Method and arrangement for improving a geometric resolution of remote sensing data

Abstract

The invention relates to a method for improving a geometric resolution of remote sensing data, - wherein at least two output sets of remote sensing data of a scene are received or present, - wherein each of the output sets comprises function values ​​for associated raster elements (G1, G2, G3, G4, H1) of a geometric raster of a detection of the scene, and wherein the function values ​​each correspond to radiation emanating from the scene and incident in the associated raster element, - wherein the geometric grids of the at least two initial sets are geometrically offset from one another, so that in an overlapping region of the geometric grids of the at least two initial sets, overlapping sub-regions (U1, U2, U3) are formed, from which the overlapping region is composed, the geometric size of which is smaller than the geometric size of the grid elements (G1, G2, G3, G4, H1) of the at least two initial sets, - for each of the plurality of overlapping sub-areas, a derived function value is formed, which is formed from the function values ​​of those raster elements (G1, G2, G3, G4, H1) of the at least two output sets, - an area integral of the derived function values ​​over the overlap area for each of the initial sets is equal to an area integral of the function values ​​of the grid elements (G1, G2, G3, G4, H1) of the initial set.

Description

[0001] The invention relates to a method and an arrangement for improving a geometric resolution of remote sensing data, in particular remote sensing image data of objects on the earth's surface and / or the atmosphere, wherein the image data can be obtained, for example, from remote sensing satellites, aircraft or other flying objects (e.g. balloons).

[0002] In the remote sensing of scenes, especially the Earth's surface, optical / thermal sensors are used, among other things, to capture a small area of ​​the surface at a given time. They receive radiation reflected / emitted from the captured surface area and generate sensor data based on their radiation sensitivity. This data can be evaluated to obtain information about the captured area. The measurement results in an intensity value corresponding to the radiation intensity or an array of intensity values, each of which is assigned to a different local area of ​​the scene. Optical / thermal sensors can, in particular, be imaging (imaging), e.g.as part of a surface scanning system mounted on a flying object, e.g. an aircraft, and / or a camera for the simultaneous recording of a large number of image points (in particular corresponding to the radiation intensities of the associated surface areas of the celestial body). Imaging sensors therefore provide, for example, values ​​of the received radiation integrated in a recorded solid angle range over a spectral range, whereby the values ​​can be represented, for example, as gray values ​​of a gray value scale. Resulting images can therefore be represented as gray value images. However, the gray values ​​can also be represented in a color-coded manner, so that, for example, each color corresponds to an intensity range.

[0003] Sensor design is sometimes subject to technical limitations, meaning sensors don't always meet user requirements. This often applies to high geometric resolution, which, if unavailable, can complicate further data processing; that is, the user may desire or require a higher geometric resolution.

[0004] To eliminate or minimize the resulting limitations, fusion techniques have been developed that combine remote sensing data from different sources to gain a better understanding of spatial and temporal patterns of phenomena and processes. For example, the combination of multispectral and panchromatic sensor data is used in many remote sensing applications to achieve high spectral and geometric resolution. Particularly in geology, land and land-use mapping and / or map updates, agriculture and forestry, the data is used for applications subsumed under the term "change detection," or for monitoring natural disasters.

[0005] In many cases, a key prerequisite for merging data is that they are compatible with each other, so that an optimized dataset can be obtained. By merging remote sensing data with additional data, entirely new information can be generated, requiring specialized methods of data processing, analysis, and interpretation.

[0006] A widely used fusion technique for improving the geometric resolution of remote sensing data is pan-sharpening. This approach fuses geometrically high-resolution panchromatic data with geometrically low-resolution multispectral data to obtain spatially and temporally highly resolved data. Such data are routinely recorded, for example, by existing remote sensing systems.

[0007] Due to the multitude of different terms for "data fusion," there is a need for standardized terminology. Common definitions can be found in the scientific literature. Many of them have in common the classification of the methods into the following levels: i) "measurement level" at the pixel level for processing gray values, ii) "attribute level" based on identified and extracted objects, and iii) "rule-based level" and "decision-based level" based on classified objects in the input data. Pan-sharpening methods are available, which can produce different results depending on the data properties and the respective application. The quality of the fusion results can be assessed visually or quantitatively. Examples are Brovey and YIQ transformations, principal component analysis, weighted fusion, andMethods that result from a combination of different techniques. To make pan-sharpening methods accessible to a broad scientific user community, corresponding methods and techniques have been implemented in conventional image processing systems (e.g., ERDAS / IMAGINE; RSI / ENVI; PCI / Geomatica). In general, however, it can be stated that a number of pan-sharpening methods are based on the following techniques: 1. Color model transformation: - RGB color composites, - Intensity-Hue-Saturation (IHS) transformation, 2. Statistical or arithmetic transformation: - Arithmetic band combination (e.g. Brovey transform, multiplicative model), - Principal Components Transformation, - Wavelet transformation (e.g. ARSIS method); - Regression variable substitution. 3. Combinations of techniques; 4. Pre-information-based (classification-based) methods: - Multi-Sensor Multi-Resolution Technique (MMT): Experimental provision of spatially high-resolution infrared data for the remote sensing of normal temperature phenomena, such as vegetation stress, by using the Multi-Sensor Multi-Resolution Technique for daytime images for the BIRD satellite. 5. Energy balancing-based transformation: EP 1 626 256 B1 6. AI (artificial intelligence)-based methods;

[0008] While the initial focus of improving the geometric resolution of multispectral data was on preparing scenes for visual interpretation, methods based on mathematical and physical principles are increasingly of interest to prepare data for further processing. However, there are technical conditions within satellite remote sensing that cannot be addressed, or can only be addressed satisfactorily, with the developed fusion methods. These include the following cases: Systems equipped with sensor packages in which: - geometrically low-resolution sensors are used to achieve large swath widths (e.g. NOAA / AVHRR), - geometrically low-resolution sensors are used because the sensitivity of the remote sensing sensor is too low, - multi- and hyperspectral sensors that are sensitive to incident radiation in a narrow spectral range (wavelength range), so that the sensor has only a low signal gain at high geometric resolution and a poor signal-to-noise ratio,

[0009] In addition to the sensor-driven aspects mentioned above, signal transmission aspects can play a role in the development of fusion technologies. A key parameter in communications / information technology is the transmission speed or data transmission rate at which a certain amount of data can be transmitted over a transmission channel within a certain time interval. However, if, for example, the amount of data to be transmitted exceeds the capacity of a transmission channel, data congestion can occur. However, if higher geometric, spectral, and radiometric resolutions are desired while simultaneously achieving a large swath width, the data transmission capacity of a transmission channel can quickly reach its technical limits. Therefore, reducing the amount of data to be transmitted appears to be a possible option, especially for transmitting large amounts of data.

