An r-Adaptive Technique for Unstructured Grids Based on the Segment Spring Analogy Method

Abstract

A simple and effective r-adaptive technique for unstructured grids based on the segment spring analogy method is proposed. The finite element method and a corresponding error estimate method using second derivatives are used for computation. The traditional segment spring analogy method is modified, based on an idea of controlling the equilibrium length of the fictitious springs, and used for mesh adjustment. The principle of making numerical errors distributed uniformly over all elements is applied. Three numerical examples involving the one-dimensional (1D) convection-diffusion equation, the two-dimensional (2D) linear parabolic equation and the 2D Euler equations are presented and the effectiveness of the proposed r-type grid adaptive technique is examined.

RMLANet: Random Multi-Level Attention Network for Shadow Detection

“…We compare our approach with one traditional methods, namely Unary-Pairwise [55], and 18 deep learning based shadow detection methods which are stacked-CNN [3], sc-GAN [56], patched-CNN [57], ST-CGAN [5], DSC [23], ADNet [58], BDRAR [25], DC-DSPF [59], DSDNet [26], MTMT-Net [27], RCMPNet [33], FDRNet [60], SDCM [61], TranShadow [30], FCSD-Net [62], RMLANet [31], [32], SDDNet [63] and SARA [64], both qualitatively and quantitatively. For fair comparison, all the predicted shadow masks or BER values of other methods are directly adopted from their paper or obtained using their official code.…”

“…In Table I, the qualitative results of our method with other methods are presented. Specifically, our method surpasses Unary-Pairwise [55], stacked-CNN [3], scGAN [56], patched-CNN [57], ST-CGAN [5], DSC [23], ADNet [58], BDRAR [25], DC-DSPF [59], DSDNet [26], MTMT-Net [27], RCMPNet [33], FDRNet [60], SDCM [61], TranShadow [30], FCSD-Net [62], RMLANet [31], [32], SDDNet [63] and SARA [64] by 89.01%, 75.00%, 69.78%, 76.21%, 66.22%, 50.81%, 48.79%, 24.45%, 43.88%, 20.29%, 12.70%, 12.14%, 9.54%, 8.94%, 13.25%, 12.70%, 7.41%, 6.46% and 4.18% respectively on the SBU dataset. More importantly, our method demonstrates the best generalization ability in terms of the performance on the UCF dataset, when directly evaluated the performance on the UCF dataset using the model trained on the SBU dataset.…”

“…More importantly, our method demonstrates the best generalization ability in terms of the performance on the UCF dataset, when directly evaluated the performance on the UCF dataset using the model trained on the SBU dataset. In particular, our method outperforms stacked-CNN [3], scGAN [56], ST-CGAN [5], DSC [23], ADNet [58], BDRAR [25], DC-DSPF [59], DSDNet [26], MTMT-Net [27], RCMPNet [33], FDRNet [60], SDCM [61], TranShadow [30], FCSD-Net [62], RMLANet [31], [32], SDDNet [63] and SARA [64] by 51.15%, 44.78%, 43.46%, 39.75%, 31.35%, 18.69%, 19.62%, 16.34%, 14.99%, 5.37%, 12.77%, 5.08%, 8.63%, 8.76%, 0.94%, 3.64% and 9.42% respectively. Moreover, our method also achieves the best performance on the ISTD dataset, by outdistancing stacked-CNN [3], scGAN [56], patched-CNN [57], DSC [23], ADNet [58], BDRAR [25], DSD-Net [26], MTMT-Net [27], RCMPNet [33], FDRNet [60], SDCM [61], TranShadow [30], FCSD-Net [62], RM-LANet [31], [32], SDDNet [63] and SARA [64] To further demonstrate the effectiveness of our method, quantitative results on SBU T estN ew and CUHK dataset are presented in Table II and Table III.…”

“…Specifically, we first adopt an off-the-shelf feature extractor (e.g., Efficient-Net [52], ResNext101 [53]) as our encoder to extract feature pyramids. Given an input shadow image for Efficient-Net B5, while C i = [64,256,512,1024,2048] for ResNext101. Give the input feature F i e , we formulate the decoder blocks which produce the decoder features F i d as follows:…”