On Two Kinds of Differential Operators on General Smooth Surfaces

Two kinds of differential operators that can be generally defined on an arbitrary smooth surface in a finite dimensional Euclid space are studied, one is termed as surface gradient and the other one as Levi-Civita gradient. The surface gradient operator is originated from the differentiability of a tensor field defined on the surface. Some integral and differential identities have been theoretically studied that play the important role in the studies on continuous mediums whose geometrical configurations can be taken as surfaces and on interactions between fluids and deformable boundaries. The definition of Levi-Civita gradient is based on Levi-Civita connections generally defined on Riemann manifolds. It can be used to set up some differential identities in the intrinsic/coordiantes-independent form that play the essential role in the theory of vorticity dynamics for two dimensional flows on general fixed smooth surfaces

A Multi-level Correction Scheme for Eigenvalue Problems

In this paper, a new type of multi-level correction scheme is proposed for solving eigenvalue problems by finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an eigenvalue problem on the coarsest finite element space. This correction scheme can improve the efficiency of solving eigenvalue problems by finite element method.Comment: 16 pages, 5 figure

A Parallel Method for Population Balance Equations Based on the Method of Characteristics

In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher dimensional population balance equation into a series of lower dimensional convection-diffusion-reaction equations which can be solved in a parallel way.Some numerical results are presented to show the accuracy and efficiency.Comment: 10 pages, 0 figur

Instance-Level Salient Object Segmentation

Image saliency detection has recently witnessed rapid progress due to deep convolutional neural networks. However, none of the existing methods is able to identify object instances in the detected salient regions. In this paper, we present a salient instance segmentation method that produces a saliency mask with distinct object instance labels for an input image. Our method consists of three steps, estimating saliency map, detecting salient object contours and identifying salient object instances. For the first two steps, we propose a multiscale saliency refinement network, which generates high-quality salient region masks and salient object contours. Once integrated with multiscale combinatorial grouping and a MAP-based subset optimization framework, our method can generate very promising salient object instance segmentation results. To promote further research and evaluation of salient instance segmentation, we also construct a new database of 1000 images and their pixelwise salient instance annotations. Experimental results demonstrate that our proposed method is capable of achieving state-of-the-art performance on all public benchmarks for salient region detection as well as on our new dataset for salient instance segmentation.Comment: To appear in CVPR201