[0010] The following explains the terms used: If a signal is sampled at a frequency no greater than twice the signal's maximum frequency (Nyquist criterion), subsequent lossless reconstruction of the signal is not possible. The resulting artifacts are referred to as aliasing. According to the Nyquist-Shannon sampling theorem, a continuous, band-limited signal with a minimum frequency of 0 Hz and a maximum frequency must be sampled at a frequency greater than twice the maximum frequency so that the original signal can be reconstructed from the discrete-time signal without any loss of information.

[0011] Remote sensing sensor: A sensor (also called a detector) is a technical component or system that records certain physical and / or chemical properties, or can qualitatively or quantitatively measure the properties and / or material composition of its environment from a distance. A sensor for recording reflected / emitted radiation is characterized by properties such as geometric, spectral, or radiometric resolution. Sensors for recording reflected / emitted radiation are particularly used for remote sensing.

[0012] Optical / electronic splitter: An optical / electronic splitter is a technical component or system that can split the path of optical radiation. In terms of image acquisition, such a splitter can be used to create two or more images.

[0013] Control unit: A control unit is a technical component or system that can determine and evaluate the status of a remote sensing sensor, convert necessary actions into control commands, and transmit them to control units via a communications unit. In particular, it can also receive commands or signals from the ground station and the satellites or missiles via communications units, evaluate them, convert necessary actions into control commands, and transmit them to control units.

[0014] Control commands are signals or signal sequences transmitted via cable, radio or other transmission channels, with which instructions for action can be transmitted to the sensor systems (e.g. to change the position and orientation of the sensor systems, to switch the sensors on and off).

[0015] A control unit is a technical component or technical system that can receive control commands from control units, evaluate them and convert them into measures for configuring sensor systems.

[0016] A communication unit is a technical component or technical system that implements the exchange of signals and data between control and management units as well as ground stations and satellites or missiles.

[0017] Upscaling / Upsampling: Upscaling is a technique for improving the quality of low-resolution data. Examples of methods include: i) pixel repetition (missing pixels are supplemented with neighboring pixel values, which does not improve image quality), ii) logical pixel completion (missing pixels are calculated using bilinear interpolation, i.e., the pixel values ​​are calculated from the averages of neighboring pixels, resulting in a smoothed and / or blurred dataset.

[0018] Downscaling / Downsampling: Downscaling is a technique for reducing high-resolution data to obtain low-resolution data. Examples include: i) bilinear, ii) bicubic, and iii) Lanczos interpolation.

[0019] The reflectance indicates what percentage or proportion of the luminous flux falling on a surface is reflected. Light surfaces have a high reflectance, while dark surfaces have a low reflectance. The reflectance can depend, in particular, on the frequency of the radiation and the angle of the incident and reflected radiation, meaning it can vary accordingly.

[0020] A process module is a work step (especially as a program part) that cannot be further subdivided and is required to process a work step.

[0021] A processor is a possible combination of process modules to enable or execute more complex processing steps.

[0022] A process environment is a framework into which a processor can / must be integrated in order to exchange information and data with other process environments.

[0023] A process chain is a sequence of parallel process environments designed to create finished information products, optionally automatically. Interactive actions by an operator may still be required.

[0024] Super Resolution: Methods that, for example, use up- and downsampling techniques to derive an initially unknown underlying high-resolution data set(s) from one or more low-resolution data sets and which are possible according to previously defined criteria are summarized under the term Super Resolution.

[0025] Information products are information tools, such as charts, maps, and decision-making and action instructions. Information products are information presented in any numerical and / or graphical format that provides a user with informational value or added value and / or can serve as a decision-making support or basis.

[0026] Shifted: In the following text, the term shifted is used as a synonym for linear and nonlinear geometric transformations between the source sets of remote sensing data. This describes a state in which a first data set can be projected onto at least one second data set (especially through linear or nonlinear geometric transformations).

[0027] As described above for "pan-sharpening algorithms," some fusion methods use color-space-related techniques in which input data with geometrically different resolutions are assigned different colors or transformed into another color space (e.g., IHS). The resolution improvement is achieved by exchanging the intensity components and transforming them back to the original color space. The improved geometric resolution of the multispectral data enables i) better visual interpretation and identification of features as well as higher accuracy in land cover and land use classification. However, these methods alter the histograms of the data sets, which complicates further quantitative processing. Frequently used methods include the IHS technique (Intensity-Hue-Saturation), Principal Components Analysis (PCA), the so-called Brovey transform, and wavelet-based image fusion.The IHS and Brovey transforms are based on the inaccurate assumption that the panchromatic image is a linear combination of the frequency bands of the spectral images. This leads to significant spectral distortion. The PCA method projects correlated channels of the spectral images into a set of uncorrelated principal components using an orthogonal transformation defined such that the first principal component has the largest variance. The gray value difference between the first principal component and the panchromatic image causes significant color distortion. Wavelet fusion also leads to spectral distortion because it directly implements the spatial details of the panchromatic image into the low-resolution spectral images, which exhibit a different gray value distribution.

[0028] A widely used fusion technique is based on principal component decomposition. The principle of this method is that the geometrically low-resolution source image is transformed in such a way that one component (here: the first principal component) largely corresponds to the (possibly similarly transformed) image with the higher spatial resolution, which usually requires an adjustment of the image statistics. Subsequently, the geometrically low-resolution component is replaced by its corresponding geometrically high-resolution one, and the inverse transformation is performed. The disadvantage of this method is the complete substitution of a component, which leads to a change in the spectral characteristics and thus to a loss of information. Furthermore, this purely statistical procedure loses the connection to the physical measured value, which complicates quantitative evaluation.

[0029] To minimize or avoid information loss due to component substitution, some fusion methods transform only the additional spatial frequency information. This is determined through filtering or multi-resolution representation, local correlation models, wavelets, and filters. These methods cause smaller changes in the spectral characteristics than the aforementioned methods, although even in this case, the correlation to the physical measured value is not always guaranteed. Furthermore, some of these methods, especially the ARSIS concept, require adaptation to the sensors used.

