Method and device for frame radiometric correction

Abstract

Systems, methods and devices for correcting frame radiometric inconsistencies are provided. More specifically, a system for correcting frame radiometric inconsistencies is provided, the system comprising a control module configured to obtain a plurality of partially overlapping frames; determine radiometric inconsistencies between the plurality of partially overlapping frames; determine, based at least in part on the radiometric inconsistencies, one or more correction surfaces; and correct, based on the one or more correction surfaces, the plurality of partially overlapping frames to obtain corrected frames. The control module may be further configured to form an image or video of arbitrary length and / or width based on the corrected frames. The control module may be further configured to capture, by an imaging system, the plurality of partially overlapping frames. Also a computer-implemented method correcting radiometric inconsistencies is provided.

Description

METHOD AND DEVICE FOR FRAME RADIOMETRIC CORRECTIONCROSS REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to EP Patent Application No. 23197243.1, filed on September 13, 2023, and entitled “METHOD AND DEVICE FOR FRAME RADIOMETRIC CORRECTION”, the entire contents of which are incorporated herein in its entirety by reference.TECHNICAL FIELD

[0002] Tire present disclosure relates generally to methods and devices for image radiometric correction. More particularly, the present disclosure is related to methods and devices for reducing or minimizing radiometric errors or anomalous inconsistencies between frames.BACKGROUND

[0003] With the intention of gathering information about the surface of the Earth, remote sensing technologies are used on board aerial or space platforms such as planes, drones or satellites, generally including imaging sensors, such as optical sensors, to capture images for Earth Observation. Several optical systems and devices are used to collect images, such as frame / area-sensor cameras which capture an entire frame at a single instant in time, pushbroom cameras which capture one line of image data over a time range and build a two-dimensional image through tire aerial or space platform motion, or the combination of both which are push-frame cameras which capture a predetermined number of lines (multiple lines) in what is called a framelet and build a complete two-dimensional image through motion of the aerial or space platform. In general, the process of capturing images using push-frame cameras involves capturing consecutive or successive satellite or aerial frames and stitching them together to compose final products. Even though the methods for capturing frames in push-frame cameras are advantageous given that it is possible to form images of arbitrary length, in these final products, stitch lines may become apparent due to radiometric inconsistencies between successively / consecutively- captured frames. These inconsistencies can arise from a combination of several sources that may include, but not exclusively, sub-optimal or drifting calibration, or stray light taking unintended paths through the optical imaging system. Some of these inconsistencies can vary per sequence of captured frames, or from frame to frame, since they can have contributions that come from scene content. It would therefore be desirable to form images of arbitrary length, captured by aerial or space imaging systems, with none or minimal radiometric inconsistencies between successively / consecutively -captured frames.SUMMARY

[0004] Considerable advantages can be realized using the methods, apparatuses and systems described herein to correct images in such a way as to eliminate or reduce radiometric errors or inconsistencies of an image formed of arbitrary length using partially overlapping captured frames, which may have been captured consecutively or successively. The radiometric errors or inconsistencies present on the images are generallyreferred to as color cast or color cast effect. In remote sensing applications, image stitching of partially overlapping frames from aerial or space imagery is usually done with instruments that are precisely calibrated geometrically, to avoid distortions or aberrations, and radiometrically, to calibrate non uniform responses and vignetting maps. This precise calibration largely simplifies the frame stitching problem as the scams between different frames are barely visible, hence the effective problem is often reduced to finding a global calibration curve. Moreover, for large swath satellites the frame stitching is frequently dismissed as it only affects a small portion of the field of view. However, for small satellites which generally have narrow swaths and whose instruments may have suboptimally performing components, some spatially varying radiometric distortions can remain. In addition to that, for small satellites the frame stitching intervals are shorter and the color (spectral) bands are also captured at different frames, therefore any imprecision in the radiometric calibration can result in annoying repetitive color artifacts sometimes with a stride proportional to the burst overlap. In order to address the correction of these radiometric artifacts, errors or inconsistencies present on images formed by frames captured from aerial or space platforms such as drones, aircrafts or satellites, embodiments provide methods, systems and devices for image radiometric correction which rely on a combination between image processing tools and payload response modelizations, instead of either blind statistical blending, or a precise calibration of the imaging system. This is advantageous since the imaging system calibration is not constant during the life of the system and therefore, even a perfectly calibrated imaging system might eventually develop artifacts. However, the solution described in the embodiments of the present disclosure would automatically compensate for this change. In addition, it allows it to keep producing good products in different sensor-focal plane-telescope configurations, reducing calibrations to its minimal expression and allowing small satellites to be more versatile and explore new capturing maneuvers.

