In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and...In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and inherently sparse.Therefore,it is very difficult to extract long-range contexts and effectively aggregate local features for semantic segmentation in 3D point cloud space.Most current methods either focus on local feature aggregation or long-range context dependency,but fail to directly establish a global-local feature extractor to complete the point cloud semantic segmentation tasks.In this paper,we propose a Transformer-based stratified graph convolutional network(SGT-Net),which enlarges the effective receptive field and builds direct long-range dependency.Specifically,we first propose a novel dense-sparse sampling strategy that provides dense local vertices and sparse long-distance vertices for subsequent graph convolutional network(GCN).Secondly,we propose a multi-key self-attention mechanism based on the Transformer to further weight augmentation for crucial neighboring relationships and enlarge the effective receptive field.In addition,to further improve the efficiency of the network,we propose a similarity measurement module to determine whether the neighborhood near the center point is effective.We demonstrate the validity and superiority of our method on the S3DIS and ShapeNet datasets.Through ablation experiments and segmentation visualization,we verify that the SGT model can improve the performance of the point cloud semantic segmentation.展开更多
A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S i...A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.展开更多
Most of local feature descriptors assume that the scene is planar. In the real scene, the captured images come from the 3-D world. 3-D corner as a novel invariant feature is important for the image matching and the ob...Most of local feature descriptors assume that the scene is planar. In the real scene, the captured images come from the 3-D world. 3-D corner as a novel invariant feature is important for the image matching and the object detection, while automatically discriminating 3-D corners from ordinary corners is difficult. A novel method for 3-D corner detection is proposed based on the image graph grammar, and it can detect the 3-D features of corners to some extent. Experimental results show that the method is valid and the 3-D corner is useful for image matching.展开更多
Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the ...Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.展开更多
Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph...Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.展开更多
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert...A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.展开更多
Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （o...Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （or simply ai） = q ＋ r ＋ dui^＋ - dui^-, bvj （or simply b j） = p ＋ r ＋ d^＋vj - d^-vj and cwk （or simply ck） =p ＋ q ＋ dwk^＋ -dwk^- as the scores of ui in U,vj in V and wk in W respectively. The set A of distinct scores of the vertices of D（U, V, W） is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai（2 ≤ i ≤ n - 1） are even positive integers and an is any positive integer, then for n 〉 3, there exists an oriented 3-partite graph with the score set A ={a1,Σ2i=1 ai,…,Σni=1 ai}, except when A = {0, 2, 3}. Some more results for score sets in oriented 3-partite graphs are obtained.展开更多
An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u...An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.展开更多
It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of ev...It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.展开更多
Cerenkov Luminescence Tomography(CLT)is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes.However,due to severe ill-posed inverse problem,obtaining accur...Cerenkov Luminescence Tomography(CLT)is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes.However,due to severe ill-posed inverse problem,obtaining accurate reconstruction results is still a challenge for traditional model-based methods.The recently emerged deep learning-based methods can directly learn the mapping relation between the surface photon intensity and the distribution of the radioactive source,which effectively improves the performance of CLT reconstruction.However,the previously proposed deep learning-based methods cannot work well when the order of input is disarranged.In this paper,a novel 3D graph convolution-based residual network,GCR-Net,is proposed,which can obtain a robust and accurate reconstruction result from the photon intensity of the surface.Additionally,it is proved that the network is insensitive to the order of input.The performance of this method was evaluated with numerical simulations and in vivo experiments.The results demonstrated that compared with the existing methods,the proposed method can achieve efficient and accurate reconstruction in localization and shape recovery by utilizing threedimensional information.展开更多
Background In this study,we propose a novel 3D scene graph prediction approach for scene understanding from point clouds.Methods It can automatically organize the entities of a scene in a graph,where objects are nodes...Background In this study,we propose a novel 3D scene graph prediction approach for scene understanding from point clouds.Methods It can automatically organize the entities of a scene in a graph,where objects are nodes and their relationships are modeled as edges.More specifically,we employ the DGCNN to capture the features of objects and their relationships in the scene.A Graph Attention Network(GAT)is introduced to exploit latent features obtained from the initial estimation to further refine the object arrangement in the graph structure.A one loss function modified from cross entropy with a variable weight is proposed to solve the multi-category problem in the prediction of object and predicate.Results Experiments reveal that the proposed approach performs favorably against the state-of-the-art methods in terms of predicate classification and relationship prediction and achieves comparable performance on object classification prediction.Conclusions The 3D scene graph prediction approach can form an abstract description of the scene space from point clouds.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos.U20A20197,62306187the Foundation of Ministry of Industry and Information Technology TC220H05X-04.