[0030] Other fusion methods are based on derived values ​​of the geometrically high-resolution data set as the basis for the fusion, e.g., based on a classification. With these techniques, the spectral information is also altered, albeit only minimally. In contrast, the method proposed in the aforementioned EP 1 626 256 B1 is physically based, in that an energy balance is established between the multispectral and panchromatic data. The basic prerequisites for this are simultaneous recording of the data and spectral overlap of the multispectral data by the panchromatic data. If these prerequisites are not met, the method will not work. In summary, it can be stated that the methods proposed to date are often not physically based and alter the spectral pixel characteristics to a greater or lesser extent.These changes can lead to errors in further quantitative processing. However, the methods mentioned are based on the assumption that high geometric resolution can be achieved in at least one channel / band.

[0031] However, there are cases in which a high geometric resolution is not / cannot yet be technically realized.

[0032] However, low geometric resolution can be caused by the following factors: 1. The sensitivity of remote sensing sensors can be influenced by factors such as platform movement, the spectral sensitivity and size of the sensor, and the quality of the optics. If the sensitivity of a sensor (material properties for detecting the wavelength range) is too low to detect a sufficient useful signal (signal-to-noise ratio; SNR = useful signal power / noise power), it is necessary to scan a larger target area in a pixel over which the signal can be acquired. Therefore, with a low SNR, a large area (coarse geometric resolution) is required that reflects / emits sufficient energy to be received to excite the sensor and record data (useful signals). Furthermore, the energy emitted / reflected by a target may be too low for high geometric resolution. In this case, a large area is required to measure a signal. 2. The selected spectral resolution of a sensor (multi- or hyperspectral sensor) is very high. The energy available in the intended band is low due to the selected spectral resolution. Therefore, high geometric resolution may not be technically feasible. 3. The sensor should cover a desired large swath width. With a high geometric resolution, the number of measuring elements increases. As a result, rapid readout of the image elements is required, so technical limitations may exist here, forcing the choice of a low geometric resolution. 4. Search objects are located in the subpixel range, but influence the data set, but are not resolved. 5. The radiometric resolution of the dataset is too high.

[0033] DE 10 2012 221 667 A1 relates to the processing of remote sensing data, wherein first image data obtained by remote sensing are processed using second digital image data obtained by remote sensing, which are image data with a higher spatial resolution than the first image data. The spatial resolution of the first digital image data is provisionally refined, at least for a sub-area of ​​the common detection area, without using image values ​​from the second digital image data, such that the spatial resolution of the provisionally refined first image data corresponds to the spatial resolution of the second digital image data, and each pixel of the second digital image data corresponds to a pixel of the provisionally refined first digital image data.For a plurality of pixels of the second digital image data, a weight value for the pixel is determined in the sub-area of ​​the common detection area, which weight value corresponds to a weight of an image value of the pixel in the ratio of the image value of the pixel to image values ​​of surrounding pixels in a local environment of the pixel.

[0034] US 2005 / 0 111 754 A1 discloses the acquisition of data for at least two images with different spatial resolutions and the determination of relationships between the images with different spatial resolutions. A relationship between a first of the at least two images with a first spatial resolution and the first of the at least two images with a second spatial resolution that is higher than the first spatial resolution is determined based on the determined relationships between the images with the different spatial resolutions. Pixel values ​​of the first of the at least two images with the second spatial resolution are determined based on pixel values ​​of the first of the at least two images with the first spatial resolution and the determined relationship between the first of the at least two images with the first spatial resolution and the first of the at least two images with the second spatial resolution.

[0035] A technical solution is being sought to improve the geometric resolution of remote sensing data.

[0036] A proposal is made for improving the geometric resolution of remote sensing data. The proposal is based on at least two sets of remote sensing data which cover the same detection area, i.e. the same scene. In other words, an overlap area results which is covered by the majority of the sets of remote sensing data. In particular, each of the sets of remote sensing data is generated or has been generated by an associated remote sensing sensor or an associated group of remote sensing sensors. As will be explained in more detail, under certain circumstances a single physical sensor may be sufficient to generate the various sets of remote sensing data. Each of the sets has a grid which corresponds to its respective geometric resolution. If the remote sensing data of a set were represented as an image, each picture element or “pixel” corresponds to an element of the grid.In other words, each of the sets for the raster elements contains at least one detection value, for example, a value for the electromagnetic radiation received in the area of ​​the raster element. In addition to electromagnetic radiation, other types of radiation, such as particle radiation, are also considered, although in practice this is usually electromagnetic radiation.

[0037] In the aforementioned source sets of remote sensing data, the values ​​assigned to the raster elements can be referred to as detection values ​​because the values ​​are based on a detection of the captured scene. More generally, the values ​​can be referred to as function values, which, as mentioned, are usually values ​​that correspond to the radiation flux density of the electromagnetic radiation detected with the raster element. This does not preclude at least one set of remote sensing data from being further processed before being used to improve the geometric resolution, as described below. Depending on the optics used, the area of ​​a raster element corresponds to a solid angle at which the electromagnetic radiation detected with the raster element is incident. Neighboring raster elements of the same raster therefore have a common boundary. The edges of the raster elements lie at these boundaries.

[0038] The grids of the different sets of remote sensing data are offset from one another, i.e., the boundaries of the grid elements of the different grids do not coincide. This creates a multitude of overlapping sub-areas of the scene captured by the different sets of remote sensing data. These overlapping sub-areas are each defined by the boundaries of the grid elements of the different sets of remote sensing data. Wherever a boundary of the grid elements of one of the different sets of remote sensing data is located, there is also a boundary of overlapping sub-areas. As a rule, opposite boundaries of a specific overlapping sub-area are defined by boundaries of different source sets of remote sensing data. Deviations from this rule can occur, particularly at the edges of the entire overlapping area.Preferably, the raster elements of the different source sets of remote sensing data are of equal size. In other words, the raster constant, the constant distance between consecutive raster element boundaries, is the same for the different rasters.

[0039] The overlapping sub-areas are therefore smaller than the raster elements of the individual sets. It is now proposed to consider the overlapping sub-areas as raster elements of a derived set of remote sensing data, which, due to the smaller size of the overlapping sub-areas, has a higher geometric resolution than the individual (source) sets of remote sensing data. In this case, each of the overlapping sub-areas is assigned a function value that is formed from the function values ​​of the overlapping raster elements of the source sets. In the special case of only two source sets, the formed function value lies between the function values ​​of the source sets in the overlapping sub-area. In general, the formation of the respective function value of the derived set of remote sensing data is based on the idea that it must be consistent with the function values ​​of the source sets.

[0040] In addition, the incident radiant power in the entire overlap area must be the same in the different sets of remote sensing data. Therefore, when the function values ​​of the overlapping sub-areas of the derived set are calculated, the area integral of the function values ​​calculated over the entire overlap area must be equal to the area integrals of the original sets. It should be noted that the dimension of the function values ​​does not necessarily have to be that of a radiant flux density, but can also be, for example, that of a reflectance. More generally, any suitable quantity can be used to express the received radiation.