[0005] In a non-limiting example, the correction of radiometric inconsistencies with the methods, systems and devices described herein may be used for minimizing the radiometric inconsistencies of push-frames captured along an area on the ground. An advantage of the embodiments described herein is that it is possible to form images of arbitrary length using a method that is scalable to sequences of arbitrary-length of push-frames reducing or eliminating the radiometric inconsistencies of the formed image. Furthermore, it is possible to form images correcting radiometric inconsistencies using all the frames without being constrained to using a reference image or frame. On the contrary, most of the available methods known in the art for color harmonization or radiometric correction have the drawback of only considering pairs of images or frames and correcting to match to a reference image or frame. In embodiments described herein, parametric models are generated to modify frames by the resulting correction surfaces, generally calculated using frame sub-sets or batches, rather than matching to a particular frame. Another common drawback of available known methods is error propagation as a consequence of the pairwise sequential algorithmics. Tire embodiments described herein provide alternative systems, methods and devices that allow processing batches of frames with data-fitting terms that bound error propagation buildup.

[0006] Furthermore, the systems, methods and devices described herein are suitable for small aerial or space platforms, such as small satellites, which generally have limited resources since for example, larger satellites like Sentinel-2 do not face this problem. Their calibration is nearly flawless, stable, and the large swath size reduces the issue of small radiometric inconsistencies at boundaries (or borders or scams) between different frames. For recent small or nanosatellites capturing push-frame exposures, the boundaries between partially overlapping frames (which may be consecutive) represent a much larger area of the final product, and radiometric inconsistencies represent a real problem. This is also magnified by the challenges of having up-to- date calibrations on a large constellation formed by numerous small or nanosatellites, even rendering some products as undeliverable unless corrected. Another advantage of the embodiments described herein is that it is assumed that the frame capture may be performed with an imperfect imaging system, hence a model is first developed, and the resulting artifacts may be subsequently corrected.

[0007] Another advantage of the embodiments described herein is that it is possible to form images of arbitrary width using sequences of partially overlapping adjacent frames with reduced or no color cast effect. The adjacency of the frames is to be interpreted as the content of the frames (e g. scenes, objects, features) being next to each other spatially, so that the overlapping regions between frames are located along at least one edge of the frames and have a partial degree of overlap from the edge of the frame in a manner in which part or all the content in the overlapping region is present in both adjacent frames. Preferably, the content of the adjacent frames is similar, for example not too far apart in time, similar time of the day, and so forth, in order to be able to correct the radiometric inconsistencies and, optionally, stitch together the partially overlapping adjacent frames to form an image of arbitrary width. In a non-limiting example, the correction of radiometric inconsistencies with the methods, systems and devices described herein may be used for minimizing the radiometric inconsistencies of images formed from partially overlapping push-frames combining, merging or connecting stripes captured from passes at different orbits either by one satellite or by more than one satellite belonging to a constellation of satellites. In this manner, the method, system or device allows to increase the sw ath by forming images by combining, merging or connecting partially overlapping stripes from several passes providing radiometric consistency to the formed image. A stripe refers to the projection of the satellite's orbit on the ground (e.g. surface of the Earth), which may be a band or area along the surface of the Earth, considering the instrument’s swath. The instrument may be any payload, for example an imaging sensor, and the sw ath may be the field of view (FoV) of the imaging sensor on board the satellite, looking at nadir.

