50 research outputs found
Constrained Texture Mapping And Foldover-free Condition
Texture mapping has been widely used in image
processing and graphics to enhance the realism of CG scenes.
However to perfectly match the feature points of a 3D model
with the corresponding pixels in texture images, the
parameterisation which maps a 3D mesh to the texture space
must satisfy the positional constraints. Despite numerous
research efforts, the construction of a mathematically robust
foldover-free parameterisation subject to internal constraints
is still a remaining issue. In this paper, we address this
challenge by developing a two-step parameterisation method.
First, we produce an initial parameterisation with a method
traditionally used to solve structural engineering problems,
called the bar-network. We then derive a mathematical
foldover-free condition, which is incorporated into a Radial
Basis Function based scheme. This method is therefore able to
guarantee that the resulting parameterization meets the hard
constraints without foldovers
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Signal-Specialized Parameterization
To reduce memory requirements for texture mapping a model, we build a surface parametrization specialized to its signal (such as color or normal). Intuitively, we want to allocate more texture samples in regions with greater signal detail. Our approach is to minimize signal approximation error --- the difference between the original surface signal and its reconstruction from the sampled texture. Specifically, our signal-stretch parametrization metric is derived from a Taylor expansion of signal error. For fast evaluation, this metric is pre-integrated over the surface as a metric tensor. We minimize this nonlinear metric using a novel coarse-to-fine hierarchical solver, further accelerated with a fine-to-coarse propagation of the integrated metric tensor. Use of metric tensors permits anisotropic squashing of the parametrization along directions of low signal gradient. Texture area can often be reduced by a factor of 4 for a desired signal accuracy compared to non-specialized parametrizations.Engineering and Applied Science
An RBF-based reparameterization method for constrained texture mapping
Texture mapping has long been used in computer graphics to
enhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous
research efforts, the construction of a mathematically robust, foldoverâfree parameterization that is subject to
positional constraints continues to be a challenge. In the
present paper, this foldover problem is addressed by developing radial basis function (RBF) based reparameterization. Given initial 2D embedding of a 3D
surface, the proposed method can reparameterize 2D embedding into a foldover âfree 2D mesh, satisfying a set
of userâspecified constraint points. In addition, this approach is meshâfree. Therefore, generating smooth texture
mapping results is possible without extra smoothing optimization
Constrained parameterization with applications to graphics and image processing.
Surface parameterization is to establish a transformation that maps the points on a surface to a specified parametric domain. It has been widely applied to computer graphics and image processing fields. The challenging issue is that the usual positional constraints always result in triangle flipping in parameterizations (also called foldovers). Additionally, distortion is inevitable in parameterizations. Thus the rigid constraint is always taken into account. In general, the constraints are application-dependent. This thesis thus focuses on the various constraints depended on applications and investigates the foldover-free constrained parameterization approaches individually. Such constraints usually include, simple positional constraints, tradeoff of positional constraints and rigid constraint, and rigid constraint. From the perspective of applications, we aim at the foldover-free parameterization methods with positional constraints, the as-rigid-as-possible parameterization with positional constraints, and the well-shaped well-spaced pre-processing procedure for low-distortion parameterizations in this thesis. The first contribution of this thesis is the development of a RBF-based re-parameterization algorithm for the application of the foldover-free constrained texture mapping. The basic idea is to split the usual parameterization procedure into two steps, 2D parameterization with the constraints of convex boundaries and 2D re-parameterization with the interior positional constraints. Moreover, we further extend the 2D re-parameterization approach with the interior positional constraints to high dimensional datasets, such as, volume data and polyhedrons. The second contribution is the development of a vector field based deformation algorithm for 2D mesh deformation and image warping. Many presented deformation approaches are used to employ the basis functions (including our proposed RBF-based re-parameterization algorithm here). The main problem is that such algorithms have infinite support, that is, any local deformation always leads to small changes over the whole domain. Our presented vector field based algorithm can effectively carry on the local deformation while reducing distortion as much as possible. The third contribution is the development of a pre-processing for surface parameterization. Except the developable surfaces, the current parameterization approaches inevitably incur large distortion. To reduce distortion, we proposed a pre-processing procedure in this thesis, including mesh partition and mesh smoothing. As a result, the resulting meshes are partitioned into a set of small patches with rectangle-like boundaries. Moreover, they are well-shaped and well-spaced. This pre-processing procedure can evidently improve the quality of meshes for low-distortion parameterizations
Pointshop 3D: An interactive system for point-based surface editing
We present a system for interactive shape and appearance editing of 3D point-sampled geometry. By generalizing conventional 2D pixel editors, our system supports a great variety of different interaction techniques to alter shape and appearance of 3D point models, including cleaning, texturing, sculpting, carving, filtering, and resampling. One key ingredient of our framework is a novel concept for interactive point cloud parameterization allowing for distortion minimal and aliasing-free texture mapping. A second one is a dynamic, adaptive resampling method which builds upon a continuous reconstruction of the model surface and its attributes. These techniques allow us to transfer the full functionality of 2D image editing operations to the irregular 3D point setting. Our system reads, processes, and writes point-sampled models without intermediate tesselation. It is intended to complement existing low cost 3D scanners and point rendering pipelines for efficient 3D content creation
A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes
In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Coxâde Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and does not require CAD information; (3) freeform shape optimization of arbitrary polygonal or polyhedral meshes. Numerical experiments indicate the effectiveness of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34540/1/1050_ftp.pd