Normal Meshes Research Articles

Scalable Intraband and Composite Wavelet-Based Coding of Semiregular Meshes

This paper proposes novel scalable mesh coding designs exploiting the intraband or composite statistical dependencies between the wavelet coefficients. A Laplacian mixture model is proposed to approximate the distribution of the wavelet coefficients. This model proves to be more accurate when compared to commonly employed single Laplacian or generalized Gaussian distribution models. Using the mixture model, we determine theoretically the optimal embedded quantizers to be used in scalable wavelet-based coding of semiregular meshes. In this sense, it is shown that the commonly employed successive approximation quantization is an acceptable, but in general, not an optimal solution. Novel scalable intraband and composite mesh coding systems are proposed, following an information-theoretic analysis of the statistical dependencies between the coefficients. The wavelet subbands are independently encoded using octree-based coding techniques. Furthermore, context-based entropy coding employing either intraband or composite models is applied. The proposed codecs provide both resolution and quality scalability. This lies in contrast to the state-of-the-art interband zerotree-based semiregular mesh coding technique, which supports only quality scalability. Additionally, the experimental results show that, on average, the proposed codecs outperform the interband state-of-the-art for both normal and nonnormal meshes. Finally, compared with a zerotree coding system, the proposed coding schemes are better suited for software/hardware parallelism, due to the independent processing of wavelet subbands.

Normal mesh based geometrical image compression

Recently the performance of nonlinear transforms have been given a lot of attention to overcome the suboptimal n-terms approximation power of tensor product wavelet methods on higher dimensions. The suboptimal performance prevails when the latter are used for a sparse representation of functions consisting of smoothly varying areas separated by smooth contours. This paper introduces a method creating normal meshes with nonsubdivision connectivity to approximate the nonsmoothness of such images efficiently. From a domain decomposition viewpoint, the method is a triangulation refinement method preserving contours. The transform is nonlinear as it depends on the actual image. This paper proposes an normal offset based compression algorithm for digital images. The discretisation causes the transform to become redundant. We further propose a model to encode the obtained coefficients. We show promising rate distortion curves and compare the results with the JPEG2000 encoder.

Change point oriented multiscale analysis using the lifting scheme

AbstractWe discuss a non‐linear, change point driven multiscale decomposition, known as normal offsets or normal meshes (in 2‐D). Unlike a wavelet transform, the proposed decomposition runs from coarse to fine scales. The coarse‐to‐fine approach can be seen as an adaptive sampler with theoretical and practical benefits in compression. It is, however, also a source of potential stability problems. Stability is crucial in applications as de‐noising, or simultaneous de‐noising and compression. As the normal offset transform is based on the lifting scheme, we investigate lifting steps that both contribute to stability and allow usage in a change point adaptive normal offset scheme. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

非構造格子を用いた津波氾濫解析の現地適用と陸上構造物の影響評価

In this study, we introduced flood analysis using unstructured meshes to tsunami inundation computation. At first, we verified its validity for the tsunami inundation case by comparing with the result provided with usual numerical simulation using normal spatial meshes. Secondary, we applied it to the supposed case of the earthquake-induced tsunami at the area of Kesennuma bay under the condition that coastal defense facilities were deposed and the effect of houses were considered as the residential dominated ratio inside the mesh or water transparent ratio from the neighboring road meshes.The simulation using unstructured meshes well reproduced local inundation flow around the land structures. And it implied that residences generally had mitigation effect for tsunami inundation disaster but it locally increased tsunami hazard especially on the road in case urbanization was progressed.

Facial shape and 3D skin

AbstractWe present novel ideas for facial shape and skin simulation on extremely detailed three‐dimensional facial meshes. Our input database is composed of a small number of scanned human faces with resolutions up to several million triangles, where even the pores are clearly distinguished. We show how to decompose the facial meshes into the global shape of the face plus skin detail (3D skin), and then to reconstitute them. Our modeling methodology allows us to simulate the exaggeration of the facial global shape, retaining the original skin detail, as well as to transfer 3D skin from one face to another. First, we represent all the input faces in terms of a homogeneous structure on the base model in low resolution by using mesh adaptation techniques. Second, the differences between the original mesh and a base mesh, which appear as skin detail, are captured and stored, so that each face is decomposed into the global shape (a base mesh) plus skin detail. Face reconstitution after global shape exaggeration and/or skin transfer enables delicate simulation of facial models. In addition, we can increase the resolution of any model scanned at a low resolution by transferring skin from a higher resolution model. Our method shows successful manipulation of the minute structure of 3D skin differently from other methods such as Normal Mapping, Displacement Mapping, Displaced Subdivision Surfaces, and Normal Meshes where none of these techniques show manipulation of minute structure like ours and only approximation is used while our method recovers the original structure. Copyright © 2006 John Wiley & Sons, Ltd.

Rate-distortion optimized compression and view-dependent transmission of 3-D normal meshes

A unified approach to rate-distortion (R-D) optimized compression and view-dependent transmission of three-dimensional (3-D) normal meshes is investigated in this work. A normal mesh is partitioned...