[0041] In particular, it is proposed: A method for improving a geometric resolution of remote sensing data, - wherein at least two output sets of remote sensing data of a scene are received or present, - wherein each of the output sets comprises function values ​​for associated raster elements of a geometric raster of a detection of the scene, and wherein the function values ​​each correspond to radiation emanating from the scene and incident in the associated raster element, - wherein the geometric grids of the at least two initial sets are offset from one another, so that in an overlapping region of the geometric grids of the at least two initial sets, a plurality of overlapping sub-regions are formed, from which the overlapping region is composed, the boundaries of which are each defined by boundaries of the grid elements of the at least two initial sets and whose geometric size is smaller than the geometric size of the grid elements of the at least two initial sets, - for each of the plurality of overlapping sub-areas, a derived function value is formed, which is formed from the function values ​​of those grid elements of the at least two initial sets whose boundaries define the respective overlapping sub-area, - the derived function values ​​are formed in such a way that the following condition is met: an area integral of the derived function values ​​over the overlap area is for each of the initial sets equal to an area integral of the function values ​​of the grid elements of the initial set and - a derived set of remote sensing data is output, which is defined by the overlap sub-areas and the derived function values.

[0042] The scope of the invention further includes an arrangement for implementing the method. The arrangement comprises, in particular, a forming device configured to form the derived function value for each of the plurality of overlapping sub-regions.

[0043] In particular, it is also proposed how a quantitative and computer-aided evaluation can be carried out following the improvement of the geometric resolution.

[0044] The derived set of remote sensing data can be output in different ways. For example, this set can simply be stored. In this case, the output is sent to a data storage device or a distributed data storage device. Alternatively, or additionally, it can be transmitted to a receiving device, such as a computer or monitor.

[0045] In particular, the function values ​​correspond to radiances (units: W m-2 sr -1 µm -1) or equivalent quantities, in contrast to the gray values ​​usually used. This enables the quality control described in detail elsewhere based on an energy and / or power balance. The measured values ​​of the sensors can of course change over time, so that the resolution improvement process can also be carried out repeatedly over time, for example according to a time cycle. Preferably, the sensors for detecting and recording the various output sets of remote sensing data are repeatedly or permanently intercalibrated. If a single sensor is used, which records the scene by scanning, for example, intercalibration can be omitted. This means in particular that the same recorded radiant energy or radiation from the various sets is obtained in the considered detection area of ​​the scene.Radiated power must be determined in order to be able to carry out an energy or power balance.

[0046] As a rule, the observed area (i.e. the scene, particularly on the Earth's surface) is not a flat surface, which is why radiation can be reflected in different directions. In addition, some of the radiation falling on the measuring sensor may have been reflected between the observed area and the measuring sensor and hit it perpendicular to the line of sight of the measuring sensor. Therefore, as part of the energy / power balance, values ​​(deviations in energy between the sensor bands) can optionally be calculated for at least one additional channel (geometrically in the intended geometric resolution of the result channel) and can therefore be used as a result for energy distribution and reconstruction in the subpixel range of the measurement channels. For example, there are satellites that do not have a multispectral sensor in the blue wavelength range of visible light.On the other hand, the detection of radiation in the blue wavelength range is necessary, for example, for the detection of aerosols. The blue wavelength range can therefore be taken into account, for example, by an additional channel.

[0047] In any case, it is preferred that the function values ​​of the output sets in the associated raster element correspond to incident radiation in the same wavelength range of the radiation.

[0048] Through the above-mentioned condition, which includes the aforementioned surface integral, a physical energy balance is carried out in particular in the sense described below. Alternatively, the physical energy balance can be achieved in another way. The physical energy balance considers the radiant energy, radiant power or an equivalent quantity spatially recorded by the measurement data. In particular, for each pixel of a coarsely resolved pixel matrix, its corresponding radiant energy, radiant power or equivalent quantity can be considered. In the physical energy balance, according to the invention, the energy / power is distributed across subpixels (here: the overlapping sub-regions) to improve resolution, although no change in the energy / power should occur in the region of the respective pixel (here: the respective raster element), i.e.No energy / power should be drawn beyond the boundaries of the pixel (raster element) or drawn into it. Therefore, the energy / power balance should preferably remain constant not only overall for all or several neighboring raster elements, but also for each individual raster element of the coarser-resolution raster matrix. At the very least, this pixel-by-pixel / element-by-element conservation of energy / power is a goal. If the approach is iterative, the radiation distribution can approach this goal with progressive iteration. Physical energy balancing is particularly suitable for quality assessment of the changed radiation distribution.

[0049] Alternatively or additionally, a mathematical energy balance is performed: In the course of mathematical optimization, it is common to minimize a previously defined, problem-specific energy. This energy need not be directly related to a physical quantity and is a measure of the deviation from one or more optimal solutions of the associated problem. If an analytical solution to a problem is not possible or known, energy minimization can be performed using numerical methods, thus finding an approximation to the best possible solution.

[0050] In particular, one embodiment involves carrying out a physical energy balance with the balancing objective of forming the derived function values ​​in such a way that, according to the derived set of remote sensing data, the same radiant energy or radiant power occurs in the geometric regions of the individual raster elements of the geometric rasters of all output data sets as according to the respective output data set. This means that no energy / power is shifted from the respective geometric region of a raster element of the output data sets to adjacent regions. This objective can be approximated by an iterative procedure when forming the derived function values ​​and can thus be met, in particular, in accordance with an accuracy requirement. This means that different solutions for a data set with a finer geometric resolution are calculated iteratively one after the other.Such a super-resolution procedure enables the conservation of radiation energy.

[0051] In other words, there is generally no analytical solution for the distribution of radiant energy across the newly generated overlapping sub-areas, i.e., across the derived grid with smaller grid element sizes. It should be noted at this point that the balancing can be an energy or power balancing. This means that an identical area covered or captured with pixels of low or high geometric resolution yields the same amount of energy or power, provided the same spectral characteristics can be assumed. Furthermore, it is particularly assumed that the source data sets are based on simultaneous capture of the scene, or at least on radiation conditions that are unchanged across the different source data sets.However, due to the fact that the dimension of power is the dimension of energy per time, a power balance also includes an energy balance. This certainly applies to the often justified assumption that the radiated power can generally be considered constant over the acquisition period of a single image of the scene.

