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Can we find a self-similar set on the line with positive Lebesgue measure and empty interior? Currently, we do not have the answer for this question for deterministic self-similar sets. In this paper we answer this question negatively for random self-similar sets which are defined with the construction introduced in the paper by Jordan et al. (2007) [6]. For the same type of random self-similar sets we prove the Palis-Takens conjecture which asserts that at least typically the algebraic difference of dynamically defined Cantor sets is either large in the sense that it contains an interval or small in the sense that it is a set of zero Lebesgue measure.

Rice is the staple food in Iran. More than 80 percent of rice area is distributed in the two northern provinces of Mazandaran and Gilan, so that investment in increasing the quantity and quality can impact an effective role in economic independence and sustainable agriculture. Increased efficiency in rice production is possible through varietal technology, advances in yield enhancement, and the successful development of hybrid technology. Nondestructive methods such as study the spectral reflectance of rice fields is a reliable way in remote sensing study. In this study we tested the possibility to predict highyielding rice varieties based on the spectral reflectance data in the red edge position (REP). Spectral reflectance of rice canopies from 350 to 2500 nm were acquired under clear sky in rice filed. The obtained results indicate that REP of Hybrid, Tarom, Neda and Khazar varieties are at longer wavelength, so they are predicted as more productive rice varieties.

In Madagascar, soil erosion is significant even when it is compared to world averages. A resulting special geomorphic feature is a form of gully erosion known as lavaka that appears in the highlands of the country. Lavakization (the generation and development of these features) is due to rather unique multifactorial environmental conditions. Among many factors (geology, soil composition, human activities, etc.), the spatial and temporal distribution of precipitation is a key factor influencing the behaviour of lithology and the vegetation cover of the island. The inter-annual variability in precipitation seems to be responsible for the enhanced generation of small cracks that might eventually lead to the development of a gully. However, the way of the development of such gullies is unknown. To what extent the actual precipitation pattern contributes to the aforementioned phenomenon has not yet been studied in great detail. This paper aims to analyze lavaka distribution with GIS methods and to study the relation between lavaka density and climatic conditions. Study areas have been designated throughout the country and lavakas have been identified using satellite imagery. Archive climate data of the study areas have been used to understand the influence of the weather on gully density. Data show that the spatial distribution of precipitation is connected to the appearance of lavakas to a given extent and its effect is further strengthened by the tropical cyclones. However, neither the amount of the precipitation, nor its variability alone can explain the high variation found in the spatial distribution of lavakas. Further multidisciplinary studies are necessary to draw conclusions about lavaka formation and to describe the process of lavaka development., En Madagascar, la erosión del suelo es muy elevada, incluso cuando se compara con los promedios del resto del mundo, dando lugar a formas de relieve especiales, conocidas como lavakas, que aparecen en las regiones montañosas de Madagascar. La “lavakización” (generación y evolución de estas formas) se debe a una multitud de condiciones ambientales únicas. De entre las muchas condiciones, (geología, composición del suelo, influencia antrópica, etc.), la distribución espacial y temporal de la precipitación es el factor más importante para explicar el comportamiento erosivo de la litología y las características de la cubierta vegetal de la isla. La ocurrencia de estaciones secas y lluviosas es aparentemente responsable del crecimiento de pequeñas grietas que eventualmente pueden conducir al desarrollo de lavakas. Sin embargo, se desconoce cómo se desarrollan esos barrancos. Además, la pregunta de hasta qué punto la precipitación y su pauta afecta al fenómeno mencionado todavía no ha sido contestada. El objetivo de este artículo es analizar la distribución de lavakas con métodos de GIS y examinar la relación entre su densidad y las condiciones climáticas. Las áreas de estudio han sido elegidas a lo largo del país, y las lavakas han sido identificadas con la ayuda de imágenes de satélite. Se han utilizado datos climáticos para comprender la influencia del clima en la densidad de los barrancos. Los datos de la precipitación nos permiten establecer una correlación entre la aparición de los barrancos y la distriubución espacial de la precipitación. Además, su efecto es incentivado adicionalmente por ciclones tropicales. No obstante, ni la cantidad o la variabilidad de la precipitación por sí solas pueden explicar la variedad existente en la distribución espacial y el tamaño de las lavakas. Nuevas investigaciones multidisciplinares son necesarias para conocer mejor los procesos de desarrollo y la aparición de lavakas.

In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor sets introduced by Per Larsson., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Water and Nitrogen (N) are critical inputs for crop production. Remote sensing data collected from multiple scales, including ground-based, aerial, and satellite, can be used for the formulation of an efficient and cost effective algorithm for the detection of N and water stress. Formulation and validation of such techniques require continuous acquisition of ground based spectral data over the canopy enabling field measurements to coincide exactly with aerial and satellite observations. In this context, a wireless sensor in situ network was developed and this paper describes the results of the first phase of the experiment along with the details of sensor development and instrumentation set up. The sensor network was established based on different spatial sampling strategies and each sensor collected spectral data in seven narrow wavebands (470, 550, 670, 700, 720, 750, 790 nm) critical for monitoring crop growth. Spectral measurements recorded at required intervals (up to 30 seconds) were relayed through a multi-hop wireless network to a base computer at the field site. These data were then accessed by the remote sensing centre computing system through broad band internet. Comparison of the data from the WSN and an industry standard ground based hyperspectral radiometer indicated that there were no significant differences in the spectral measurements for all the wavebands except for 790nm. Combining sensor and wireless technologies provides a robust means of aerial and satellite data calibration and an enhanced understanding of issues of variations in the scale for the effective water and nutrient management in wheat.