Rate-distortion optimized compression and view-dependent transmission of 3-D normal meshes

A unified approach to rate-distortion (R-D) optimized compression and view-dependent transmission of three-dimensional (3-D) normal meshes is investigated in this work. A normal mesh is partitioned into several segments, which are then encoded independently. The bitstream of each segment is truncated optimally using a geometry distortion model based on the subdivision hierarchy. It is shown that the proposed compression algorithm yields a higher coding gain than the conventional algorithm. Moreover, to facilitate interactive transmission of 3-D data according to a client's viewing position, the server can allocate an adaptive bitrate to each segment based on its visibility priority. Simulation results demonstrate that the view-dependent transmission technique can reduce the bandwidth requirement considerably, while maintaining a good visual quality.

An efficient bit allocation for compressing normal meshes with an error-driven quantization

We propose a new wavelet compression algorithm based on the rate-distortion optimization for densely sampled triangular meshes. Exploiting the normal remesher of Guskov et al., the proposed algorithm includes a wavelet transform and an original bit allocation optimizing the quantization of the wavelet coefficients. The allocation process minimizes the reconstruction error for a given bit budget. As distortion measure, we use the mean square error of the normal mesh quantization, expressed according to the quantization error of each subband. We show that this metric is a suitable criterion to evaluate the reconstruction error, i.e., the geometric distance between the input mesh and the quantized normal one. Moreover, to design a fast bit allocation, we propose a model-based approach, depending on distribution of the wavelet coefficients. Compared to the state-of-the-art methods for normal meshes, our algorithm provides improvements in coding performance, up to + 2.5 dB compared to the original zerotree coder.

Multiscale approximation of piecewise smooth two-dimensional functions using normal triangulated meshes

Multiresolution triangulation meshes are widely used in computer graphics for representing three-dimensional (3-d) shapes. We propose to use these tools to represent 2-d piecewise smooth functions such as grayscale images, because triangles have potential to more efficiently approximate the discontinuities between the smooth pieces than other standard tools like wavelets. We show that normal mesh subdivision is an efficient triangulation, thanks to its local adaptivity to the discontinuities. Indeed, we prove that, within a certain function class, the normal mesh representation has an optimal asymptotic error decay rate as the number of terms in the representation grows. This function class is the so-called horizon class comprising constant regions separated by smooth discontinuities, where the line of discontinuity is C 2 continuous. This optimal decay rate is possible because normal meshes automatically generate a polyline (piecewise linear) approximation of each discontinuity, unlike the blocky piecewise constant approximation of tensor product wavelets. In this way, the proposed nonlinear multiscale normal mesh decomposition is an anisotropic representation of the 2-d function. The same idea of anisotropic representations lies at the basis of decompositions such as wedgelet and curvelet transforms, but the proposed normal mesh approach has a unique construction.

Variational normal meshes

Hierarchical representations of surfaces have many advantages for digital geometry processing applications. <i>Normal meshes</i> are particularly attractive since their level-to-level displacements are in the local normal direction only. Consequently, they only require scalar coefficients to specify. In this article, we propose a novel method to approximate a given mesh with a normal mesh. Instead of building an associated parameterization on the fly, we assume a globally smooth parameterization at the beginning and cast the problem as one of perturbing this parameterization. Controlling the magnitude of this perturbation gives us explicit control over the range between fully constrained (only scalar coefficients) and unconstrained (3-vector coefficients) approximations. With the unconstrained problem giving the lowest approximation error, we can thus characterize the error cost of normal meshes as a function of the number of nonnormal offsets---we find a significant gain for little (error) cost. Because the normal mesh construction creates a <i>geometry driven</i> approximation, we can replace the difficult geometric distance minimization problem with a much simpler least squares problem. This variational approach reduces magnitude <i>and</i> structure (aliasing) of the error further. Our method separates the parameterization construction into an initial setup followed only by subsequent perturbations, giving us an algorithm which is far simpler to implement, more robust, and significantly faster.

Remeshing into normal meshes with boundaries using subdivision

In this paper, we present a remeshing algorithm using the recursive subdivision of irregular meshes with boundaries. A mesh remeshed by subdivision has several advantages. It has a topological regularity, which enables it to be used as a multiresolution model and to represent an original model with less data. Topological regularity is essential for the multiresolutional analysis of the given meshes and makes additional topological information unnecessary. Moreover, we use a normal mesh to reduce the geometric data size requirements at each resolution level of the regularized meshes. The normal mesh uses one scalar value, i.e. normal offset as wavelet, to represent a vertex position, while the other remeshing schemes use one three-dimensional vector at each vertex. The normal offset is a normal distance from a base face, which is the simplified original mesh. Since the normal offset cannot be properly used for the boundaries of a mesh, we use a combined subdivision scheme that resolves the problem of the proposed normal offset method at the boundaries. Finally, we show examples that demonstrate the effectiveness of the proposed scheme in terms of reducing the data requirements of mesh models.

Normal Meshes for Multiresolution Analysis of Irregular Meshes with Boundaries.

In this paper we present a remeshing algorithm for irregular meshes with boundaries. The irregular meshes are approximated by regular meshes that have topological regularity, which is essential for the multiresolution analysis of the given irregular meshes. Normal meshes are used to reduce the necessary data size at each resolution level of the regularized meshes. The normal mesh uses one scalar value, i. e., normal offset value that is calculated by the regular rule of a uniform subdivision and normal sampling, while other remeshing schemes use one 3D vector at each vertex. Since the normal offset cannot be adopted for the boundaries of meshes, we use a combined subdivision scheme that resolves the problem of the proposed normal offset method at the boundaries. Lastly, an example showing the effectiveness of the proposed scheme to reduce the data size of a mesh model is included.