Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error {\delta}, minimal interior angle {\theta} and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound {\delta} as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. In this way our optimization framework greedily searches for the coarsest mesh with minimal interior angle above {\theta} and approximation error bounded by {\delta}. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization and Computer Graphic

Smear fitting: a new deconvolution method for interferometric data

A new technique is presented for producing images from interferometric data. The method, ``smear fitting'', makes the constraints necessary for interferometric imaging double as a model, with uncertainties, of the sky brightness distribution. It does this by modelling the sky with a set of functions and then convolving each component with its own elliptical gaussian to account for the uncertainty in its shape and location that arises from noise. This yields much sharper resolution than CLEAN for significantly detected features, without sacrificing any sensitivity. Using appropriate functional forms for the components provides both a scientifically interesting model and imaging constraints that tend to be better than those used by traditional deconvolution methods. This allows it to avoid the most serious problems that limit the imaging quality of those methods. Comparisons of smear fitting to CLEAN and maximum entropy are given, using both real and simulated observations. It is also shown that the famous Rayleigh criterion (resolution = wavelength / baseline) is inappropriate for interferometers as it does not consider the reliability of the measurements.Comment: 16 pages, 38 figures (some have been lossily compressed for astro-ph). Uses the hyperref LaTeX package. Accepted for publication by the Monthly Notices of the Royal Astronomical Societ

Efficient Multi-Template Learning for Structured Prediction

Conditional random field (CRF) and Structural Support Vector Machine (Structural SVM) are two state-of-the-art methods for structured prediction which captures the interdependencies among output variables. The success of these methods is attributed to the fact that their discriminative models are able to account for overlapping features on the whole input observations. These features are usually generated by applying a given set of templates on labeled data, but improper templates may lead to degraded performance. To alleviate this issue, in this paper, we propose a novel multiple template learning paradigm to learn structured prediction and the importance of each template simultaneously, so that hundreds of arbitrary templates could be added into the learning model without caution. This paradigm can be formulated as a special multiple kernel learning problem with exponential number of constraints. Then we introduce an efficient cutting plane algorithm to solve this problem in the primal, and its convergence is presented. We also evaluate the proposed learning paradigm on two widely-studied structured prediction tasks, \emph{i.e.} sequence labeling and dependency parsing. Extensive experimental results show that the proposed method outperforms CRFs and Structural SVMs due to exploiting the importance of each template. Our complexity analysis and empirical results also show that our proposed method is more efficient than OnlineMKL on very sparse and high-dimensional data. We further extend this paradigm for structured prediction using generalized $p$-block norm regularization with $p>1$, and experiments show competitive performances when $p \in [1,2)$