遥感多维空间数据场特征的角度分析与应用

科学计算的可视化是空间数据场的可视化。标题、矢量、张量是线性电磁系统中定义多维数据的基本参数。从瞬变电磁系统的因果律出发，可以将遥感传感器对电磁波的响应看作是地表电磁场量的映射，像元是记录电磁场量的一种方式。由于电磁场量的线性关联，多波段遥感数字图像可以表示为多维空间数据场量。在多维向量空间中可以对数据场量进行度量、分解和构造向量角度函数。遥感多维空间数据场有效弱信息提取方法则是基于多维空间数据场角度分析展开的。     

面向虚拟地球的三维气象场可视化方法

三维气象场是一个多维变化的环境,可视化是研究其内在规律的重要方法。针对三维气象场的全球范围、多维多尺度、海量数据等特征,提出了基于体元对象的数据模型和多级体元索引机制,并在此基础上设计了面向三维气象场的可视化方法,包括基于箭头模型的矢量场可视化方法和改进后的基于三维纹理映射体绘制的标量场可视化方法。最后基于虚拟地球平台进行了可视化和时空检索分析实验。实验验证了该方法的可行性和有效性。     

基于几何代数的GIS计算模型研究

正空间分析是地理信息系统(GIS)的核心功能,也是GIS深化应用与服务的重要支撑。现有空间数据分析方法在多维对象的自适应表达、空间数据的统一分析以及多维统一分析框架的构建方面仍显不足,无法满足海量、高维度、多要素的密集型GIS空间数据的分析需求。引入几何代数的多维表达结构及统一运算结构,从底层理论上对现有表达与计算方法进行创新,设计面向多维度、多要素复杂数据的计算模型,是突破传统GIS分析方法     

采用张量子空间的高光谱影像多维滤波算法

本文提出了一种基于张量子空间的多维滤波算法,将其应用于高光谱遥感影像降噪。该方法将高光谱影像数据视为三阶张量,引入张量数据表达,通过张量子空间分解将含噪影像投影到信号子空间,根据影像信号与噪声在子空间中分布的不同滤除噪声并保留原始影像的信号成分。利用该算法作用于多组含噪高光谱数据,对比逐波段二维维纳滤波算法、小波降噪算法等传统数字图像降噪算法的结果,实验证明了这种新型降噪算法的有效性。     

基于三维GIS的海洋标量场数据动态可视化

针对海洋标量场数据的多维、多格式、动态性等特点,设计了基于NetCDF的海洋标量数据通用数据模型,详细阐述了模型的存储格式及其特点。基于三维GIS场景,构建了标量场多维动态渲染模型,探讨了基于几何对象的海洋标量场数据多维可视化方法,实现了海洋标量数据的直观、多维、动态可视化表达。技术试验表明,该方法高效、可行,可为其它海洋环境要素数据的可视化与分析提供技术借鉴。     

采用张量子空间的高光谱影像多维滤波算法

提出一种基于张量子空间的多维滤波算法,将其应用于高光谱遥感影像降噪。该方法将高光谱影像数据视为三阶张量,引入张量数据表达,通过张量子空间分解将含噪影像投影到信号子空间,根据影像信号与噪声在子空间中分布的不同滤除噪声并保留原始影像的信号成分。利用该算法作用于多组含噪高光谱数据,对比逐波段二维维纳滤波算法、小波降噪算法等传统数字图像降噪算法的结果,试验证明了这种新型降噪算法的有效性。     

张量组稀疏表示的高光谱图像去噪算法

提出了一种基于张量组稀疏表示的高光谱遥感影像降噪。高光谱影像数据可视为三阶张量。首先,高光谱图像被划分为小的张量分块,然后,对相似的张量分块进行聚类,并对聚类分组进行稀疏表示。基于高光谱图像的空间非局部自相似性和光谱相关性,将张量组稀疏表示模型分解为一系列无约束低秩张量的近似问题,进而通过张量分解进行求解。对模拟和真实高光谱数据进行试验,验证了该算法的有效性。     