[0052] An arrangement for carrying out the method can, in particular, have two system parts. A first part can consist of sensor hardware comprising a first (for example, optical and / or thermal) remote sensing sensor system and a second (for example, optical and / or thermal) remote sensing sensor system. As already mentioned, however, there are also variants in which a single sensor is sufficient to generate the various output data sets. The hardware system can further comprise a computer or a computer arrangement, a storage system, and a transmitter for data transmission. A second part can comprise software that serves to merge the data from the first sensor system and the data from the second sensor system. This data fusion takes place according to the method according to the invention in one of its embodiments.The method can be described as a physically based numerical procedure for improving the geometric resolution of similar remote sensing data from (at least) two sensor systems. In particular, the system serves to automatically obtain physically and / or mathematically based, geometrically higher-resolution remote sensing data, which can optionally be further processed in subsequent quantitative evaluation procedures.

[0053] The output sets of the remote sensing radiation data capture the radiation reflected and / or emitted by the scene and, in particular, have the same geometric and spectral resolution. In particular, the remote sensing data from the output sets can be acquired and recorded simultaneously. However, a slight time offset in the acquisition and / or recording of the different output sets is also possible. It is important that the radiation state of the scene is still comparable.

[0054] The hardware component can comprise the following elements: 1) optics, 2) optical / electronic splitter, and 3) at least two (or more) detectors, 4) memory for storing the data. The software component can comprise the following modules: 1) data preprocessing (e.g., derivation of radiance), 2) mathematical modeling, 3) geometric energy balancing, 4) fusion, and 5) quality control.

[0055] The improved geometric resolution can be achieved by mathematically merging two (or more) geometrically shifted data sets, particularly those with the same geometric and spectral resolution, using image modeling and spatial-geometric power / energy balancing. Specifically, initial data sets shifted relative to each other in the x- and y-directions relative to an xy-coordinate system of the scene can be merged with the result of the improved resolution. A control / quality module can adaptively improve the result if necessary.

[0056] The following are worth highlighting in the solution proposed here: 1. Combination / fusion of output data sets of a specially configured detection system for recording remote sensing data and a coordinated evaluation system with a fully physical-mathematical approach based on a balance of radiances (W m -2 sr -1 µm -1 ), namely a power and / or energy balance, for the geometric improvement of the data sets; 2. Use of geometrically coarse-resolution data without including a) additional, geometrically higher-resolution data (such as pan-sharpening) or b) introduction of at least one virtual channel for spectral energy balancing for missing and / or overlapping areas of spectral channels; 3. The preferably simultaneous acquisition and recording of the data of the output sets, which are spatially shifted from each other in the intended geometric resolution and cover an identical spectral range; 4. The execution of a process step (quality control), e.g. by executing a computer program, to identify at least physical discrepancies in the energy balance and / or power balance; 5. Using quality control to iteratively improve the result.

[0057] In addition to data acquisition, a key aspect of satellite-based remote sensing is the data transmission from the satellite sensor configuration to a receiving station. Specifically for high-resolution remote sensing data, such as hyperspectral data, the X-band or Ka-band are used (in the terminology commonly used in the field). In Ka-band, for example, a data throughput of greater than 70 Gbit / s can be achieved. The acquisition of hyperspectral data requires high transmission rates. For very fast data acquisitions or extremely large data volumes, the carrier frequency (e.g., X-band) may not be able to guarantee the required transmission rate. In the case of hyperspectral remote sensing, the choice of a high geometric resolution and a large swath may exceed the performance limits of a data transmission channel (S-band, X-band, Ka-band). Technical data reduction can then be a solution to the problem.Following this reduction, another data compression technique can then be applied to the data.

[0058] The method according to the invention can be carried out, in particular, by a computer program. In this case, it is a computer-implemented method.

[0059] Furthermore, the scope of the invention includes a device for data processing which has means for carrying out the method, in particular the method in one of the described embodiments.

[0060] The device can, for example, consist of a single computer or a computer network, or can comprise the computer or the computer network. The computer, or at least one of the computers, can, in particular, be an analog computer, a digital computer, and / or a hybrid computer in terms of its mode of operation. In terms of its size and design, it can be a smartphone, a personal digital assistant (PDA), a tablet computer, an embedded system (e.g., embedded in the control computer of a coordinate measuring machine), a single- or multi-board computer, a personal computer (PC), a desktop computer, a workstation computer, a host computer or server integrated into a computer network, a thin client computer, a netbook, a notebook, a laptop, a mainframe computer, or a supercomputer, whereby some of the aforementioned types can also be implemented by a single computer, such as a PC with multiple boards.Furthermore, the computer, or at least one of the computers, may have one or more central processing units (CPUs) and / or one or more processing cores per CPU. Graphics cards or other dedicated cards with processing units that are part of a computer may also represent the means for executing the method, either exclusively or in combination with other computers or processing units.

[0061] Furthermore, it should be pointed out that although the computer or computers are preferably caused to carry out the method by a computer program, the means for carrying out the method can also comprise at least a hardware-implemented, preferably programmable arrangement (for example an arrangement of logic gates), such as an ASIC (Application-Specific Integrated Circuit), a PLD (Programmable Logic Device) or an FPGA (Field Programmable Gate Array).

[0062] Furthermore, the scope of the invention includes a computer program comprising instructions which, when the program is executed by a computer, or by a computer network, cause the computer to carry out the method, in particular to carry out the method in one of the described embodiments.

[0063] A data carrier signal that transmits the computer program and a computer-readable medium are also within the scope of the invention. The computer-readable medium contains instructions that, when executed by a computer, cause the computer or, when executed by a computer network, cause the computer to execute the method, in particular the method in one of the described embodiments.

[0064] The mentioned computer network or one of the mentioned computer networks can be a local area network or a non-local area network, or a combination thereof. In particular, a local area network can be a body area network (BAN), a wireless body area network (WBAN), a personal area network (PAN), a wireless personal area network (WPAN), a local area network (LAN), or a wireless LAN (WLAN). A non-local area network can, in particular, be a metropolitan area network (MAN), a wide area network (WAN), a global area network (GAN), a virtual private network (VPN), or a storage area network (SAN).

[0065] The computer-readable medium may also be referred to as a storage medium and is, for example, a digital medium such as a compact disc (CD), a floppy disk, a digital versatile disc (DVD), a hard disk, a memory card or a mass storage device, or it may also be an analog computer-readable medium such as text (which is, for example, an expression of program code), an image, an arrangement of images or an analog disk-shaped or disc-shaped data carrier.

