Random Iteration Algorithm Research Articles

Estimation of the Living Vegetation Volume (LVV) for Individual Urban Street Trees Based on Vehicle-Mounted LiDAR Data

The living vegetation volume (LVV) can accurately describe the spatial structure of greening trees and quantitatively represent the relationship between this greening and its environment. Because of the mostly line shape distribution and the complex species of street trees, as well as interference from artificial objects, current LVV survey methods are normally limited in their efficiency and accuracy. In this study, we propose an improved methodology based on vehicle-mounted LiDAR data to estimate the LVV of urban street trees. First, a point-cloud-based CSP (comparative shortest-path) algorithm was used to segment the individual tree point clouds, and an artificial objects and low shrubs identification algorithm was developed to extract the street trees. Second, a DBSCAN (density-based spatial clustering of applications with noise) algorithm was utilized to remove the branch point clouds, and a bottom-up slicing method combined with the random sampling consistency iterative method algorithm (RANSAC) was employed to calculate the diameters of the tree trunks and obtain the canopy by comparing the variation in trunk diameters in the vertical direction. Finally, an envelope was fitted to the canopy point cloud using the adaptive AlphaShape algorithm to calculate the LVVs and their ecological benefits (e.g., O2 production and CO2 absorption). The results show that the CSP algorithm had a relatively high overall accuracy in segmenting individual trees (overall accuracy = 95.8%). The accuracies of the tree height and DBH extraction based on vehicle-mounted LiDAR point clouds were 1.66~3.92% (rRMSE) and 4.23~15.37% (rRMSE), respectively. For the plots on Zijin Mountain, the LVV contribution by the maple poplar was the highest (1049.667 m3), followed by the sycamore tree species (557.907 m3), and privet’s was the lowest (16.681 m3).

A Semi-Supervised Method for PatchMatch Multi-View Stereo with Sparse Points

Recently, the deep-learning-based PatchMatch method has been rapidly developed in 3D reconstruction, based on which boundary regions are filled with other parts that most closely match edge parts, but limited PatchMatch data hinder the generalization of the method to unknown settings. If various large-scale PatchMatch datasets are generated, the process would require considerable time and resources when performing neighborhood point-matching calculations using random iterative algorithms. To solve this issue, we first propose a new, sparse, semi-supervised stereo-matching framework called SGT-PatchMatchNet, which can reconstruct reliable 3D structures with a small number of 3D points using the ground truth of surface frame values. Secondly, in order to solve the problem of the luminosity inconsistency of some pixels in other views, a photometric similar-point loss function is proposed to improve the performance of 3D reconstruction, which causes the neighborhood information to project the depth value of the predicted depth to meet the same 3D coordinates. Finally, in order to solve the problem of the edge blurring of the depth map obtained using the network model, we propose a robust-point consistency loss function to improve the integrity and robustness of the occlusion and edge areas. The experimental results show that the proposed method not only has good visual effects and performance indicators but can also effectively reduce the amount of computation and improve the calculation time.

An Unsupervised Crop Classification Method Based on Principal Components Isometric Binning

The accurate and timely access to the spatial distribution information of crops is of great importance for agricultural production management. Although widely used, supervised classification mapping requires a large number of field samples, and is consequently costly in terms of time and money. In order to reduce the need for sample size, this paper proposes an unsupervised classification method based on principal components isometric binning (PCIB). In particular, principal component analysis (PCA) dimensionality reduction is applied to the classification features, followed by the division of the top k principal components into equidistant bins. Bins of the same category are subsequently merged as a class label. Multitemporal Gaofen 1 satellite (GF-1) remote sensing images were collected over the southwest of Hulin City and Luobei County of Hegang City, Heilongjiang Province, China in order to map crop types in 2016 and 2017. Our proposed method was compared with commonly used classifiers (random forest, K-means and Iterative Self-Organizing Data Analysis Techniques Algorithm (ISODATA)). Results demonstrate PCIB and random forest to have the highest classification accuracies, reaching 82% in 2016 in the southwest of Hulin City. In Luobei County in 2016, the accuracies of PCIB and random forest were determined as 81% and 82%, respectively. It can be concluded that the overall accuracy of our proposed method meets the basic requirements of classification accuracy. Despite exhibiting a lower accuracy than that of random forest, PCIB does not require a large field sample size, thus making it more suitable for large-scale crop mapping.

