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Sharp edges are important shape features and their extraction has been extensively studied both on point clouds and surfaces. We consider the problem of extracting sharp edges from a sparse set of colour-and-depth (RGB-D) images. The noise-ridden depth measurements are challenging for existing feature extraction methods that work solely in the geometric domain (e.g. points or meshes). By utilizing both colour and depth information, we propose a novel feature extraction method that produces much cleaner and more coherent feature lines. We make two technical contributions. First, we show that intensity edges can augment the depth map to improve normal estimation and feature localization from a single RGB-D image. Second, we designed a novel algorithm for consolidating feature points obtained from multiple RGB-D images. By utilizing normals and ridge/valley types associated with the feature points, our algorithm is effective in suppressing noise without smearing nearby features.

Time- and state-domain methods are two common approaches to nonparametric prediction. Whereas the former uses data predominantly from recent history, the latter relies mainly on historical information. Combining these two pieces of valuable information is an interesting challenge in statistics. We surmount this problem by dynamically integrating information from both the time and state domains. The estimators from these two domains are optimally combined based on a data-driven weighting strategy, which provides a more efficient estimator of volatility. Asymptotic normality is separately established for the time domain, the state domain, and the integrated estimators. By comparing the efficiency of the estimators, we demonstrate that the proposed integrated estimator uniformly dominates the other two estimators. The proposed dynamic integration approach is also applicable to other estimation problems in time

We present a hybrid asymptotic/numerical method for the accurate computation of single- and double-layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called “geometrically induced stiffness,” meaning that formally high-order accurate methods require excessively small time steps before the rapid convergence rate is observed. This can be overcome by analytic integration in time, requiring the evaluation of a collection of spatial boundary integral operators with non-physical, weakly singular kernels. In our hybrid scheme, we combine a local asymptotic approximation with the evaluation of a few boundary integral operators involving only Gaussian kernels, which are easily accelerated by a new version of the fast Gauss transform. This new scheme is robust, avoids geometrically induced stiffness, and is easy to use in the presence of moving geometries. Its extension to three dimensions is natural and straightforward, and should permit layer heat potentials to become flexible and powerful tools for modeling diffusion processes.