基于张量分解的超光谱图像降秩与压缩

超光谱图像在常规的二维图像中加入了光谱维度,具有更大的信息量的同时也带来了较大的光谱冗余性,这给图像压缩带来了新的挑战。提出了一种基于张量分解的超光谱图像降秩与压缩方法,将超光谱图像视为三阶张量数据表示,并使用张量分解技术将原始观测张量分解为核张量与多个投影矩阵的乘积形式。这样,超光谱图像被压缩为了低秩张量,它可以通过张量反投影进行图像重构。实验证明张量分解技术能够将超光谱图像压缩到很低的比率,同时保持较低的重构相对误差。     

面向过程的建设用地全程监管时空数据组织模型

本文针对建设用地全程监管多环节、多数据及关系复杂等特点,基于全程监管业务过程和业务需求,提出了面向过程的建设用地全程监管时空数据组织管理模型,探讨了模型组织与存储方式以及回溯与重建操作的实现方法。该模型实现了对建设用地全程监管时空数据语义的一体化组织和表达,可以通过增加辅助表的方式在关系型数据中实现,并能够简单高效的支持用地地块和用地项目的回溯与重建操作,提高建设用地全程监管的效率。     

结合轨迹数据的居民出行模式及功能识别研究

城市人群的出行特征通过车辆轨迹数据隐含的行为信息可以体现,但传统的单维度模型将不再适用于轨迹数据隐含的多维信息的挖掘.本文将海口市中心城区根据路网划分区域,使用能够挖掘多维信息的非负稀疏约束下张量分解基于"滴滴出行"轨迹数据,从时空维度挖掘居民出行规律并进行区域功能特征识别.结果表明:居民出行时间符合工作日,休息日的早...     

Toute la Geodesie sans ellipsoide Les reperes laplaciens Application plus particuliere aux travaux a latitude elevee

Resume Après de nombreuses années d’hésitation, on a finalement reconnu, au Congrès de Florence, en 1955, que dans le repérage des altitudes, seule la notion depotentiel était claire et sans ambigu?té, l’altitude au sens courant du terme étant conventionnelle. De la même fa?on, pour le repérage géométrique des points à la surface de la Terre, les coordonnées (X Y Z) des points, dans letrièdre cartésien terrestre général, sont les inconnues fondamentales; les coordonnées géodésiques couramment utilisées (longitude, latitude altitude H au-dessus de l’ellipso?de) sont conventionnelles. Mais pratiquement, afin d’écrire commodément les relations d’observation, il para?t intéressant de passer par l’intermédiaire detrièdres locaux (trièdres laplaciens), liés de fa?on invariable au système cartésien général, et de repérer toutes les grandeurs dans ces trièdres locaux. Toutes les observations utilisées en Géodésie s’expriment de fa?on simple et sans singularités dans ces trièdres locaux. La jonction des triangulations classiques, l’Astrogéodésie, la synthèse des Géodésies classique et spatiale sont facilitées. En astronomie de position, les grandeurs longitude, latitude, azimut, sont avantageusement remplacées par: déviation Est-Ouest, déviation Nord-Sud, azimut de Laplace. Les relations d’observation s’écrivent sans difficulté, même dans les régions polaires. L’application pratique des nouvelles formules obtenues a été réalisée avec succès par L.F. Gregerson (Service Géodésique du Canada).

---

Summary At Florence, in 1955, it was accepted that, in the problems of levelling, the notion ofpotential was scientifically clear, and that the altitude could derive from it only through a conventional process. In the same manner, when we want to have a geometric reference of the points at the earth surface, we use the coordinates (X Y Z) in thegeneral cartesian trihedron as fundamental unknowns, the geodetic coordinates (λϕH) deriving from (X Y Z) through a conventional process. Practically, in order to set up the observation equations, it is necessary to define local trihedrons (laplacian trihedrons), deriving from the cartesian general system through a fixed transformation, and to refer all the unknowns in these local trihedrons. All the observations used in Geodesy can be expressed simply and without any singularity in these local trihedrons. The links between classical geodetic nets, the astrogeodesy, the combination between classical and spatial geodesy, become easier. In astronomical controls, “longitude, latitude, azimut” must be replaced by: W-E deflection, N-S deflection and Laplace azimuth. Thus all the observation equations can be set, even in polar regions. A practical application of the new formulae was done successfully by L.F. Gregerson (Geodetic Survey of Canada).

