Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEigen Space of Mesh Distortion Energy Hessian
75
0
0.0
(
0
)
Added by
Yufeng Zhu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Yufeng Zhu
Ask ChatGPT about the research
No Arabic abstract
Mesh distortion optimization is a popular research topic and has wide range of applications in computer graphics, including geometry modeling, variational shape interpolation, UV parameterization, elastoplastic simulation, etc. In recent years, many solvers have been proposed to solve this nonlinear optimization efficiently, among which projected Newton has been shown to have best convergence rate and work well in both 2D and 3D applications. Traditional Newton approach suffers from ill conditioning and indefiniteness of local energy approximation. A crucial step in projected Newton is to fix this issue by projecting energy Hessian onto symmetric positive definite (SPD) cone so as to guarantee the search direction always pointing to decrease the energy locally. Such step relies on time consuming eigen decomposition of element Hessian, which has been addressed by several work before on how to obtain a conjugacy that is as diagonal as possible. In this report, we demonstrate an analytic form of Hessian eigen system for distortion energy defined using principal stretches, which is the most general representation. Compared with existing projected Newton diagonalization approaches, our formulation is more general as it doesnt require the energy to be representable by tensor invariants. In this report, we will only show the derivation for 3D and the extension to 2D case is straightforward.
rate research
Read More
Feature-preserving mesh denoising has received noticeable attention recently. Many methods often design great weighting for anisotropic surfaces and small weighting for isotropic surfaces, to preserve sharp features. However, they often disregard the fact that small weights still pose negative impacts to the denoising outcomes. Furthermore, it may increase the difficulty in parameter tuning, especially for users without any background knowledge. In this paper, we propose a novel clustering method for mesh denoising, which can avoid the disturbance of anisotropic information and be easily embedded into commonly-used mesh denoising frameworks. Extensive experiments have been conducted to validate our method, and demonstrate that it can enhance the denoising results of some existing methods remarkably both visually and quantitatively. It also largely relaxes the parameter tuning procedure for users, in terms of increasing stability for existing mesh denoising methods.
Capturing the 3D geometry of transparent objects is a challenging task, ill-suited for general-purpose scanning and reconstruction techniques, since these cannot handle specular light transport phenomena. Existing state-of-the-art methods, designed specifically for this task, either involve a complex setup to reconstruct complete refractive ray paths, or leverage a data-driven approach based on synthetic training data. In either case, the reconstructed 3D models suffer from over-smoothing and loss of fine detail. This paper introduces a novel, high precision, 3D acquisition and reconstruction method for solid transparent objects. Using a static background with a coded pattern, we establish a mapping between the camera view rays and locations on the background. Differentiable tracing of refractive ray paths is then used to directly optimize a 3D mesh approximation of the object, while simultaneously ensuring silhouette consistency and smoothness. Extensive experiments and comparisons demonstrate the superior accuracy of our method.
In this paper, we extend our earlier polycube-based all-hexahedral mesh generation method to hexahedral-dominant mesh generation, and present the HexDom software package. Given the boundary representation of a solid model, HexDom creates a hex-dominant mesh by using a semi-automated polycube-based mesh generation method. The resulting hexahedral dominant mesh includes hexahedra, tetrahedra, and triangular prisms. By adding non-hexahedral elements, we are able to generate better quality hexahedral elements than in all-hexahedral meshes. We explain the underlying algorithms in four modules including segmentation, polycube construction, hex-dominant mesh generation and quality improvement, and use a rockerarm model to explain how to run the software. We also apply our software to a number of other complex models to test their robustness. The software package and all tested models are availabe in github (https://github.com/CMU-CBML/HexDom).
Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of these vertices is non-trivial. We call these vertices distortion points. We present a novel and automatic method to detect distortion points using a voting strategy. Our method integrates two components: candidate generation and candidate voting. Given a closed triangular mesh, we generate candidate distortion points by executing a three-step procedure repeatedly: (1) randomly cut an input to a disk topology; (2) compute a low conformal distortion parameterization; and (3) detect the distortion points. Finally, we count the candidate points and generate the final distortion points by voting. We demonstrate that our algorithm succeeds when employed on various closed meshes with a genus of zero or higher. The distortion points generated by our method are utilized in three applications, including planar parameterization, semi-automatic landmark correspondence, and isotropic remeshing. Compared to other state-of-the-art methods, our method demonstrates stronger practical robustness in distortion point detection.
Rate-distortion (RD) theory is at the heart of lossy data compression. Here we aim to model the generalized RD (GRD) trade-off between the visual quality of a compressed video and its encoding profiles (e.g., bitrate and spatial resolution). We first define the theoretical functional space $mathcal{W}$ of the GRD function by analyzing its mathematical properties.We show that $mathcal{W}$ is a convex set in a Hilbert space, inspiring a computational model of the GRD function, and a method of estimating model parameters from sparse measurements. To demonstrate the feasibility of our idea, we collect a large-scale database of real-world GRD functions, which turn out to live in a low-dimensional subspace of $mathcal{W}$. Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD method to accurately estimate the GRD function of a source video content from only a few queries. Experimental results on the database show that the learned GRD method significantly outperforms state-of-the-art empirical RD estimation methods both in accuracy and efficiency. Last, we demonstrate the promise of the proposed model in video codec comparison.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