[0008] In another non-limiting example, the methods, systems and devices described herein may be used for correction of radiometric inconsistencies in multispectral or hyperspectral images. For example, partially overlapping (consecutive or not) frames may be captured by an imaging system comprising an area imaging device having a plurality of pixel sensors and an optical filter including one or more spectral bands placed within an optical path of the area imaging device. Firstly, overlapping regions for the one or more spectral bands of partially overlapping frames are determined, then radiometric inconsistencies affecting the captured framesare modeled using correction surfaces, and finally the frames are corrected based at least in part on the correction surfaces determined based on the frames and the overlapping regions. The advantage of modeling radiometric inconsistencies as described throughout the Detailed Description, based at least in part on determining overlapping regions between spectral bands, is that it is possible to correct radiometric inconsistencies, not only in multispectral images but also in hyperspectral images, since it is possible to model radiometric inconsistencies originated from elements of the imaging system that may be used in multispectral and / or hyperspectral imaging systems, taking into account, for example, the performance of the sensor (e.g. area imaging device), or the performance of optical elements such as a telescope or a lens.

[0009] Embodiments include systems, devices, and methods to characterize the intensity differences along the overlapping regions of partially overlapping frames (consecutive or not), which is what is minimized by other methods also disclosed within the Detailed Description. These provide a specialized metric for radiometric inconsistencies in a push-frame system in which exposures are acquired within a short time range, providing a quantification map and overall value for the inconsistencies. This is useful, for instance, for real-time correction of radiometric inconsistencies. For example, a satellite may capture push-frames and, at predetermined time intervals or continuously, the satellite may determine intensity differences along overlapping regions of partially overlapping push-frames (captured consecutively or not). A radiometric inconsistency parameter may be calculated based at least in part on the intensity differences, so that if the parameter is above, equal or below a predetennined threshold, the satellite may determine a set of instructions including, but not limited to. adjust the correction of radiometric inconsistencies, adjust the push-frame acquisition, or instruct other satellite(s) of the constellation to capture frames over the same geographical region. In some instances, the satellite may capture stripes and divide the stripes in tiles in order to determine the intensity differences along overlapping regions of partially overlapping push-frames.

[0010] The examples above show a non-Iimited list of applications that the methods, systems and devices described herein can have. It should be understood that examples in which said applications are combined in any way are also envisaged by the present disclosure. Moreover, additional applications are also envisaged within the scope of the present disclosure.

[0011] Tire present disclosure provides a system for correcting frame radiometric inconsistencies, the system comprising a control module configured to obtain a plurality of partially overlapping frames; determine radiometric inconsistencies between the plurality of partially overlapping frames: detennine, based at least in part on the radiometric inconsistencies, one or more correction surfaces: and correct, based on the one or more correction surfaces, the plurality of partially overlapping frames to obtain corrected frames.

[0012] According to some embodiments of the present disclosure, the control module is configured to determine one or more correction surfaces by determining a set of equations representing at least one radiometric inconsistency present within at least one frame of the plurality of partially overlapping frames; wherein the set of equations include one or more parameters and is determined based on at least one of theintensity values of pixels within a frame, the intensity values of spatially overlapping pixels of partially overlapping frames, and the geolocation or coregistered coordinates of objects, features, or frames.

[0013] According to some embodiments of the present disclosure, the control module is further configured to determine one or more correction surfaces based on at least one of intensity pixel values of samples of a same object, geographical area, or feature on the surface of Earth present in the plurality of partially overlapping frames, characteristics of dominant underlying physical phenomena causing the radiometric inconsistencies, spectral bands present in the plurality of partially overlapping frames, or a pixel coordinate system.