Ecosystems provide several services for human well-being. The quality of these ecosystem services is among others affected by agriculture, the main land user in Europe. Thus, it is essential to provide information about land use in agricultural areas. In this research, land use classification of agricultural areas is carried out based on high-resolution Spotlight TerraSAR-X images (TSX-images) of two different polarisations (HH and VV). A stack of several radar images taken during the vegetation season is used for multi-temporal classification of land cover. The typical phenology of agricultural vegetation types and their individual phenological development during the year cause differences in the backscatter of the radar signal over time. Two different study areas are investigated, one in the North East of the city of Hannover, Germany called "Fuhrberger Feld" and one in the "Gorajec area" in the very South East of Poland. These two areas represent extremely diverse European regions with regard to agro-technological level, population density, cultivation form as well as geological and geomorphological conditions. Thereby, the radar signal backscatter for different regions is tested. Preliminary results show significant differences in the backscatter of crop types in SAR data of about 3 m, especially for grasslands, grain and broad-leaved crops. Furthermore the VV polarised radar signal has clearly lower backscattering for grains during summertime and for grasslands in general than for broad-leaved crops.

In this article we present a method that extracts plantations from satellite imagery by finding and exploiting appropriate feature space projections. Segmentation is done using an automatic two-region segmentation based on the level set method. The behaviour of this algorithm is defined by a statistical region model that describes the similarity of regions using distances in arbitrary feature spaces. Subsequently different feature spaces will be evaluated regarding their plantation classification quality in an automatic fashion. The segmentation quality of our method is assessed by testing several orthophotos depicting a wide range of landscape types and comparing them with a manual segmentation. We show that a combination of simple texture based features like the structure tensor and the Hessian matrix are sufficient to facilitate an effective plantation segmentation scheme.

Since the first demonstration of the potential of the differential SAR interferometry in the early 1990s a lot of effort has been made to accurately estimate ground deformation with imaging radar sensors. This led to the invention of the Persistent Scatterer Interferometry (PSI) in the late 1990s. PSI enables the estimation of ground deformation for a set of temporally stable radar reflectors, the so called PS, with millimeter accuracy. The main advantage compared to methods commonly used for ground deformation monitoring like GPS is the possibility to cover large areas very economically. One of the main drawbacks is the opportunistic sampling of the target area, which is mainly governed by the distribution of stable radar reflectors within the scene. Besides problems caused by undersampling the main issue is due to the face, that the real world feature related to a PS is usually not known. This makes the interpretation of the results particularly difficult. While the assignment of these real world features is very difficult in the case of ERS like sensors, modern high resolution SAR sensors like TerraSAR-X (TSX) render this task possible. We investigate the use of SAR simulation to match real world features with PS extracted from a TSX stack acquired over the city of Berlin Germany. The simulation is based on a 3D city model of the area around the Potsdamer Platz, Berlin.

Land cover classification plays a key role for various geo-based applications. Numerous approaches for the classification of settlements in remote sensing imagery have been developed. Most of them assume the features of neighbouring image sites to be conditionally independent. Using spatial context information may enhance classification accuracy, because dependencies of neighbouring areas are taken into account. Conditional Random Fields (CRF) have become popular in the field of pattern recognition for incorporating contextual information because of their ability to model dependencies not only between the class labels of neighbouring image sites, but also between the labels and the image features. In this work we investigate the potential of CRF for the classification of settlements in high resolution satellite imagery. To highlight the power of CRF, tests were carried out using only a minimum set of features and a simple model of context. Experiments were performed on an Ikonos scene of a rural area in Germany. In our experiments, completeness and correctness values of 90% and better could be achieved, the CRF approach was clearly outperforming a standard Maximum-Likelihood-classification based on the same set of features.

As a consequence of the wide-spread application of digital geo-data in Geoinformation Systems (GIS), quality control has become increasingly important. A high degree of automation is required in order to make quality control efficient enough for practical application. In order to achieve this goal we have designed and implemented a semi-automatic technique for the verification of cropland and grassland GIS objects using 1 m pan-sharpened multispectral IKONOS imagery. The approach compares the GIS objects and compares them with data derived from high resolution remote sensing imagery using image analysis techniques. Textural, structural, and spectral features are assessed in a classification based on Support Vector Machines (SVM) in order to check whether a cropland or grassland object in the GIS is correct or not. The approach is explained in detail, and an evaluation is presented using reference data. Both the potential and the limitations of the system are discussed.