文摘In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and inherently sparse.Therefore,it is very difficult to extract long-range contexts and effectively aggregate local features for semantic segmentation in 3D point cloud space.Most current methods either focus on local feature aggregation or long-range context dependency,but fail to directly establish a global-local feature extractor to complete the point cloud semantic segmentation tasks.In this paper,we propose a Transformer-based stratified graph convolutional network(SGT-Net),which enlarges the effective receptive field and builds direct long-range dependency.Specifically,we first propose a novel dense-sparse sampling strategy that provides dense local vertices and sparse long-distance vertices for subsequent graph convolutional network(GCN).Secondly,we propose a multi-key self-attention mechanism based on the Transformer to further weight augmentation for crucial neighboring relationships and enlarge the effective receptive field.In addition,to further improve the efficiency of the network,we propose a similarity measurement module to determine whether the neighborhood near the center point is effective.We demonstrate the validity and superiority of our method on the S3DIS and ShapeNet datasets.Through ablation experiments and segmentation visualization,we verify that the SGT model can improve the performance of the point cloud semantic segmentation.
基金Supported by NSFC(Grant Nos.11801148 and 11626089)the Foundation for the Doctor of Henan Polytechnic University(Grant No.B2014-060)。
文摘A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.
文摘Most of local feature descriptors assume that the scene is planar. In the real scene, the captured images come from the 3-D world. 3-D corner as a novel invariant feature is important for the image matching and the object detection, while automatically discriminating 3-D corners from ordinary corners is difficult. A novel method for 3-D corner detection is proposed based on the image graph grammar, and it can detect the 3-D features of corners to some extent. Experimental results show that the method is valid and the 3-D corner is useful for image matching.
基金Supported by National Natural Science Foundation of China(Grant Nos.51275438,51405421)Hebei Provincial Natural Science Foundation of China(Grant No.E2015203101)
文摘Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.
文摘Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.
文摘A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.
文摘Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （or simply ai） = q ＋ r ＋ dui^＋ - dui^-, bvj （or simply b j） = p ＋ r ＋ d^＋vj - d^-vj and cwk （or simply ck） =p ＋ q ＋ dwk^＋ -dwk^- as the scores of ui in U,vj in V and wk in W respectively. The set A of distinct scores of the vertices of D（U, V, W） is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai（2 ≤ i ≤ n - 1） are even positive integers and an is any positive integer, then for n 〉 3, there exists an oriented 3-partite graph with the score set A ={a1,Σ2i=1 ai,…,Σni=1 ai}, except when A = {0, 2, 3}. Some more results for score sets in oriented 3-partite graphs are obtained.
基金The NSF (60673048) of China the NSF (KJ2009B002,KJ2009B237Z) of Education Ministry of Anhui Province.
文摘An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.
基金Supported by National Natural Science Foundation of China(Grant No.12071442)the Fundamental Research Funds for the Central Universities under(Grant No.020314380035)。
文摘It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.
基金National Key Research and Development Program of China (2019YFC1521102)National Natural Science Foundation of China (61701403,61806164,62101439,61906154)+4 种基金China Postdoctoral Science Foundation (2018M643719)Natural Science Foundation of Shaanxi Province (2020JQ-601)Young Talent Support Program of the Shaanxi Association for Science and Technology (20190107)Key Research and Development Program of Shaanxi Province (2019GY-215,2021ZDLSF06-04)Major research and development project of Qinghai (2020-SF-143).
文摘Cerenkov Luminescence Tomography(CLT)is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes.However,due to severe ill-posed inverse problem,obtaining accurate reconstruction results is still a challenge for traditional model-based methods.The recently emerged deep learning-based methods can directly learn the mapping relation between the surface photon intensity and the distribution of the radioactive source,which effectively improves the performance of CLT reconstruction.However,the previously proposed deep learning-based methods cannot work well when the order of input is disarranged.In this paper,a novel 3D graph convolution-based residual network,GCR-Net,is proposed,which can obtain a robust and accurate reconstruction result from the photon intensity of the surface.Additionally,it is proved that the network is insensitive to the order of input.The performance of this method was evaluated with numerical simulations and in vivo experiments.The results demonstrated that compared with the existing methods,the proposed method can achieve efficient and accurate reconstruction in localization and shape recovery by utilizing threedimensional information.
基金Supported by National Natural Science Foundation of China(61872024)National Key R&D Program of China under Grant(2018YFB2100603).
文摘Background In this study,we propose a novel 3D scene graph prediction approach for scene understanding from point clouds.Methods It can automatically organize the entities of a scene in a graph,where objects are nodes and their relationships are modeled as edges.More specifically,we employ the DGCNN to capture the features of objects and their relationships in the scene.A Graph Attention Network(GAT)is introduced to exploit latent features obtained from the initial estimation to further refine the object arrangement in the graph structure.A one loss function modified from cross entropy with a variable weight is proposed to solve the multi-category problem in the prediction of object and predicate.Results Experiments reveal that the proposed approach performs favorably against the state-of-the-art methods in terms of predicate classification and relationship prediction and achieves comparable performance on object classification prediction.Conclusions The 3D scene graph prediction approach can form an abstract description of the scene space from point clouds.