An equivalency iterative algorithm for cancer risk assessment of chemical mixtures with additive effects

To better estimate cumulative cancer risks and avoid the overestimated risk from the linear extrapolation, an equivalency iterative algorithm associated with a carcinogenesis hypothesis was introduced for a mixture of chemicals with the same mode of action (MOA). A lognormal dose-response function was applied for carcinogenic chemicals. Under some circumstances, the repetitive random iterative algorithm could be transformed into the nonrepetitive one. It was also demonstrated that the equivalent value for a lognormal-based equivalency iterative algorithm with the same shape parameter was independent of the operation order. Based on the theorems of the algorithm and Plackett and Hewlett’s minimum effective dose assumption, the sum of toxicity-weighted dose for a mixture of chemicals was mathematically derived. Compared to the estimation of risk by the linear extrapolation method (e.g., cancer slope factors), the equivalency iterative algorithm for lognormal functions can avoid overestimated risk significantly, which can help better estimate the cumulative cancer risk for a mixture of chemicals with the same MOA.

Weakly contractive iterated function systems and beyond: a manual

ABSTRACT We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity of the random iteration algorithm (‘chaos game’), can be obtained rather easily for weakly contractive systems. We show that the class of attractors of weakly contractive IFSs is essentially wider than the class of classical IFSs' fractals. On the other hand, we show that, in reasonable spaces, a typical compact set is not an attractor of any weakly contractive IFS. We explore the possibilities and restrictions to break the contractivity barrier by employing several tools from fixed point theory: geometry of balls, average contractions, remetrization technique, ordered sets, and measures of noncompactness. From these considerations it follows that while the existence of invariant sets and invariant measures can be assured rather easily for general iterated function systems under mild conditions, to establish the existence of attractors and unique invariant measures is a substantially more difficult problem. This explains the central role of contractive systems in the theory of IFSs.

Random iterative algorithms and almost sure stability in Banach spaces

Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized ?-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.

On random variational-like inclusion involving relaxed monotone random operators

The study was conducted with the aim to find out random variational-like inclusion involving relaxed monotone, random operators in Hilbert space and construct a new iterative algorithm. The study also proves the existence of random solution of random variational-like inclusion problem and convergence of random iterative sequences generated by random iterative algorithm. The results in this paper unify, improve and extend some well-known results from the literature.

Generic Animation Method for Multi-Objects in IFS Fractal Form

Both non-metamorphic animation and metamorphic animation of objects or multi-objects in IFS fractal form as basic animation method can be implemented by a modified version of the random iteration algorithm as basic algorithm. In this way it is possible to create an attractive animation based on the combination of both animation methods as a generic animation method, as discussed in this paper. The proposed method can be used as an alternative for or as an extension of the existing animation methods in classical geometry, which are restricted to objects with regular forms. The proposed method can be used to produce more attractive media for interactively learning about the behavior of manipulated objects of any form.

Random iteration for infinite nonexpansive iterated function systems.

We prove that the random iteration algorithm works for strict attractors of infinite iterated function systems. The system is assumed to be compactly branching and nonexpansive. The orbit recovering an attractor is generated by a deterministic process and the algorithm is always convergent. We also formulate a version of the random iteration for uncountable equicontinuous systems.

Random backward iteration algorithm for Julia sets of rational semigroups

We provide proof that a random backward iteration algorithm for approximating Julia sets of rational semigroups, previously proven to work in the context of iteration of a rational function of degree two or more, extends to rational semigroups (of a certain type). We also provide some consequences of this result.

Markovian stochastic approximation with expanding projections

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We study a stochastic approximation procedure with expanding projections similar to Andradóttir [Oper. Res. 43 (1995) 1037–1048]. We focus on Markovian noise and show the stability and convergence under general conditions. Our framework also incorporates the possibility to use a random step size sequence, which allows us to consider settings with a non-smooth family of Markov kernels. We apply the theory to stochastic approximation expectation maximisation with particle independent Metropolis–Hastings sampling.

