The Hierarchical Subspace Iteration Method for Laplace–Beltrami Eigenproblems

Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace–Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The Subspace Iteration Method is a robust solver for these problems. In practice, however, Lanczos schemes are often faster. In this article, we introduce the Hierarchical Subspace Iteration Method (HSIM) , a novel solver for sparse eigenproblems that operates on a hierarchy of nested vector spaces. The hierarchy is constructed such that on the coarsest space all eigenpairs can be computed with a dense eigensolver. HSIM uses these eigenpairs as initialization and iterates from coarse to fine over the hierarchy. On each level, subspace iterations, initialized with the solution from the previous level, are used to approximate the eigenpairs. This approach substantially reduces the number of iterations needed on the finest grid compared to the non-hierarchical Subspace Iteration Method. Our experiments show that HSIM can solve Laplace–Beltrami eigenproblems on meshes faster than state-of-the-art methods based on Lanczos iterations, preconditioned conjugate gradients, and subspace iterations.

A Coarse-to-Fine Registration Approach for Point Cloud Data with Bipartite Graph Structure

Alignment is a critical aspect of point cloud data (PCD) processing, and we propose a coarse-to-fine registration method based on bipartite graph matching in this paper. After data pre-processing, the registration progress can be detailed as follows: Firstly, a top-tail (TT) strategy is designed to normalize and estimate the scale factor of two given PCD sets, which can combine with the coarse alignment process flexibly. Secondly, we utilize the 3D scale-invariant feature transform (3D SIFT) method to extract point features and adopt fast point feature histograms (FPFH) to describe corresponding feature points simultaneously. Thirdly, we construct a similarity weight matrix of the source and target point data sets with bipartite graph structure. Moreover, the similarity weight threshold is used to reject some bipartite graph matching error-point pairs, which determines the dependencies of two data sets and completes the coarse alignment process. Finally, we introduce the trimmed iterative closest point (TrICP) algorithm to perform fine registration. A series of extensive experiments have been conducted to validate that, compared with other algorithms based on ICP and several representative coarse-to-fine alignment methods, the registration accuracy and efficiency of our method are more stable and robust in various scenes and are especially more applicable with scale factors.

Progressive edge-sensing dynamic scene deblurring

Deblurring images of dynamic scenes is a challenging task because blurring occurs due to a combination of many factors. In recent years, the use of multi-scale pyramid methods to recover high-resolution sharp images has been extensively studied. We have made improvements to the lack of detail recovery in the cascade structure through a network using progressive integration of data streams. Our new multi-scale structure and edge feature perception design deals with changes in blurring at different spatial scales and enhances the sensitivity of the network to blurred edges. The coarse-to-fine architecture restores the image structure, first performing global adjustments, and then performing local refinement. In this way, not only is global correlation considered, but also residual information is used to significantly improve image restoration and enhance texture details. Experimental results show quantitative and qualitative improvements over existing methods.

Flood Detection Using Multiple Chinese Satellite Datasets during 2020 China Summer Floods

Multiple source satellite datasets, including the Gaofen (GF) series and Zhuhai-1 hyperspectral, are provided to detect and monitor the floods. Considering the complexity of land cover changes within the flooded areas and the different characteristics of the multi-source remote sensing dataset, we proposed a new coarse-to-fine framework for detecting floods at a large scale. Firstly, the coarse results of the water body were generated by the binary segmentation of GF-3 SAR, the water indexes of GF-1/6 multispectral, and Zhuhai-1 hyperspectral images. Secondly, the fine results were achieved by the deep neural networks with noisy-label learning. More specifically, the Unet with the T-revision is adopted as the noisy label learning method. The results demonstrated the reliability and accuracy of water mapping retrieved by the noisy learning method. Finally, the differences in flooding patterns in different regions were also revealed. We presented examples of Poyang Lake to show the results of our framework. The rapid and robust flood monitoring method proposed is of great practical significance to the dynamic monitoring of flood situations and the quantitative assessment of flood disasters based on multiple Chinese satellite datasets.

3D corrective nose reconstruction from a single image

There is a steadily growing range of applications that can benefit from facial reconstruction techniques, leading to an increasing demand for reconstruction of high-quality 3D face models. While it is an important expressive part of the human face, the nose has received less attention than other expressive regions in the face reconstruction literature. When applying existing reconstruction methods to facial images, the reconstructed nose models are often inconsistent with the desired shape and expression. In this paper, we propose a coarse-to-fine 3D nose reconstruction and correction pipeline to build a nose model from a single image, where 3D and 2D nose curve correspondences are adaptively updated and refined. We first correct the reconstruction result coarsely using constraints of 3D-2D sparse landmark correspondences, and then heuristically update a dense 3D-2D curve correspondence based on the coarsely corrected result. A final refinement step is performed to correct the shape based on the updated 3D-2D dense curve constraints. Experimental results show the advantages of our method for 3D nose reconstruction over existing methods.