用微分方法求解不定积分问题

微分和积分是一对逆运算，但是微分比积分更容易运算。用常规方法求解不定积分问题是相当困难的。本文给出求不定积分的一种新方法。该方法易掌握，特别是使用该方法对无理函数积分更容易求得结果。     

基于分数阶微分的土壤含水量高光谱响应特征与估测模型构建

面向滨湖地区土壤含水量信息的高效获取,以洪湖272个土壤样本为例,测定可见-近红外反射光谱,对原始和两种预处理后的光谱进行0～2阶分数阶微分处理（间隔为0.2阶）,探究土壤含水量的分数阶微分（fractional-order derivative,FOD）光谱响应特征;以此为基础构建土壤含水量估测模型并进行对比,探究最佳的预处理与微分阶数组合。结果表明：随着微分阶数的增加,土壤光谱在水分特征波段1 450 nm、1 950 nm和2 200 nm附近谷值逐渐突出,1 950 nm处的VIP峰值逐渐增强;分数阶微分在特定波长和阶数下能提高土壤含水量和光谱之间的相关性,使用Savitzky-Golay(SG)平滑+0.6阶微分的光谱数据建立的模型精度最佳,预测决定系数为0.86,相对分析误差值为2.62,且在不同用地类型的交叉验证中都取得了良好效果。     

基于车载激光点云的高精地图矢量化成图

针对车载激光点云中对各特征物提取结果后矢量化成图时的自动化问题,本文基于双方向积分法实现了边缘检测及矢量化成图,旨在保证特征物基本特征的同时,也保证点云的绝对精度。将输入的特征点云进行离群点过滤,以保证外包框算法特征点云的准确度;将三维点云按照外包框算法投影至最优平面,为后续沿各方向积分提供输入;利用八邻域KD-tree算法求出样本特征点云的均值邻域半径,依据邻域半径对各方向积分提供积分域中的微分元;根据提供的微分元沿各方向进行积分,在该积分元内找到距平面最值的最优解;按照积分结果构建点云索引,并根据点云特征构建模型,最终得到高精地图的矢量化点云。试验证明了该方法在处理实际问题时的可行性。     

球外部空间的Neumann逆问题及逆 Stokes公式

基于修改的Poisson积分 ,首先给出了球面扰动位向上延拓的积分表达式。在此基础上 ,由微分原理得出了球外部空间Neumann逆问题的解式 ,利用物理大地测量学的基本微分方程 ,导出了球外部空间的逆Stokes公式 ,并对这两类积分公式的核函数进行了讨论     

积分变换公式的几何证明

计算多重积分时,经常使用变换量替换。用分析方法证变换公式时,比较两个体积元之间的关系甚为复杂。本文利用微分几何中的外形式,很快找到了两个体积元之间的关系。     

洎水河流域重金属污染区五节芒叶片光谱特征响应研究

利用污染物富集因子和污染指数对洎水河流域采样点河滩表层土壤重金属污染状况进行评价。通过分析五节芒叶片重金属富集率,发现五节芒对Cu、Zn、Cr等金属元素有较强的吸收能力,而且,重金属富集率与河滩表层土壤的重金属污染程度呈相反的变化趋势。将五节芒叶片光谱特征参数——可见光波段(450~670 nm)反射率积分值(A1)、近红外波段(760~980 nm)反射率积分值(A2)与五节芒叶片中3种重金属(Cu、Zn、Cr)的质量分数进行相关分析,分别建立2个谱段的光谱特征参数与3种重金属质量分数的多元线性回归方程。结果表明,五节芒叶片中重金属Cu、Zn和Cr的质量分数可以很好地模拟(复相关系数R20.93)五节芒叶片在重金属胁迫下的光谱特征变化。     

南方丘陵地区路域植被光谱处理与分析

以长沙—湘潭高速公路路域植被为研究对象,进行植被实地调查和野外光谱测定,分析主要植被类型光谱曲线,健康植被与非健康植被光谱差异,对植被光谱数据进行一阶微分和微分增量处理对比研究。研究表明:光谱反射率一阶微分和微分增量处理对消除土壤背景对地物光谱影响均有效,但微分增量处理更能突出植被信息。研究对遥感植被光谱分析具有一定参考价值。     

基于微分形态学断面的遥感影像分割方法

介绍形态学测地重建与开闭重建运算,提出基于微分形态学断面的影像分割方法。首先生成原始影像的微分形态学断面影像,然后比较得到像点的微分断面特征,最后以微分断面特征为基础实现影像分割。以IKONOS卫星影像为例,该方法能够有效地分割噪声严重、反差较低的遥感影像,同时在保持物体的形状、大小信息等方面具有优势。     

