Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be recognized as data living on manifold surfaces. So interpolation and approximation for these data are of general interest. This paper presents two approaches for manifold data interpolation and approximation through the properties of Laplace-Beltrami operator (Laplace operator defined on a manifold surface). The first one is to use Laplace operator minimizing the membrane energy of a scalar function defined on a manifold. The second one is to use bi-Laplace operator minimizing the thin plate energy of a scalar function defined on a manifold. These two approaches can process data living on high genus meshed surfaces. The approach based on Laplace operator is more suitable for manifold data approximation and can be applied manifold data smoothing, while the one based on bi-Laplace operator is more suitable for manifold data interpolation and can be applied image extremal envelope computation. All the application examples demonstrate that our procedures are robust and efficient.
We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection(LOP) operator.Our algorithm includes two new developments.First,a weight term related to surface variation at each point is introduced to the classic LOP operator.It produces output points with a spatially adaptive distribution.Second,for speeding up the convergence of our method,an initialization process is proposed based on geometry-aware stochastic sampling.Owing to the initialization,the relaxation process achieves a faster convergence rate than those initialized by uniform sampling.Our simplification method possesses a number of distinguishing features.In particular,it provides resilience to noise and outliers,and an intuitively controllable distribution of simplification.Finally,we show the results of our approach with publicly available point cloud data,and compare the results with those obtained using previous methods.Our method outperforms these methods on raw scanned data.
Among the human users of the Internet of Things,the hearing-impaired is a special group of people for whom normal information expression forms,such as voice and video are unaccessible,and most of them have some difficulty in understanding information in text form.The hearing-impaired are accustomed to receiving information expressed in sign language.For this situation,a new information expression form for the Internet of Things oriented toward the hearing-impaired is proposed in this paper,and the new expression is based on sign language video synthesis.Under the sign synthesis frame,three modules are necessary:constructing database,searching for appropriate sign language video units and transition units,and generating interpolated frames.With this method,text information could be transformed into sign language expression for the hearing-impaired.