[0014] According to some embodiments of the present disclosure, the control module is configured to determine the one or more correction surfaces by determining one or more spatially overlapping pixels between at least two partially overlapping frames; determining an intensity value and pixel coordinates of tire one or more spatially overlapping pixels; solving, based on the intensity value and the pixel coordinates, the set of equations to obtain one or more parameter's values; and determining, based on the one or more parameter's values, the one or more correction surfaces.

[0015] According to some embodiments of the present disclosure, the control module is further configured to divide the plurality of partially overlapping frames into one or more batches.

[0016] According to some embodiments of the present disclosure, the control module is configured to use frames from the plurality of partially overlapping frames from different batches as look-ahead or look-behind frames.

[0017] According to some embodiments of the present disclosure, the control module is further configured to determine, based at least in part on a variability of the radiometric inconsistencies, one correction surface for the plurality of partially overlapping frames or for the plurality of partially overlapping frames within a batch, or one correction surface for each frame of the plurality of partially overlapping frames or for each frame of the plurality of partially overlapping frames within a batch.

[0018] According to some embodiments of the present disclosure, the set of equations comprises one or more correction terms and one or more fitting or regularization terms, and the one or more parameter values are determined by solving the set of equations.

[0019] According to some embodiments of the present disclosure, the control module is configured to determine the one or more correction surfaces based on an additive correction surface model or a multiplicative correction surface model.

[0020] According to some embodiments of the present disclosure, to correct the plurality of partially overlapping frames, the control module is configured to subtract or divide intensity pixel values of the one or more correction surfaces from intensity pixel values of each one of the plurality of partially overlapping frames.

[0021] According to some embodiments of the present disclosure, the control module is further configured to combine, throughout some or all of the plurality of partially overlapping frames, pixel intensity values of one or more groups or clusters of adjacent pixels into a single pixel intensity value.

[0022] According to some embodiments of the present disclosure, the control module is further configured to discard unreliable information contained in spatially overlapping pixels by masking some or all the spatially overlapping pixels.

[0023] According to some embodiments of the present disclosure, the control module is further configured to apply a dithering technique to make less perceivable quantization artifacts or distortions in the corrected frames.

[0024] According to some embodiments of the present disclosure, the system further comprises a spectral filter comprising a plurality of spectral bands, and wherein the control module is configured to determine at least one correction surface for each spectral band.

[0025] According to some embodiments of the present disclosure, tire system further comprises an imaging module configured to form an image or a video of arbitrary’ length or width, by stitching together the corrected frames.

[0026] According to some embodiments of the present disclosure, the system further comprises an imaging system; and wherein the control module is further configured to control the imaging system to capture the plurality of partially overlapping frames.

[0027] According to embodiments, the imaging system is all or partially on board a manned or unmanned aerial or space vehicle.

[0028] The present disclosure provides a computer-implemented method for correcting frame radiometric inconsistencies, the method comprising, for at least two partially overlapping frames, determining, based on the at least two partially overlapping frames, one or more correction surfaces; and correcting, based on the one or more correction surfaces, the at least two partially overlapping frames to obtain at least two corrected partially overlapping frames.

[0029] According to some embodiments of the present disclosure, the method further comprises, determining whether determined radiometric inconsistencies between the at least two partially overlapping frames vary, frame by frame or within a frame, above a variation threshold; determining a correction surface from the one or more correction surfaces for each frame if it is determined that the radiometric inconsistencies vary, frame by frame or within a frame, above the variation threshold; and determining a correction surface from the one or more correction surfaces for all frames of the at least two partially overlapping frames if it is determined that the radiometric inconsistencies do not vary, frame by frame or within a frame, above the variation threshold. In some embodiments, the variation threshold corresponds to a first threshold for a variation frame by frame, and a second threshold for variations within a frame, wherein the first threshold and the second threshold may be the similar or may be different. Similar should be interpreted as differing within a certain range.