     

Estimate of heavy metals in soil and streams using combined geochemistry and field spectroscopy in Wan-sheng mining area,Chongqing, China

Heavy metals contaminated soils and water will become a major environmental issue in the mining areas. This paper intends to use field hyper-spectra to estimate the heavy metals in the soil and water in Wan-sheng mining area in Chongqing. With analyzing the spectra of soil and water, the spectral features deriving from the spectral of the soils and water can be found to build the models between these features and the contents of Al, Cu and Cr in the soil and water by using the Stepwise Multiple Linear Regression (SMLR). The spectral features of Al are: 480 nm, 500 nm, 565 nm, 610 nm, 680 nm, 750 nm, 1000 nm, 1430 nm, 1755 nm, 1887 nm, 1920 nm, 1950 nm, 2210 nm, 2260 nm; The spectral features of Cu are: 480 nm, 500 nm, 610 nm, 750 nm, 860 nm, 1300 nm, 1430 nm, 1920 nm, 2150 nm, 2260 nm; And the spectral features of Cr are: 480 nm, 500 nm, 610 nm, 715 nm, 750 nm, 860 nm, 1300 nm, 1430 nm, 1755 nm, 1920 nm, 1950 nm. With these features, the best models to estimate the heavy metals in the study area were built according to the maximal R². The R² of the models of estimating Al, Cu and Cr in the soil and water are 0.813, 0.638, 0.604 and 0.742, 0.584, 0.513 respectively. And the gradient maps of these three types of heavy metals’ concentrations can be created by using the Inverse distance weighted (IDW).The gradient maps indicate that the heavy metals in the soil have similar patterns, but in the North-west of the streams in the study area, the contents are of great differences. These results show that it is feasible to predict contaminated heavy metals in the soils and streams due to mining activities by using the rapid and cost-effective field spectroscopy.     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

Determination of the factors governing soil erodibility using hyperspectral visible and near-infrared reflectance spectroscopy

Soil erodibility, which is difficult to estimate and upscaling, was determined in this study using multiple spectral models of soil properties (soil organic matter (SOM), water-stable aggregates (WSA) > 0.25 mm, the geometric mean radius (D_g)). Herein, the soil erodibility indicators were calculated, and soil properties were quantitatively analyzed based on laboratory simulation experiments involving two selected contrasting soils. In addition, continuous wavelet transformation was applied to the reflectance spectra (350–2500 nm) of 65 soil samples from the study area. To build the relationship, the soil properties that control erodibility were identified prior to the spectral analysis. In this study, the SOM, D_g and WSA >0.25 mm were selected to represent the most significant soil properties controlling erodibility and describe the erodibility indicator based on a logarithmic regression model as a function of SOM or WSA > 0.25 mm. Five, six and three wavelet features were observed to calibrate the estimated soil properties model, and the best performance was obtained with a combination feature regression model for SOM (R² = 0.86, p < 0.01), D_g (R² = 0.79, p < 0.01) and WSA >0.25 mm (R² = 0.61, p < 0.01), respectively. One part of the wavelet features captured amplitude variations in the broad shape of the reflectance spectra, and another part captured variations in the shape and depth of the soil dry substances. The wavelet features for the validated dataset used to predict the SOM, WSA >0.25 mm and D_g were not significantly different compared with the calibrated dataset. The synthesized spectral models of soil properties, and the formation of a new equation for soil erodibility transformed from the spectral models of soil properties are presented in this study. These results show that a spectral analytical approach can be applied to complex datasets and provide new insights into emerging dynamic variation with erodibility estimation.     