[0066] Embodiments of the invention will now be described with reference to the accompanying drawings. The individual figures of the drawing show: Fig. 1 an embodiment of an arrangement for carrying out the method according to the invention, Fig. 2 shows an embodiment of a sensor arrangement with two sensors that detect radiation emanating from the same scene, Fig. 3 a perspective view of two grids shown one above the other, indicating which grid with a finer spatial resolution can be formed from them, Fig. 4 a plan view of the Fig. 3, wherein for each raster element of the coarser resolution raster it is indicated which four raster elements of the finer resolution raster can result from it, Fig. 5 schematically shows the creation of a derived raster from the raster elements of three source data sets.

[0067] Fig. Figure 1 shows a carrier platform 1 with a plurality of sensors 2 of the same design and, in particular, of the same series. An intercalibration device 3 for the sensors 2 is connected to the sensors 2, which allows the sensors 2 to be intercalibrated as described above. The carrier platform 1 further comprises a transmitter 4 for data transmission. The sets of remote sensing data generated by the sensors 2 can be transmitted via the transmitter 4 during operation of the arrangement.

[0068] A ground unit 5, which can be considered an intermediate processor, has a receiver 6 for receiving the data transmitted by the transmitter 4. Optionally, the ground unit 5 has a buffer for temporarily storing the received data. For the purposes of the above description of the invention, the data are the output data sets of the various sensors 2.

[0069] A processing unit 7 is connected to the ground unit 5, which comprises the following: a mathematically and physically based optimization module 8; a warping module 9 for geometric co-registration of the data sets from the different sensors 2; a blurring module 10 for implementing a point spread function, which is preferably designed as a Gaussian filter; a downsampling module 11; a quality module 12 for performing a quality or conformity test; and; a decision module 13. Reference numeral 14 designates the product, namely the geometrically high-resolution data set.

[0070] The multisensory support platform 1 carries at least two sensors 2 of the same design, which, depending on the intended geometric resolution, are preferably geometrically shifted relative to one another in the x- and y-direction of the xy-coordinate system of the captured scene by an n-th part of the grid constant of the source data sets. In the case of, for example, three sensors, the grids of the individual data sets are therefore shifted relative to one another by one-third of the grid constant. As an alternative to the at least two sensors, or if a larger number of data sets are to be generated from a number of sensors, the platform carries the means to generate multiple data sets from one sensor. In general, the xy-coordinate systems of the source data sets do not have to lie in the same plane in three-dimensional space, as long as they can be transferred into the xy-coordinate system of the captured scene by means of linear or nonlinear projection.The coordinate systems can therefore also be shifted relative to each other, for example, in a direction perpendicular to the xy coordinate system. In other words, each of these represents an individual xy coordinate system for the respective data set. As mentioned elsewhere, the xy coordinate systems do not have to be shifted exactly by an nth part of the grid constant of the original data sets. The method according to the invention can also be implemented accordingly with a different shift.

[0071] Fig. Figure 2 shows a specific embodiment of a sensor system. Coming from above, the radiation strikes an optical system 21 and is directed by the optical system 21 to an optical splitter 23, which splits the radiation. The radiation therefore strikes two different detector fields 24, 25, which are assigned to the different sensors. The images thus generated by the detector fields 24, 25 are stored in the data memories 26, 27 and are available for transmission. The optical splitter 23 and the detector fields 24, 25 are arranged such that the desired geometric displacement is realized. The embodiment of Fig. Figure 2 is intended to be schematic, and modifications are possible. For example, an electronic splitter can be used instead of the optical splitter 23.

[0072] In order to provide the data required to refine the spatial resolution, one of the following two recording strategies can be used. They are a single-sensor and a multi-sensor configuration. In the single-sensor configuration (preferably a scan array), a single sensor is used to generate the overlapping images. For this to happen, the sensor's recording frequency must be high enough that a point on the planet's surface, for example in the case of a satellite in the direction of flight, is recorded multiple times in the spatially shifted raster elements of the chronologically successive satellite data. By pivoting the sensor or tilting, for example, a mirror or prism, a shift orthogonal to the direction of flight can then be generated.In the case of a multi-sensor configuration, several intercalibrated sensors, preferably of the same design, are shifted relative to each other along their optical recording axes such that the shifted raster elements of the data of a defined point on a planet's surface recorded simultaneously by the sensors record this point offset from each other by an offset. In both cases, the point on a planet's surface recorded in the overlapping raster elements is recorded at a position shifted by an offset.

[0073] Returning to Fig. 1, the data from the various sensors 2 have the same geometric resolution, the same spectral bandwidth and spectral characteristics, and record the same sub-areas with the same radiation intensity. Drones, aircraft, satellites, balloons, or rockets, for example, can serve as a multi-sensor carrier platform 1. The spatially low-resolution output remote sensing data is transmitted on the carrier platform 1 to the transmitter 4, where it is processed so that it can be transmitted between the transmitter 4 and the receiver 6 over the distance to the ground unit 5. In addition, data measured with the intercalibration device 3 of the sensors 2 is recorded so that a sensor-specific spectral / radiometric correction of the data can be made. This data is also transmitted from the transmitter 4 to the receiver 6.

[0074] After receiving the data by the receiver 6, the data can be temporarily stored. The data is sent to the processing unit 7, where the radiances (W m -2 sr -1 µm -1 ) can be calculated.

[0075] The following physical modeling approach assumes that the apparent reflectance of the spectral band of a first sensor and the apparent reflectance of the spectral band of a second sensor are determined according to equation (1): ρ*=πd2⋅LE⋅cos θS

[0076] Where: p* is the apparent reflectance of the first sensor S1 of the i-th channel, d is the Earth-Sun distance (in astronomical units AU), L is the measured radiance (in W m -2 · sr -1 · µm -1 ), E solar irradiance (W m -2 ), θ S solar zenith angle (sr).

[0077] If the gray values ​​for the measured bands are known, the radiance in watts / (m 2. sr. µm). The relationship between the measured radiance L and a gray value of a pixel (DN, Digital Number) is defined by equation 2: L=c0+c1∗DN

[0078] Where DN (Digital Number) is the gray value of a pixel, and c0 and c1 are regression parameters (gain and offset) (in W . m -2 . sr -1 . µm-1). Combining equations (1) and (2), equation (3) determines the apparent reflectance using the gray values ​​of a data set: ρ*=πd2(c0+c1∗DN)⋅LE cos θS

[0079] Analogous to equations (1) and (3), corresponding equations can be formulated for the multi- or hyperspectral pixels (raster elements) of the second band, which overlay the raster elements of the first band. The current distance d between the Sun and Earth can be approximately determined using equation (4): d=1+0.0167 sinπ(Doy−93.5)Loy

[0080] Doy means “Day of Year” and Loy means “Length of Year”, i.e. 365 for non-leap years and 366 for leap years.

