Super-resolution enhancement of UAV images based on fractional calculus and POCS

Abstract

A super-resolution enhancement algorithm was proposed based on the combination of fractional calculus and Projection onto Convex Sets (POCS) for unmanned aerial vehicles (UAVs) images. The representative problems of UAV images including motion blur, fisheye effect distortion, overexposed, and so on can be improved by the proposed algorithm. The fractional calculus operator is used to enhance the high-resolution and low-resolution reference frames for POCS. The affine transformation parameters between low-resolution images and reference frame are calculated by Scale Invariant Feature Transform (SIFT) for matching. The point spread function of POCS is simulated by a fractional integral filter instead of Gaussian filter for more clarity of texture and detail. The objective indices and subjective effect are compared between the proposed and other methods. The experimental results indicate that the proposed method outperforms other algorithms in most cases, especially in the structure and detail clarity of the reconstructed images.     

A spatiotemporal calculus for reasoning about land-use trajectories

Earth observation images are a powerful source of data about changes in our planet. Given the magnitude of global environmental changes taking place, it is important that Earth Science researchers have access to spatiotemporal reasoning tools. One area of particular interest is land-use change. Using data obtained from images, researchers would like to express abstractions such as ‘land abandonment’, ‘forest regrowth’, and ‘agricultural intensification’. These abstractions are specific types of land-use trajectories, defined as multi-year paths from one land cover into another. Given this need, this paper introduces a spatiotemporal calculus for reasoning about land-use trajectories. Using Allen’s interval logic as a basis, we introduce new predicates that express cases of recurrence, conversion and evolution in land-use change. The proposed predicates are sufficient and necessary to express different kinds of land-use trajectories. Users can build expressions that describe how humans modify Earth’s terrestrial surface. In this way, scientists can better understand the environmental and economic effects of land-use change.     

天体运行轨道的背景介质理论导引与自相似分形测度计算的分维微积分基础

通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设,介绍了天体运行轨道的具体方程形式及理论框架概要;进一步地通过讨论天体运行轨道Binet方程的一般形式及其行星近日点进动角的解,给出了连续轨道理论与Newton理论及Einstein广义相对论的联系与区别;通过讨论天体运行轨道的分维扩展方程,给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道（稳定性轨道）方程及其预言数据.特别地,作为对天体在较为广泛区域作用曲线的初步探讨推论,指出仅由天体引力难以形成质量密度趋于无穷大的理想黑洞.通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设,进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式,给出分维导数与分数阶导数的区别,随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式,给出了其与目前Hausdorff测度方法（覆盖方法）的区别,并对包括三分Cantor集合、Koch曲线、Sierpinski垫片及正交十字星形等自相似分形在内的测度进行了计算分析.     

A review on stochastic differential equations for applications in hydrology

Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources.     

钻孔轴线空间曲线方程的建立及探讨

为了提高钻孔测斜数据的处理精度，提出钻孔的方位角及倾角在相邻测斜点之间是均匀变化的假设。以微积分学为工具，推导出钻孔轴线空间参数方程及其在平、部面上的投影方程；以实例对现行的数据处理方法所得结果和按曲线方程处理所得结果进行比较，认为该种处理方法比较接近实际情况，同时能为自动绘图提供方便。     

综合小波分析与分形方法进行弱磁异常识别

利用小波分析塔式算法对单一分形模型数据进行处理,结合“随机共振”理论,对高精度弱磁异常中的噪声和误差进行有效的分析评价,依据趋势分析方法获得的剩余磁异常,提出“加窗移动”最小二乘方法对应用非整数阶微积分的布郎运动正态随机行走进行控制,为高精度弱磁异常的有效识别提供有益的指导。     

An iterative pressure‐stabilized fractional step algorithm in saturated soil dynamics

This paper presents an iterative, incremental pressure‐stabilized fractional step algorithm for coupled hydro‐mechanical problems with mixed formulations of the displacement–pressure ( u –p) model in saturated soil dynamics that allows the use of finite elements with equal low order of interpolation approximation of u and p. In comparison with the original fractional step algorithm, the distinct features of the proposed algorithm lie in its enhanced stability owing to the introduction of both an iteration procedure and a finite increment calculus (FIC) process into the algorithm. The introduction of the iterative procedure makes the velocity term satisfy the momentum conservation equation in an implicit sense and allows much larger time step sizes to be used than those limited in existing explicit and semi‐implicit versions of the algorithm. The introduction of the FIC process removes the dependence of the stability of the proposed algorithm on the time step size, as a result it allows to using the incremental version of the algorithm and evades the minimum time step size requirement presented in the existing versions of the fractional step algorithm that restricts the application of the algorithm to saturated soil dynamics problems with high frequencies. Numerical experiments demonstrate the effectiveness and improved performance of the proposed iterative pressure‐stabilized fractional step algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

东秦岭石界河群中石榴石成分环带所记录的PTt轨迹

位于河南省西峡县北部地区的石界河群榴云片岩中的石榴石发育有很好的结构和成分环带。本文应用微分热力学方法对其环带成分进行计算,确定出一条顺时针方向的PTt轨迹。该轨迹与应用矿物共生组合世代关系确定的PTt轨迹十分吻合。     

TOVS卫星反演资料变分分析的试验研究与应用

为弥补海洋、高原等地带常规资料的不足,分析使用非常规卫星资料得到越来越多的重视,其中TOVS资料的精度及与常规资料的误差减少的研究尤为重要。本文采用变分分析技术对TOVS卫星反演资料进行同化分析研究,结果表明,变分结果分析场能充分体现常规与非常规资料的优势,使得天气系统能得到更精确的表示。