指示冬小麦条锈病严重度的两个新的红边参数

通过人工田间诱发不同等级条锈病,在不同生育期测定了36条感染不同严重程度条锈病的冬小麦冠层光谱及相应叶片的生理生化参量。对测定的冬小麦红边一阶微分光谱进行分析,发现随着病情严重度的增加,红边一阶微分的前峰(700nm附近)越来越明显,后峰(约在725—740nm)越来越不突出,以红边一阶微分的双峰特征随病情指数的变化为基础,设计了两个新型的红边参数:DSr和Ar,它们可以分别用来描述红边一阶微分光谱曲线的陡峭度和不对称性,与其他常用的红边参数(红边位置、红边一阶微分最大值,红边一阶微分所包围面积)相比,新参数反演病情严重度的精度更高。     

基于高光谱的湿地植被分类研究

光谱特征的选择对于湿地植被的识别精度和效率有直接的影响。本文以萨克拉门托-圣华金三角洲为研究区,基于Hy Map航空高光谱遥感影像数据,分析湿地植被的一阶微分和二阶微分光谱特征。在上述分析的基础上基于均值置信区间的波段选择法对一阶微分、二阶微分进行波段选择,根据获取的有效特征波段构建特征集,利用C5决策树分类算法产生规则集,并对实验区的湿地植被进行了分类研究。结果表明:湿地植被的一阶微分、二阶微分能够突出不同湿地植被光谱曲线在不同波段的增速不同,利用均值置信区间的波段选择法能够对特征波段起到降维效果,根据降维后的特征波段采用C5决策树分类算法,可以实现湿地植被在物种水平上的识别,并达到较好的分类精度。     

GF-2支持下的干旱区稀疏植被区植被覆盖度估算

现有像元二分模型MODIS植被覆盖度模型因其形式简单、适用性较强的特点被广泛应用于区域植被覆盖度（FVC）的估算。然而,研究表明在沙漠和低植被覆盖的西部干旱区,从250 m的影像上很难精准地获取NDVI_veg（全植被覆盖植被指数）和NDVI_soil（全裸土区植被指数）参数。利用常用的直方图累计法获取模型所需参数NDVI_veg和NDVI_soil,估算结果存在普遍高估现象。为此,本文首先引入同期获取的GF-2号卫星数据,从GF-2号影像上提取植被覆盖像元;然后,利用Pixel Aggregate方法重采样至250 m分辨率,获取250 m空间分辨率下纯植被和纯裸土像元;最后,将纯植被和纯裸土像元各自空间位置相对应的MODIS NDVI数据最大值作为模型所需NDVI_veg和NDVI_soil参数,实现研究区内植被覆盖度的估算。试验通过与线性回归法、多项式回归法和直方图累计像元二分模型法估算结果进行精度对比,结果表明：利用GF-2影像辅助的像元二分模型,精准地获取了低植被覆盖区NDVI_veg和NDVI_soil模型参数,提高了干旱区植被覆盖度的估算精度,并有效地抑制了受稀疏植被影响NDVI在干旱区普遍偏高问题导致的FVC高估的现象。     

Characterizing bi-temporal patterns of land surface temperature using landscape metrics based on sub-pixel classifications from Landsat TM/ETM+

Landscape patterns in a region have different sizes, shapes and spatial arrangements, which contribute to the spatial heterogeneity of the landscape and are linked to the distinct behavior of thermal environments. There is a lack of research generating landscape metrics from discretized percent impervious surface area data (ISA), which can be used as an indicator of urban spatial structure and level of development, and quantitatively characterizing the spatial patterns of landscapes and land surface temperatures (LST). In this study, linear spectral mixture analysis (LSMA) is used to derive sub-pixel ISA. Continuous fractional cover thresholds are used to discretize percent ISA into different categories related to urban land cover patterns. Landscape metrics are calculated based on different ISA categories and used to quantify urban landscape patterns and LST configurations. The characteristics of LST and percent ISA are quantified by landscape metrics such as indices of patch density, aggregation, connectedness, shape and shape complexity. The urban thermal intensity is also analyzed based on percent ISA. The results indicate that landscape metrics are sensitive to the variation of pixel values of fractional ISA, and the integration of LST, LSMA. Landscape metrics provide a quantitative method for describing the spatial distribution and seasonal variation in urban thermal patterns in response to associated urban land cover patterns.     