Hybrid Animation Model of Multi-object in Fractal Form based on Metamorphic Interpolation and Partitioned-Random Iteration Algorithms

Traditionally simple object is drawn to the screen by drawing functions in pixels, so the slight different form of object should be redrawn by different function. On the other hand, naturally fractal object is drawn by a single algorithm through drawing pixels at the position according to the code of fractal such as IFS code, and interactively to change the form of or to animate the fractal object is accomplished simply by changing the code of fractal at any time. So in this case, animation model of objects in fractal form has an advantage over animation model of objects in traditional form. IFS code is one way of the inverse problem representation of object in fractal form. The IFS fractal objects can be reconstructed by random iteration algorithm and the multi-object of fractal can be reconstructed by partitioned-random iteration algorithm from the IFS code sets. To have the metamorphic animation, the interpolation between the IFS code of source and target objects can be done by a metamorphic animation algorithm. The hybrid animation model is the combination model of a metamorphic animation on one type of object and the multi-object animation independently with or without synchronized mode based on the metamorphic interpolation of IFS code coefficients for the metamorphic animation and the partitioned-random iteration algorithm for the multi- object animation.

Implementation of Artificial Neural Network and Random Iteration Algorithm Uses in Medical Images

Implementation of Artificial Neural Network and Random Iteration Algorithm Uses in Medical Images

Animation Model of Multi-object in Fractal form based on Partitioned-random Iteration Algorithm

Animation model of objects in fractal form has many advantages over animation model of objects in traditional form. Traditionally simple object is drawn by drawing functions and the slight different form of object should be redrawn by different function, so every manipulation effort to change or to animate the form of object should call the different function. Naturally fractal object is drawn by a single algorithm through drawing pixels at the position according the code of fractal, so to change the form of or to animate the fractal object is done simply by changing the code of fractal such as IFS code at any time interactively. IFS code is the inverse problem representation of object in fractal form. The IFS fractal objects can be reconstructed by random iteration algorithm and the multi-object of fractal can be reconstructed by partitioned-random iteration algorithm from the IFS code sets.

Set-Valued Non-Linear Random Implicit Quasivariational Inclusions

In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.

Almost sure T-stability and convergence for random iterative algorithms

The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of ϕ-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.

On Generalized Multivalued Random Variational-Like Inclusions

In this paper, we posed a random iterative algorithm for generalized multivalued random variational like inclusions. We define the random relaxed Lipschitz and relaxed monotone mappings and prove the existence and convergence of solutions of the random iterative sequences generated by a random iterative algorithm.

A Generalized Nonlinear Random Equations with Random Fuzzy Mappings in Uniformly Smooth Banach Spaces

We introduce and study the general nonlinear random -accretive equations with random fuzzy mappings. By using the resolvent technique for the -accretive operators, we prove the existence theorems and convergence theorems of the generalized random iterative algorithm for this nonlinear random equations with random fuzzy mappings in -uniformly smooth Banach spaces. Our result in this paper improves and generalizes some known corresponding results in the literature.

A new approach to superfractals

V-variable fractals and superfractals have recently been introduced by Barnsley [Barnsley Michael, Hutchinson John, Stenflo Örjan. A fractal valued random iteration algorithm and fractal hierarchy. Fractals 2005;13(2):111–46 [MR2151094 (2006b:28014)]] to the world of mathematics and computer graphics. In this paper, we introduce superior iterates to study the role of contractive and non-contractive operators in relation to superfractals. A modified algorithm along with details of computer implementation is also provided to compute V-variable fractals. A brief discussion about the various aspects of the computed figures indicates usefulness of the study.

Statistical Comparative Study of Multiple Sequence Alignment Scores of Iterative Refinement Algorithms

Iterative refinement algorithm is a useful method to improve the alignment results. In this paper, we evaluated different iterative refinement algorithms statistically. There are four iterative refinement algorithms: remove first (RF), bestfirst (BF), random (RD), and tree-based (Tb) iterative refinement algorithm. And there are two scoring functions for measuring the iteration judgment step: log expectation (LE) and weighted sum-of-pairs (SP) scores. There are two sequence clustering methods: neighbor-joining (NJ) method and unweighted pair-group method with arithmetic mean (UPGMA). We performed comprehensive analyses of these alignment strategies and compared these strategies using BAliBASE SP (BSP) score. We observed the behavior of scores from the view point of cumulative frequency (CF) and other basic statistical parameters. Ultimately, we tested the statistical significance of all alignment results by using Friedman nonparametric analysis of variance (ANOVA) test for ranks and Scheffe multiple comparison test.