A few words concerning the formulae for the simple transformation of coordinates

Zusammenfassung Der Verfasser bringt zun?chst die verschiedenen Formeln, die für einfache Koordinatentransformationen, d. h. zur Umrechnung von zwei unver?nderlich miteinander verbundenen Punkten ohne Wechsel des Referenzellipsoides, angewendet werden, in Erinnerung und empfiehlt dann die Formeln (4) und (5) mit den Verbesserungsausdrücken (9), wobei die Bezeichnungenr, s, t, q durch die Gleichungen (6) und (8) definiert sind. Diese Formeln sind trotz ihrer Einfachheit genauer als diejenigen vonHelmert undHristow, denn füre=0 stellen sie die genauen sph?rischen Formeln (2) und (3) dar. Die Verformung der geschlossenen Polygone, entsprechend den ?nderungen der Krümmung des Ellipsoids, ist schon fühlbar durch die Glieder mite ²α² und macht eine erh?hte formelle Genauigkeit trügerisch.

---

Resumen Después de recordar las diferentes fórmulas aplicadas para las transformaciones sencillas de las coordenadas, es decir, para el desplazamiento de puntos invariablemente ligados, sin cambiar el elipsoide de referencia, el autor recomienda las fórmulas. (4) y (5) con los términos correctivos (9), en que las cantidaderr, s, t, q, están definidas por las ecuaciones (6) y (8). Estas fórmulas, a pesar de su sencillez, son más precisas que las deHelmert yHristow, porque parae=0 son las fórmulas esféricas exactas (2) y (3). Las deformaciones de los poligonos cerrados, debidas a las variaciones de curvatura del elipsoide, es ya sensible por los términos en e² σ² y hace, en consecuencia, illusoria una precisión superior

---

Résumé Après avoir rappelé les différentes formules appliquées pour les transformations simples des coordonnées, c'est-à-dire pour le déplacement de points invariablement liés, sans changer l'ellipso?de de référence, l'auteur recommande les formules (4) et (5) avec les termes correctifs (9), dont les termesr, s, t, q sont définis par les équations (6) et (8). Ces formules, malgré leur simplicité, sont plus précises que celles d'Helmert etHristow, car poure=0 ce sont les formules sphériques exactes (2) et (3). La déformation des polygones fermés, due aux variations de courbure de l'ellipso?de, est déjà sensible par les termes en e² σ², et rend en conséquence illusoire une précision formelle supérieure.

---

Sommario Dopo richiamate le varie formule fin qui proposte per la trasformazione delle coordinate sull'ellissoide in un moto rigido sulla superficie dello stesso, l'autore raccomanda le formule (4) et (5) con i termini correttivi (9), i cui coefficientir, s, t, q, sono definiti dalle equazioni (6) ed (8). Queste formule, malgrado la loro semplicità, sono più precise di quelle diHelmert e diHristov, in quanto pere=0 esse forniscono le formule sferiche esatte (2) e (3). La deformazione dei poligoni chiusi, dovute alle variazioni nella curvatura dell'ellisoide, si rende già sensibile nei termini in e² σ², e rende illusoria una maggiore precisione formale.

     

Neue Analyse der Chandler-Bewegung

Summary TheChandler movement is essentially an oscillation having an assumed period of the order of time of a double revolution of the moon’s nodes. The variation in its period is only apparent and relies upon a sudden change of phase which occurred at the beginning of 1928. If attention is paid to the residuals, a secondary oscillation with an 11-year period can be detected. This explains theWitting perturbations, and is possibly connected with the sun-spot cycle.

---

Resumen El movimientoChandler es en su esencia un balanceo que tiene una duración admitida del órden de la doble revolución de los nodos de la Luna. La variabilidad de su periodo no es más que simulada, debido a un salto de fase situada en el comienzo del a?o 1928. Utilizando los residuos, se puede demostrar un balanceo suplementario de 11 a?os, que explica lasperturbacionésWitting y que está posiblemente relacionado con el periodo de las manchas solares.

---

Résumé La période deChandler correspond, dans son essence, à un balancement ayant une durée présumée de l’ordre de la double révolution des nœuds de la Lune. La variabilité de sa période n’est que dissimulée et ceci grace à un saut de phase situé au commencement de l’année 1928. En utilisant les résidus, on peut démontrer un balancement supplémentaire de 11 ans, qui explique les perturbationsWitting, et qui est en liaison possible avec la période des taches solaires.