[0030] According to some embodiments of the present disclosure, correcting the at least two partially overlapping frames comprises subtracting or dividing intensity pixel values of the one or more correction surfaces from intensity pixel values of each one of the at least two partially overlapping frames.

[0031] According to some embodiments of the present disclosure, determining the one or more correction surfaces comprises, for the at least two partially overlapping frames, determining one or more spatially overlapping pixels between the at least two partially overlapping frames; determining an intensity value and pixel coordinates of the one or more overlapping pixels; solving, based on the intensity value and pixel coordinates of the one or more overlapping pixels, a set of equations to obtain one or more parameter values; and obtaining, based on the one or more parameter values, the one or more correction surfaces.

[0032] According to some embodiments of the present disclosure, the set of equations comprises one or more correction terms and one or more fitting or regularization terms.

[0033] According to some embodiments of the present disclosure, the set of equations is a linear system and the one or more correction surfaces comprises an additive correction surface model or a multiplicative correction surface model.

[0034] According to some embodiments of the present disclosure, the method further comprises modeling the one or more correction surfaces as two-dimensional polynomials of arbitrary order, wherein the polynomial order is selected based on characteristics of the underlying physical phenomena causing the radiometric inconsistencies.

[0035] According to some embodiments of the present disclosure, the at least two partially overlapping frames are part of a batch of a plurality of batches, wherein a plurality of partially overlapping frames are divided into the plurality of batches.

[0036] According to some embodiments of the present disclosure, at least one partially overlapping frame from the plurality of partially overlapping frames from different batches is used as a look-ahead frame or a look- behind frame.

[0037] According to some embodiments of the present disclosure, the method further comprises forming an image or video of arbitrary width or length by stitching together the at least two corrected partially overlapping frames.

[0038] The present disclosure provides a computer-implemented method for measuring frame radiometric inconsistencies, the method comprising determining an overlapping region between at least two partially overlapping frames; calculating a difference between intensity pixel values within the overlapping region of the at least two partially overlapping frames; normalizing the difference to obtain a normalized difference; and filtering the normalized difference to obtain a difference map.

[0039] According to some embodiments of the present disclosure, the at least two partially overlapping frames are part of a tile of an aerial or satellite image, and the steps are repeated for some or all the partially overlapping frames contained within the tile of the aerial or satellite image; and optionally for all the tiles of the aerial or satellite image.

[0040] According to some embodiments of the present disclosure, one or more statistical values based on the difference map are computed for some or all the tiles of the aerial or satellite image.

[0041] According to some embodiments of the present disclosure, the pixel intensity values of a group or cluster of adjacent pixels of the partially overlapping frames are combined into a single pixel intensity value.

[0042] Further features and advantages, as well as the structure and operation of various embodiments are described in detail below, with reference to the accompanying drawings. It is noted that the invention is not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Additional embodiments will be apparent to persons skilled in the relevant art(s), based on the teachings contained herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Tire Detailed Description is set forth with reference to the accompanying figures. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Tire use of the same reference numbers in different figures indicates similar or identical items.

[0044] FIG. 1 shows a block diagram of an example system according to embodiments of present disclosure usable to correct radiometric inconsistencies from aerial or space imagery.

[0045] FIG. 2 shows an example of an image formed with color cast artifacts due to radiometric inconsistencies in partially overlapping frames captured by a satellite.

[0046] FIG. 3 is a flow diagram showing an example overview process according to embodiments of present disclosure, for correcting radiometric inconsistencies on a plurality of frames.

[0047] FIG. 4 is a flow diagram showing an example ovendew process according to embodiments of present disclosure, for measuring the color cast effect on frames.

[0048] FIG. 5 illustrates an example of a stripe captured by a satellite divided in tiles, according to embodiments of present disclosure.

[0049] FIG. 6 illustrates an example of portions of stripes separated per spectral band, according to embodiments of present disclosure.

