number of polygons contained within their virtual environments to avoid rendering at low frame rates and inducing simulator sickness. The most robust and rapid approach to keeping the overall number of polygons low is to use mesh simplification algorithms to create low-poly versions of pre-existing, high-poly models. Unfortunately, most existing mesh simplification algorithms cannot adequately handle meshes with lots of boundaries or nonmanifold meshes, which are common attributes of many 3D models.In this article, we present QEM4VR, a high-fidelity mesh simplification algorithm specifically designed for VR. This algorithm addresses the deficiencies o...

Proceedings. International Conference on Image Processing, 2002

MESHGRID is a novel, compact, multiscalable and animation-friendly surface representation method, which has been introduced in MPEG-4 [1]. The MESHGRID representation attaches a description of the "global connectivity" between the vertices on the object's surface (i.e., the 3-D connectivity wireframe) to a regular 3-D grid of points (i.e., the reference grid). MESHGRID efficiently encodes the 3-D connectivity wireframe by using a new type of 3-D extension of Freeman chain-code. MESHGRID does not explicitly store the polygons of the surface, since the 3-D connectivity wireframe has particular connectivity properties allowing for the unambiguous derivation of the triangulation. The reference grid is a smooth vector field defined on a regular discrete 3-D space. This grid is efficiently compressed by using an embedded 3-D wavelet-based multiresolution intra-band coding algorithm. MESHGRID can be efficiently exploited for QoS since it allows for three types of scalability in both view-dependent and view-independent scenarios, including: 1) resolution scalability, i.e., the adaptation of the number of transmitted vertices; 2) shape precision, i.e., the adaptive reconstruction of the reference grid positions; and 3) vertex position scalability, i.e., the change of the precision of known vertex positions with respect to the reference grid. Furthermore, in addition to the classical vertex-based animation, MESHGRID also supports specific animation capabilities, such as: 1) rippling effects by changing the position of the vertices relative to corresponding reference grid points and 2) reshaping on a hierarchical basis of the regular reference grid and its attached vertices. in 1989 and the M.Sc. degree in applied computer science from Vrije Universiteit Brussel (VUB), Brussels, Belgium, in 1994, where he is currently working toward the Ph.D. degree. Since October 1995, he has been a member of the Department of Electronics and Information Processing (ETRO), VUB. His research experience has focused on software design and development of tools for image and data visualization, image analysis, and telemedicine. His research has evolved in the direction of surface extraction, coding, and animation of polygonal surface meshes, and he is currently finishing his doctoral work on this topic. Since 2000, he has been actively involved in the Synthetic Natural Hybrid Coding (SNHC) Group of MPEG-4 and is the main contributor to the MESHGRID surface representation in SNHC. He is the author/coauthor of more than 30 scientific publications, patent applications, and contributions to standards.

IEEE Transactions on Circuits and Systems for Video Technology, 2004

MESHGRID is a novel, compact, multiscalable and animation-friendly surface representation method, which has been introduced in MPEG-4 [1]. The MESHGRID representation attaches a description of the "global connectivity" between the vertices on the object's surface (i.e., the 3-D connectivity wireframe) to a regular 3-D grid of points (i.e., the reference grid). MESHGRID efficiently encodes the 3-D connectivity wireframe by using a new type of 3-D extension of Freeman chain-code. MESHGRID does not explicitly store the polygons of the surface, since the 3-D connectivity wireframe has particular connectivity properties allowing for the unambiguous derivation of the triangulation. The reference grid is a smooth vector field defined on a regular discrete 3-D space. This grid is efficiently compressed by using an embedded 3-D wavelet-based multiresolution intra-band coding algorithm. MESHGRID can be efficiently exploited for QoS since it allows for three types of scalability in both view-dependent and view-independent scenarios, including: 1) resolution scalability, i.e., the adaptation of the number of transmitted vertices; 2) shape precision, i.e., the adaptive reconstruction of the reference grid positions; and 3) vertex position scalability, i.e., the change of the precision of known vertex positions with respect to the reference grid. Furthermore, in addition to the classical vertex-based animation, MESHGRID also supports specific animation capabilities, such as: 1) rippling effects by changing the position of the vertices relative to corresponding reference grid points and 2) reshaping on a hierarchical basis of the regular reference grid and its attached vertices. in 1989 and the M.Sc. degree in applied computer science from Vrije Universiteit Brussel (VUB), Brussels, Belgium, in 1994, where he is currently working toward the Ph.D. degree. Since October 1995, he has been a member of the Department of Electronics and Information Processing (ETRO), VUB. His research experience has focused on software design and development of tools for image and data visualization, image analysis, and telemedicine. His research has evolved in the direction of surface extraction, coding, and animation of polygonal surface meshes, and he is currently finishing his doctoral work on this topic. Since 2000, he has been actively involved in the Synthetic Natural Hybrid Coding (SNHC) Group of MPEG-4 and is the main contributor to the MESHGRID surface representation in SNHC. He is the author/coauthor of more than 30 scientific publications, patent applications, and contributions to standards.

2009 IEEE 17th Signal Processing and Communications Applications Conference, 2009

, 115 pages Polygonal meshes are a common way of representing 3D surface models in many different areas of computer graphics and geometry processing. However, these models are becoming more and more complex which increases the cost of processing these models. In order to reduce this cost, mesh simplification algorithms are developed. Another important property of a polygonal mesh model is that whether it is regular or not. Regular meshes have many advantages over the irregular ones in terms of memory requirements, efficient processing, rendering etc. In this thesis work, both mesh simplification and regular remeshing algorithms are studied. Moreover, some of the popular mesh libraries are compared with respect to their approaches and performance to the mesh simplification. In addition, mesh models with disk topology are remeshed and converted to regular ones.