---

Sommario Il movimento diChandler è essenzialmente un’oscillazione avente presumibilmente un periodo doppio della rivoluzione dei nodi lunari. La variabilità di questo periodo è soltanto apparente, in consequenza di un salto di fase situato al principio del 1928. Utilizzando i residui, si può mostrare un’oscillazione supplementare del periodo di 11 anni, che spiega la perturbazione diWitting e che sta forse in relazione con il periodo delle macchie solari.

---

---

Communication présentée à l’Assemblée Générale de Bruxelles     

1979年—2014年三峡库区月平均气温的时空变化分析

三峡区域气温变化长期以来受到科研人员和公众的关注。受三峡复杂地形的影响,仅仅基于气象站点观测数据很难准确获取区域气温变化的空间格局,遥感技术则可以通过提供空间连续的地表观测数据来辅助气温变化分析。以广义加性模型GAM (General Additive Model)为插值算法,以高程和夜间地表温度(LST_night)遥感产品为辅助变量,估算三峡库区1979年—2014年1 km空间分辨率的月气温数据,在此基础上分析了气温变化趋势的时空特征及其与高程和森林覆盖率的关系。研究表明,(1)在插值算法中引入遥感产品LST_night作为辅助变量可以明显改善气温估算精度,冬春季的改善幅度高于夏秋季;(2)三峡库区年平均气温在1997年后明显上升,但在2003年库区蓄水后无明显变化趋势,几乎所有月(除12月以外)的气温都呈现上升趋势,增温趋势最显著是3月和9月,3月增温主要来自于库区东部山区的贡献,而9月增温主要来自于库区西部平原的贡献;(3)多数月份(除7月、8月、9月以外)的低温上升速度超过高温上升速度,导致区域气温的动态变化范围缩小;(4)三峡库区年平均气温上升速度与高程呈正相关,即海拔越高,升温越快,但在同一海拔高度处,森林覆盖率越高,年均气温上升速度越慢,暗示森林具有抑制增温的作用。     

Guaszscher Algorithmus (Doolittle-Methode) und Boltzsches Entwicklungsverfahren

Zusammenfassung Die jüngsten Arbeiten von Prof.Jenne (Potsdam) über die unbestimmte Aufl?sung der Normalgleichungen für Winkelbedingungen und eine von Dr.Dupuy 1948 aufgeworfene Frage geben Anla\ zu einer Gegenüberstellung der verschiedenen Verfahren zur Aufl?sung von Normalgleichungen, insbes. des Gau\schen Algorithmus und des Boltzschen Entwicklungsverfahrens. Im Hinblick auf den beachtlichen Vorsprung im Aufl?sungsproze?, den die Mitbenützung der fertig ausgerechneten Korrelatentabellen für die Dreieckswinkelgleichungen gew?hren, kommt man zu dem Schlu?, da? es weniger der Gegensatz als vielmehr die geschickte Verbindung der beiden vorgenannten Verfahren ist, welche eine besondere Beachtung und Würdigung verdient.

---

Summary The most recent work of ProfessorJenne (of Potsdam) on the algebraical solution of normal angle condition equations, and on a question raised in 1948 by DrDupuy, gives us the opportunity of comparing various methods for the solution of normal equations, in particular the Gaussian algorithm and Boltz’s development method. Having taken account of the valuable saving introduced, in the methods of solution, by the use of tables of correlatives, calculated from the angle equations, one arrives at the conclusion that there is some value in giving detailed consideration to the judicious combination of the two methods mentioned above—rather than drawing attention to their differences.

---

Resumen Los trabajos más recientes del ProfesorJenne (de Potsdam) sobre la resolución indeterminada de las ecuaciones normales de condición para los ángulos así como una cuestión planteada en 1948 por el Dr.Dupuy, nos proporcionan la ocasión de comparar los diversos métodos de resolución de las ecuaciones normales, en particular el algoritmo deGauss y el método de desarrollo deBoltz. Teniendo en cuenta el progreso notable llevado al proceso de resolución, por el empleo de los correlativos, calculados del todo con las ecuaciones de ángulos, se llega a la conclusión que conviene prestar una atención y una consideración particulares a la feliz combinación de los dos métodos antes mencionados, mucho más que a la oposición de los mismos.