[0081] In addition to preprocessing, processing unit 7 includes submodules 8, 9, 10, 11, 12, and 13. Optimization module 8 is used to solve systems of equations for calculating the image energy of the high-resolution image. The prerequisite for establishing a physical energy balance between the spectral pixels (raster elements) of the first band and the spectral raster elements of the second band is the calculation of the integral for the apparent reflectance ρ* of the raster element components of the second band that completely or partially cover the respective raster element of the first band. In the simplest case, the integral can be represented by the mean of the overlapping components.

[0082] This allows for grid arrangements such as those in Fig. 3 or Fig. 4, the relationship between the first data set and the second data set can be established (equation 5), so that for the apparent reflectance ρ* of the raster element of the first band, an average apparent reflectance ρ2*¯ can be calculated for a virtual raster element of the second band: ρ2*¯=1m⋅m∑i=1,j=1m,mρ2(i,j)*

[0083] If the entire data set Band 2 is examined in the same way with a sliding window, then a virtual data set corresponding to Band 1 can be created. Subsequently, the calculated mean apparent reflectance ρ2*¯ of the virtual band 2 is compared with the apparent reflectance ρ* of band 1. Using the mean value, a weighting matrix can then be calculated for the entire band 1. The individual weighting factors for the pixels of the first band can be calculated using equation (6). wi,j=ρ2*(i,j)ρ1*

[0084] Analogously, this step can also be carried out in reverse for band 2 with reference to the partial raster elements of band 1 superimposing the raster elements of band 2, so that a virtual band 1 can be determined for calculating a weighting matrix for the entire band 2.

[0085] As already mentioned, the local energy E l of a grid element over the area in each band is a constant value, which must also be maintained if this area is composed of smaller sub-areas. If the local energy E laccording to the neighborhood analysis by a contribution ΔE l , then a correction factor k l to be calculated according to equation (7): kl(k)=El(k)+ΔEl(k)El(k) for all 1 ≤ k ≤ n+1, which is to be applied to all corresponding local partial contributions E(i,j,k) with 1 ≤ i, j ≤ m in the respective spectral band k according to equation (8). El(i,j,k)=E(i,j,k)kl(k) for all 1 ≤ k ≤ n+1,

[0086] Furthermore, the processing unit 7 has the downsampling module 11 for coarsening the geometrically higher-resolution results obtained from the optimization module 8. The processing results by modules 8, 9, and 10 are transferred to the downsampling module 11. For this purpose, the results are converted back to the geometric output resolution of the input data and made available to the quality module 12 to perform the data quality check with regard to physical consistency. The quality results are then made available to the decision module 13, which decides which dataset will be provided as the output dataset. This allows a further iteration step to be performed if the results of the spatial resolution refinement do not achieve a quality level. If the result is assessed as qualitatively acceptable, the result and thus the "product" is a geometrically high-resolution dataset 14.In decision module 13, the optimized data set, with reduced geometric resolution, is compared against the original data set to determine whether further optimization is necessary or whether the process can be considered complete. Once the process is complete, product 14 is returned as a high-resolution geometric data set.

[0087] Fig. 3 and Fig. 4 each show two spatially shifted grids. In Fig. 3, a first grid is shown above a second grid. The representation of the two grids in one of two superimposed levels merely serves to improve the recognizability of the grids. In practice, the same detection area of ​​a scene is recorded with the corresponding output data sets. Four grid elements of each of the two grids are shown as square areas. These four grid elements of the second grid shown below are in Fig. 3 labeled G1, G2, G3, G4. From the left rear in Fig. The raster element H1 of the first raster shown in Figure 3 represents a perpendicular projection onto the plane of the second raster. The projection surface, like the projected raster element, is square. Due to the spatial displacement (in the two directions x, y of a two-dimensional, Cartesian coordinate system extending in the respective raster plane, such as the xy coordinate system shown for the plane of the first, upper raster) of the first raster relative to the second raster, the projection surface lies with its center point at the common boundary point of the four raster elements shown in the second raster. This results in four equally sized squares in the projection surface as overlapping sub-areas, the boundaries of which are each defined by the boundaries of the raster elements of the rasters of the two original sets.Each of the grid elements G1, G2, G3, and G4 of the second grid forms two of the perpendicular boundaries of the square overlapping sub-areas. The other two boundaries of the square overlapping sub-areas are defined by the boundaries of the projected grid element of the first grid. In other words, each of the overlapping sub-areas has four boundaries, namely the four edges of the square.

[0088] Fig. 4 shows the first grid and the second grid from Fig. 3 in plan view, ie in the representation of the Fig. 3 from the top. The grid elements of the second grid are again labeled G1, G2, G3, G4. Furthermore, the grid elements described above with reference to Fig. 3, which corresponds to the grid element H1 of the first grid. It consists of the four square overlapping areas T G1,3 , T G2,4 , T G3,2 , T G4,1 together.

[0089] Outside of the grid element G1, it is indicated that the complete projection of the two grids onto each other results in overlapping areas not only for the one projected grid element H1, but for all grid elements of both grids. For the grid element G1, this results in the area shown in the top right corner. Fig. 4 shown division into four overlapping sub-areas T G1,0 , T G1,2 , T G1,4 , T G1,3 . It should be noted that the overlapping sub-area T G1,3 is the same overlapping area that was already mentioned. It is located in the representation of the Fig. 4 bottom right in the grid element G1.

[0090] The function value, for example, of the overlap sub-area T G1,3 can be formed taking into account the function values ​​of the grid elements H1 of the first grid and G1 of the second grid, since the overlapping sub-area T G1,3lies within these two grid elements. For example, if the function value of grid element H1 is higher than the function value of grid element G1, the function value of the overlapping sub-area T G1,3 in the area in between. Furthermore, it can already be stated that the sum of the function values ​​of the other overlapping sub-areas located within grid element H1 must increase relative to the function value of grid element H1 in order to maintain the energy balance of grid element H1. Conversely, for the other overlapping sub-areas located within grid element G1, their sum of the function values ​​must decrease relative to the function value of grid element G1 in order to maintain the energy balance of grid element G1. This energy balance maintenance should, in any case, be ensured as a priority.

[0091] As already mentioned, the invention is not limited to just two source data sets. An example of how a derived locally refined grid is formed from the grids of three source data sets is shown schematically in Fig. 5. This Fig. Figure 5 shows only one raster element F1, G1, and H1 from each of the three source data sets. Raster element F1 belongs to the first source data set, raster element G1 to the second source data set, and raster element H1 to the third source data set. It can be seen that the raster elements F1, G1, and H1 of the various source data sets are spatially shifted relative to one another, preferably by one-third of the raster constant, as shown. The raster constant results from the size of the raster elements F1, G1, and H1 and is the same for the three source data sets.

