Hausdorff distance measure is one of the widely adopted feature-based image matching algo- rithms due to its simplicity and accuracy. However, it is considered that its robustness still needs to be improved. In this p...Hausdorff distance measure is one of the widely adopted feature-based image matching algo- rithms due to its simplicity and accuracy. However, it is considered that its robustness still needs to be improved. In this paper, various forms of original and improved Hausdorff distance （HD） and their limitations are studied. Focusing on robust Hausdorff distance （ RHD）, an improved RHD with an adaptive outlier point threshold selection method is proposed. Furthermore, another new form of the Hausdorff distance which possesses the merits of RHD and M-HD is prsented. Finally, a recur- sire algorithm is introduced to accelerate the image matching speed of Hausdorff algorithms. Exten- sive simulation and experiment results are presented to validate the feasibility of the proposed Haus- dorff distance algorithm.展开更多
Object matching between two-dimensional images is an important problem in computer vision. The purpose of object matching is to decide the similarity between two objects. A new robust image matching method based on di...Object matching between two-dimensional images is an important problem in computer vision. The purpose of object matching is to decide the similarity between two objects. A new robust image matching method based on distance reciprocal was presented. The distance reciprocal is based on human visual perception. This method is simple and effective. Moreover, it is robust against noise. The experiments show that this method outperforms the Hausdorff distance, when the images with noise interfered need to be recognized.展开更多
Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ...Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.展开更多
The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean ...The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean Riesz space possessing a weak unit e and a maximal disjoint division{e i:i∈I} in which each e i is a proj ection element. Concerning the following statements:(1) There exists a completel y regular Hausdorff space X such that E is Riesz isomorphic to C(X);(2) For every i∈I there exi sts a completely regular Hausdorff space X i such that the band generated by e i is Riesz isomorphic to C(X i).It is shown that (1) implies (2),and find some conditions for the inverse bein g true are found.Furthermore,if each X i in (2) is a compact Ha usdorff space, a necessary and sufficient condition is established under which E can be represented as a C(X) for some compact Hausdorff space X.As corollaries, corresponding results for late rally complete Riesz spaces are obtained.展开更多
In this paper we introduce the concept of pairwise singular sets and pairwise singular maps between pairwise locally compact and pairwise hausdorff spaces and study the properties of pairwise singular maps.
基金Supported by the National Natural Science Foundation of China(No.61072088)
文摘Hausdorff distance measure is one of the widely adopted feature-based image matching algo- rithms due to its simplicity and accuracy. However, it is considered that its robustness still needs to be improved. In this paper, various forms of original and improved Hausdorff distance （HD） and their limitations are studied. Focusing on robust Hausdorff distance （ RHD）, an improved RHD with an adaptive outlier point threshold selection method is proposed. Furthermore, another new form of the Hausdorff distance which possesses the merits of RHD and M-HD is prsented. Finally, a recur- sire algorithm is introduced to accelerate the image matching speed of Hausdorff algorithms. Exten- sive simulation and experiment results are presented to validate the feasibility of the proposed Haus- dorff distance algorithm.
文摘Object matching between two-dimensional images is an important problem in computer vision. The purpose of object matching is to decide the similarity between two objects. A new robust image matching method based on distance reciprocal was presented. The distance reciprocal is based on human visual perception. This method is simple and effective. Moreover, it is robust against noise. The experiments show that this method outperforms the Hausdorff distance, when the images with noise interfered need to be recognized.
基金Project supported by the National Natural Science Foundation ofChina (No. 10171090) and the Scientific Research Fund of ZhejiangProvincial Education Department (No. 20030341) China
文摘Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.
文摘The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean Riesz space possessing a weak unit e and a maximal disjoint division{e i:i∈I} in which each e i is a proj ection element. Concerning the following statements:(1) There exists a completel y regular Hausdorff space X such that E is Riesz isomorphic to C(X);(2) For every i∈I there exi sts a completely regular Hausdorff space X i such that the band generated by e i is Riesz isomorphic to C(X i).It is shown that (1) implies (2),and find some conditions for the inverse bein g true are found.Furthermore,if each X i in (2) is a compact Ha usdorff space, a necessary and sufficient condition is established under which E can be represented as a C(X) for some compact Hausdorff space X.As corollaries, corresponding results for late rally complete Riesz spaces are obtained.
文摘In this paper we introduce the concept of pairwise singular sets and pairwise singular maps between pairwise locally compact and pairwise hausdorff spaces and study the properties of pairwise singular maps.