Evaluating effects of spectral training data distribution on continuous field mapping performance

Continuous field mapping has to address two conflicting remote sensing requirements when collecting training data. On one hand, continuous field mapping trains fractional land cover and thus favours mixed training pixels. On the other hand, the spectral signature has to be preferably distinct and thus favours pure training pixels. The aim of this study was to evaluate the sensitivity of training data distribution along fractional and spectral gradients on the resulting mapping performance.We derived four continuous fields (tree, shrubherb, bare, water) from aerial photographs as response variables and processed corresponding spectral signatures from multitemporal Landsat 5 TM data as explanatory variables. Subsequent controlled experiments along fractional cover gradients were then based on generalised linear models.Resulting fractional and spectral distribution differed between single continuous fields, but could be satisfactorily trained and mapped. Pixels with fractional or without respective cover were much more critical than pure full cover pixels. Error distribution of continuous field models was non-uniform with respect to horizontal and vertical spatial distribution of target fields. We conclude that a sampling for continuous field training data should be based on extent and densities in the fractional and spectral, rather than the real spatial space. Consequently, adequate training plots are most probably not systematically distributed in the real spatial space, but cover the gradient and covariate structure of the fractional and spectral space well.     

南水北调中线水源区植被覆盖度遥感监测分析

南水北调中线工程是我国大规模跨流域调水工程的一部分,开展该区域植被覆盖度变化的研究与分析,对于保护该区域的生态环境及水质具有重要意义。该文以2000年和2009年两期遥感图像为本底数据,利用基于NDVI的像元二分模型对南水北调中线水源区的植被覆盖度进行了估算,并分析了该区植被覆盖度的时空变化特征。结果表明:2000年该水源区植被覆盖度的平均值为67.5%,2009年的平均值达到72%,植被覆盖度总体呈增长趋势;植被覆盖度增幅的空间特征表现为水源区中部地区高,东西部地区相对较低;在不同植被类型中,落叶针叶林的覆盖度平均值增幅最大,草地覆盖度增幅最小;位于水源区的大多数县(市)的植被覆盖度在近十年来都有不同程度的增加,其中柞水县的植被覆盖度平均值增长幅度最大,这与国家实施退耕还林、封山育林、基本农田建设等政策有关。     

分形图形生成的一种新方法

本文提出分形图形生成的一种新方法。采用分数维布朗运动来合成分形图形,分数维布朗运动用一种新的方法──递归空间滤波来获得。由分数维布朗运动的功率谱确定其二维成形滤波器的频率响应,然后采用以一维原形滤波器加旋转变换的方法来设计具有圆对称和指数衰减频率响应的成形滤波器。用成形滤波器对高斯分布的白色过程滤波,便可以得到具有期望分数维的布朗运动分形图形。     

基于分形理论和形态学的遥感图像地物检测

利用分形理论和数学形态学的方法对大比例尺遥感影像上面状地物飞机进行了检测。经实验结果得出,利用“地毯覆盖法”提出的分形斜率截距法对遥感影像飞机检测,结果要优于灰度统计法、经典边缘检测算子和形态学算子检测的结果。     

基于分形理论的水系要素制图综合研究

在研究水系要素具有分形现象的基础上，提出了水系要素的分维数的确定方法，并利用水系的分数维规律进行地图制图综合，取到了较好的结果。     

Analytical dynamic orbit improvement for the evaluation of geodetic-geodynamic satellite data

Summary Given an analytical solution (solution of the equations of motion using analytical integration techniques) an integration of the variational equations is not necessary but simply a differentiation of the analytical solution. Based on a high-precision analytical solution explicit expressions for the coefficients of the observation equations to improve state variables and force model parameters have been derived.The definition of suitable unknowns for a pure dynamic orbital improvement can be based then on an analysis of the information content of the data at hand by using those expressions.Regarding the Fourier series structure of orbital perturbations as well as the special properties of crossover difference data, the proposed technique is particularly favourable for an evaluation of Remote Sensing Data such as altimeter, SST and gradiometer data from satellites in repeating orbits.After a general discussion of the observation equations for crossover data our present results using GEOSAT altimeter data are discussed as one example for applications. Some short remarks about further applications are given.     

Comparison of ETM+ and MODIS Data for Tropical Forest Degradation Monitoring in the Peninsular Malaysia

This study was undertaken the use of course and moderate spatial resolution remote sensing data to assess the forest degradation in the Peninsular Malaysia. Moderate Resolution Imaging Spectroradiometer (MODIS) imagery was used as coarse spatial resolution data, while Landsat Enhanced Thematic Mapper⁺ (ETM⁺) imagery was used as moderate spatial resolution to compare the accuracy. Geometric and radiometric correction and re-sampling were performed in pre-processing to enhance the analysis and results. Canopy fractional cover was used as an approach to assess the forest degradation in this study. Then, an optimum vegetation index was selected to apply on canopy fractional cover to enhance the detection of forest canopy damage. At the same time, accuracy assessment for the approach was referred to the location of Neobalanocarpus Heimii and correlate with global evapotranspiration rate. The forest degradation analysis was also applied and compared for all of the states in the Peninsular Malaysia. In conclusion, Landsat ETM⁺ imagery obtained higher accuracy compare to MODIS using canopy fractional cover approach for forest degradation assessment, and can be more broadly applicable to use for forest degradation investigation.     

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.