---

Résumé Les travaux les plus récents du ProfesseurJenne (de Potsdam) sur larésolution indéterminée des équations normales de condition aux angles et une question soulevée en 1948 par le DrDupuy nous donnent l’occasion de comparer les diverses méthodes de résolution des équations normales, en particulier l’algorithme deGauss et la méthode de développement deBoltz. Compte tenu du progrès notable apporté, dans le processus de résolution, par l’emploi des corrélatifs tout calculés des équations aux angles, on arrive à la conclusion qu’il convient d’accorder une attention et une considération particulières à l’adroite combinaison des deux méthodes ci-dessus mentionnées—beaucoup plus qu’à leur opposition.

---

Sommario I lavori più recenti del prof.Jenne (di Potsdam) sulla risoluzione indeterminata delle equazioni normali·di condizione agli angoli, ed una questione sollevata dal Dr.Dupuy, ci offrono lo spunto per confrontare i diversi metodi di risoluzione delle equazioni normali, in particolare l’algoritmo diGauss ed il metodo di sviluppo diBoltz. Tenuto conto del notevole progresso apportato, nel procedimento di risoluzione, dall’impiego dei correlativi precalcolati delle equazioni agli angoli, si giunge alla conclusione che conviene rivolgere l’attenzione alla possibilità di accordare, piuttosto che di contrapporre, i due metodi menzionati.

     

Demonstration of sub-meter GPS orbit determination and 1.5 parts in 108 three-dimensional baseline accuracy

Differential tracking of theGPS satellites in high-earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the fullGPS constellation. To demonstrate this capability, we have determined baselines of up to2000 km in North America by estimating high-accuracyGPS orbits and ground receiver positions simultaneously. The2000 km baselines agree with very long baseline interferometry(VLBI) solutions at the level of1.5 parts in10 ⁸ and showrms daily repeatability of0.3–2 parts in10 ⁸. The orbits determined for the most thoroughly trackedGPS satellites are accurate to better than1 m. GPS orbit accuracy was assessed from orbit predictions, comparisons with independent data sets, and the accuracy of the continental baselines determined along with the orbits. The bestGPS orbit strategies included data arcs of at least one week, process noise models for tropospheric fluctuations, estimation ofGPS solar pressure coefficients, and combined processing ofGPS carrier phase and pseudorange data. For data arcs of two weeks, constrained process noise models forGPS dynamic parameters significantly improved the solutions.     

Determination of the crop row orientations from Formosat-2 multi-temporal and panchromatic images

This paper presents a technique developed for the retrieval of the orientation of crop rows, over anthropic lands dedicated to agriculture in order to further improve estimate of crop production and soil erosion management. Five crop types are considered: wheat, barley, rapeseed, sunflower, corn and hemp. The study is part of the multi-sensor crop-monitoring experiment, conducted in 2010 throughout the agricultural season (MCM’10) over an area located in southwestern France, near Toulouse. The proposed methodology is based on the use of satellite images acquired by Formosat-2, at high spatial resolution in panchromatic and multispectral modes (with spatial resolution of 2 and 8 m, respectively). Orientations are derived and evaluated for each image and for each plot, using directional spatial filters (45° and 135°) and mathematical morphology algorithms. “Single-date” and “multi-temporal” approaches are considered. The single-date analyses confirm the good performances of the proposed method, but emphasize the limitation of the approach for estimating the crop row orientation over the whole landscape with only one date. The multi-date analyses allow (1) determining the most suitable agricultural period for the detection of the row orientations, and (2) extending the estimation to the entire footprint of the study area. For the winter crops (wheat, barley and rapeseed), best results are obtained with images acquired just after harvest, when surfaces are covered by stubbles or during the period of deep tillage (0.27 > R² > 0.99 and 7.15° > RMSE > 43.02°). For the summer crops (sunflower, corn and hemp), results are strongly crop and date dependents (0 > R² > 0.96, 10.22° > RMSE > 80°), with a well-marked impact of flowering, irrigation equipment and/or maximum crop development. Last, the extent of the method to the whole studied zone allows mapping 90% of the crop row orientations (more than 45,000 ha) with an error inferior to 40°, associated to a confidence index ranging from 1 to 5 for each agricultural plot.