[0092] Already from the representation of only one grid element F1, G1, H1 for each of the source data sets in Fig. 5 shows that the boundaries or edges of the raster elements F1, G1, H1 form overlapping sub-areas U1, U2, U3. For example, the overlapping sub-area U2 lies within the boundaries of all three raster elements F1, G1, H1. Although the overlapping sub-areas U1, U3 only lie within the boundaries of one of the three raster elements F1, G1, H1 shown, namely within the boundaries of the raster element G1, the boundaries of the overlapping sub-areas U1, U3 are already clearly recognizable. If the other raster elements of the three original data sets were considered, a regular, refined raster of the overlapping sub-areas would result, which are all square and the size of the Fig. 5 shown overlapping sub-areas U1, U2, U3.

[0093] The following section discusses the modeling of the relationship between source data sets of different geometric resolution. The following function Ak(F):=D(B(Wk(F))) describes the derivation of a k-th low-resolution data set from an underlying high-resolution data set F. The individual geometric transformation to project a data set onto a specified reference plane is described by the function W k The function B models the blurring of the data, which may result from, for example, the design of the optical system or movements. A common choice for B is, for example, convolution of the data with a Gaussian filter. The function D describes a downsampling of the high-resolution data. A low-resolution data set f̃ k results from a high-resolution data set F corresponding to f˜k:=Ak(F)+nk, where n kthe noise of the recording process is modeled.

[0094] The basic idea of ​​the algorithm is to determine a high-resolution data set whose corresponding low-resolution data sets ƒ̃ are the best possible approximation to the data sets ƒ k (given low-resolution data sets), while at the same time ensuring the unique solvability of the problem by means of a smoothness condition for the high-resolution data set F. The desired high-resolution data set F is determined using an iterative algorithm. At the beginning, an arbitrary initialization of the high-resolution data set F is carried out. In each iteration, the k corresponding low-resolution data sets ƒ̃ are then calculated from the currently available high-resolution data set F. k The high-resolution data set F is then calculated based on the deviations between the data sets ƒ̃ k and ƒ̃ kand the discontinuity of the current high-resolution data set F. With each iteration, a continuous minimization of the two points mentioned (deviations and discontinuity) takes place. This ensures that the best possible solution F is found. This also applies to a high-quality approximation to the principle of energy conservation, which is achieved by balancing the ƒ̃ k and ƒ̃ k is ensured.

Claims

[1] Method for improving a geometric resolution of remote sensing data, - wherein at least two output sets of remote sensing data of a scene are received or present, - wherein each of the output sets comprises function values ​​for associated raster elements (G1, G2, G3, G4, H1) of a geometric raster of a detection of the scene, and wherein the function values ​​each correspond to radiation emanating from the scene and incident in the associated raster element (G1, G2, G3, G4, H1), - wherein the geometric grids of the at least two output sets are offset from one another, so that in an overlapping region of the geometric grids of the at least two output sets, a plurality of overlapping sub-regions (U1, U2, U3) are formed, from which the overlapping region is composed, the boundaries of which are each defined by boundaries of the grid elements (G1, G2, G3, G4, H1) of the at least two output sets and whose geometric size is smaller than the geometric size of the grid elements (G1, G2, G3, G4, H1) of the at least two output sets, - for each of the plurality of overlapping sub-areas, a derived function value is formed, which is formed from the function values ​​of those grid elements (G1, G2, G3, G4, H1) of the at least two output sets whose boundaries define the respective overlapping sub-area (U1, U2, U3), - the derived function values ​​are formed in such a way that the following condition is met: an area integral of the derived function values ​​over the overlap area is for each of the initial sets equal to an area integral of the function values ​​of the grid elements (G1, G2, G3, G4, H1) of the initial set and - a derived set of remote sensing data is output, which is defined by the overlap sub-areas and the derived function values. [2] Method according to claim 1, wherein the condition mentioned in claim 1 is met by an iterative procedure in the formation of the derived function values ​​for the overlapping sub-areas (U1, U2, U3). [3] Method according to claim 1 or 2, wherein a physical energy balance is carried out with the balancing objective of forming the derived function values ​​in such a way that, in accordance with the derived set of remote sensing data, in the geometric areas of the individual grid elements (G1, G2, G3, G4, H1) of the geometric grids, the same radiation energy or radiation power has been encountered by all of the at least two initial sets as in accordance with the respective initial set, wherein the balancing objective is approximated by an iterative procedure in the formation of the derived function values. [4] Method according to one of claims 1 to 3, wherein the function values ​​of the output sets in the associated raster element correspond to incident radiation in the same wavelength range of the radiation. [5] A computer program comprising instructions which, when executed by a computer or by a computer network, cause the computer to carry out the method according to any one of claims 1 to 4. [6] Arrangement for carrying out the method for improving a geometric resolution of remote sensing data according to one of claims 1 to 4, - wherein the arrangement is designed to receive or process at least two output sets of remote sensing data of a scene, - wherein each of the output sets comprises function values ​​for associated raster elements (G1, G2, G3, G4, H1) of a geometric raster of a detection of the scene, and wherein the function values ​​each correspond to radiation emanating from the scene and incident in the associated raster element (G1, G2, G3, G4, H1), - wherein the geometric grids of the at least two output sets are offset from one another, so that in an overlapping region of the geometric grids of the at least two output sets, a plurality of overlapping sub-regions (U1, U2, U3) are formed, from which the overlapping region is composed, the boundaries of which are each defined by boundaries of the grid elements (G1, G2, G3, G4, H1) of the at least two output sets and whose geometric size is smaller than the geometric size of the grid elements (G1, G2, G3, G4, H1) of the at least two output sets, - wherein the arrangement comprises a forming device which is designed to form a derived function value for each of the plurality of overlapping sub-areas (U1, U2, U3), which derived function value is formed from the function values ​​of those raster elements (G1, G2, G3, G4, H1) of the at least two output sets whose boundaries define the respective overlapping sub-area (U1, U2, U3), - the educational institution is designed to form the derived function values ​​in such a way that the following condition is met: an area integral of the derived function values ​​over the overlap area is for each of the initial sets equal to an area integral of the function values ​​of the grid elements (G1, G2, G3, G4, H1) of the initial set and - wherein the arrangement is designed to output a derived set of remote sensing data which is defined by the overlap sub-areas (U1, U2, U3) and the derived function values.

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