城市竣工测绘典型要素语义分割PointNet++深度学习模型适用性分析

处理三维激光扫描仪获取的城市竣工测绘点云场景数据的传统方法存在较多局限性,无法适应信息化社会对产品高效处理的需求。基于此,本文分析了城市竣工测绘点云场景分类需求,研究了利用深度学习网络模型对点云场景进行自动化处理的方法。首先,对输入的城市竣工测绘数据进行预处理,以实现点云降采样、去噪、地面点与非地面点分割;然后,人工标注5个区域场景数据毫米级标签,进行数据增强;最后,测试PointNet++网络在城市竣工测绘点云场景下的语义分割性能和效果。测试结果表明,在少量样本下,PointNet++网络可以较好地实现城市竣工测绘点云场景的激光点云语义分割,总体mIoU达73.06%,能够满足城市竣工测绘点云语义自动化分割需求,为城市竣工测绘点云数据处理提供了新思路。

An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings

In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].

ITERATIVE APPROXIMATION OF FIXED POINTS OF (ASYMPTOTICALLY) NONEXPANSIVE MAPPINGS

Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.

Analysis and confirmation of fixed points in logistic mapping digital-flow chaos

The fixed points in logistic mapping digital-flow chaos strange attractor arestudied in detail. When k=n in logistic equation, there exist no more than 2n fixed points, whichare deduced and proved theoretically. Three corollaries about the fixed points of logistic mappingare proposed and proved respectively. These theorem and corollaries provide a theoretical basis forchoosing parameter of chaotic sequences in chaotic secure communication and chaotic digitalwatermarking. And they are testified by simulation.

Some New Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces

The purpose of this paper is to introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.

NEW FIXED POINT THEOREMS OF CONDENSING MAPPINGS SATISFYING THE INTERIOR CONDITION IN BANACH SPACES

In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman＇s theorem, Roth＇s theorem and Petryshyn＇s theorem are extended to condensing mappings satisfying the interior condition.

Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable

The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.

Fixed Points Associated to Power of Normal Completely Positive Maps*

Let be a normal completely positive map with Kraus operators . An operator X is said to be a fixed point of , if . Let be the fixed points set of . In this paper, fixed points of are considered for , where means j-power of . We obtain that and for integral when A is self-adjoint and commutable. Moreover, holds under certain condition.

A FIXED POINT THEOREM FOR SET-VALUED MAPPINGS

Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.

DEGREE THEORY FOR MULTIVALUED (S) TYPE MAPPINGS AND FIXED POINT THEOREMS

The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.

A Common Fixed Point Theorem for Compatible Mappings of Type (C)

We establish a common fixed-point theorem for six self maps under the compatible mappings of type (C) with a contractive condition [1], which is independent of earlier contractive conditions.

Some Common Fixed Point Theorems for Four Mappings in Dislocated Metric Space

In this article, we establish some common fixed point theorems for two pairs of weakly compatible mappings with (E. A.) and (CLR) property in dislocated metric space which generalize and extend some similar results in the literature.

COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.

ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES

The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.

FIXED POINT THEOREM OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES

Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:for all x,y in K,where then T has a unique fixed point in K.

Some Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces

In 1975, Kramosil and Michalek [1] first introduced the concept of a fuzzy metric space. In 1994, George and Veeramani [2] slightly modified the concept of fuzzy metric space introduced by Kramosil and Michalek, defined a Hausdorff topology and proved some known results. In 1969, Rheinboldt [3] initiated the study of iterated contraction. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability in metric spaces. In this paper we introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.

CHAIN RECURRENT POINTS AND TOPOLOGICAL ENTROPY OF A TREE MAP

Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.

ISHIKAWA ITERATIVE PROCEDURE FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS

It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence.

Second Descendible Self-Mapping with Closed Periodic Points Set

Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point of the set orb (y,f) is a isolated point of the set w (z,f);3) For any z ε R(f), the set w (z,f) is finite;4) For any z ε R(f), the set w' (z,f) is finite. The consult give another condition of f with closed periodic set other than [1].