The classification of point cloud data is the key technology of point cloud data information acquisition and 3D reconstruction, which has a wide range of applications. However, the existing point cloud classification ...The classification of point cloud data is the key technology of point cloud data information acquisition and 3D reconstruction, which has a wide range of applications. However, the existing point cloud classification methods have some shortcomings when extracting point cloud features, such as insufficient extraction of local information and overlooking the information in other neighborhood features in the point cloud, and not focusing on the point cloud channel information and spatial information. To solve the above problems, a point cloud classification network based on graph convolution and fusion attention mechanism is proposed to achieve more accurate classification results. Firstly, the point cloud is regarded as a node on the graph, the k-nearest neighbor algorithm is used to compose the graph and the information between points is dynamically captured by stacking multiple graph convolution layers;then, with the assistance of 2D experience of attention mechanism, an attention mechanism which has the capability to integrate more attention to point cloud spatial and channel information is introduced to increase the feature information of point cloud, aggregate local useful features and suppress useless features. Through the classification experiments on ModelNet40 dataset, the experimental results show that compared with PointNet network without considering the local feature information of the point cloud, the average classification accuracy of the proposed model has a 4.4% improvement and the overall classification accuracy has a 4.4% improvement. Compared with other networks, the classification accuracy of the proposed model has also been improved.展开更多
In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph fo...In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.展开更多
The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the mol...The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the molecular graphs.展开更多
The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is containe...The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is contained in the closure of the set R(f) of recurrent points of f.展开更多
文摘The classification of point cloud data is the key technology of point cloud data information acquisition and 3D reconstruction, which has a wide range of applications. However, the existing point cloud classification methods have some shortcomings when extracting point cloud features, such as insufficient extraction of local information and overlooking the information in other neighborhood features in the point cloud, and not focusing on the point cloud channel information and spatial information. To solve the above problems, a point cloud classification network based on graph convolution and fusion attention mechanism is proposed to achieve more accurate classification results. Firstly, the point cloud is regarded as a node on the graph, the k-nearest neighbor algorithm is used to compose the graph and the information between points is dynamically captured by stacking multiple graph convolution layers;then, with the assistance of 2D experience of attention mechanism, an attention mechanism which has the capability to integrate more attention to point cloud spatial and channel information is introduced to increase the feature information of point cloud, aggregate local useful features and suppress useless features. Through the classification experiments on ModelNet40 dataset, the experimental results show that compared with PointNet network without considering the local feature information of the point cloud, the average classification accuracy of the proposed model has a 4.4% improvement and the overall classification accuracy has a 4.4% improvement. Compared with other networks, the classification accuracy of the proposed model has also been improved.
文摘In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.
文摘The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the molecular graphs.
基金The first author is supported by the Natural Science Foundation of the Committee of Education ofJiangsu Province ( 0 2 KJB1 1 0 0 0 8)
文摘The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is contained in the closure of the set R(f) of recurrent points of f.