[0050] FIG. 7 illustrates an example of color cast metrics for tiles for different spectral bands, according to embodiments of present disclosure.DETAILED DESCRIPTION OF EMBODIMENTS

[0051] The processes, systems, and devices described herein may be implemented in a number of ways. Example implementations are provided below with reference to the following figures to aid in illustration, although those examples are not meant to be taken in a limiting sense.

[0052] Embodiments include systems, methods and devices for correcting or reducing radiometric inconsistencies or radiometric errors in images or videos so that the intensity of an object or point on the surface of the Earth captured on one frame has a similar intensity in one or more partially overlapping frames, which may have been captured consecutively or not. providing radiometric consistency throughout the frames while allowing to maintain the fidelity of the original radiometry of the captured frames. The correction is mainlybased on modeling radiometric inconsistencies as corrections surfaces as having been added or multiplied to ideal unaffected frames to result in the observed affected ones (captured frames). These correction surfaces may be determined or modeled from a sequence of exposures or frames (exposures and frames are terms used interchangeably throughout the Detailed Description), which may be subtracted from the exposures to yield the corrected exposures (or alternatively dividing instead of subtracting if the model used is multiplicative instead of additive). The sequence of exposures or frames may be obtained from a database, for example a database including images captured by a satellite as stripes which, in some instances, may be divided in tiles, may be received by an aerial or space vehicle, or may be captured by an imaging system. The imaging system may be all or partially on the ground or on board an aerial or space platform or system. The sequence of exposures or frames may be captured by the same imaging device of an imaging system, for example a camera on board a satellite, or by different imaging devices, for example different cameras on board different satellites of a constellation. Embodiments may also include fonning an image or video of arbitrary length and / or width by stitching together the corrected exposures in order to obtain an image or video of arbitrary length and / or width which is radiometrically consistent.

[0053] There are different effects that generate radiometric inconsistencies, and the correction surfaces may be determined based on tire underlying phenomena generating the radiometric inconsistencies. In some circumstances, tire radiometric inconsistencies may be originated from unwanted or undesired light captured by the imaging system, such as stray light, which may be due to unintended paths taken by the light passing through the optical elements of the imaging system, or due to light from a light source other than the intended source, for example light from a star or a celestial body other that the light reflected from the Earth. This type of phenomena usually adds more light to the pixel that the original value, for example the original value may be the light reflected from an object on the surface of the Earth onto the active surface of the sensor and the added light may be the light also reflected from the object but taking undesired paths inside the imaging system and adding unintended light onto the active surface of the sensor. A correction surface to correct radiometric inconsistencies originating from stray light may be modeled as an additive correction surface. In other circumstances, the radiometric inconsistencies may have originated from causes other than stray light, for example from characteristics of the imaging system, such as vignetting, which is a reduction of an image's brightness or saturation toward the periphery compared to the image center. A correction surface to correct radiometric inconsistencies originating from vignetting may be modeled as a multiplicative correction surface taking into account the areas of the sensor affected by the vignetting effect, as explained elsewhere in the Detailed Description.

[0054] The radiometric inconsistencies may be modeled as correction surfaces based, at least in part, on intensity values of spatially overlapping pixels between spatially partially overlapping frames (consecutive or not). For example, an additive correction surface may be determined for a first (aerial or satellite) exposure, based on the intensity values of tire pixels of the first exposure and based on at least one of an overlappingregion determined between the first exposure and a second (aerial or satellite) exposure, the second exposure taken or captured consecutively after the first exposure or at a later time under similar conditions (e.g. time, season, light), such that the intensity value of the pixels within the overlapping region of the second exposure arc increased with respect to the intensity value of the pixels within the overlapping region of the first exposure generating, for example, a color cast effect. The overlapping region may be determined as a portion of the exposures including the same geographical area, objects or features on the surface of the Earth in both first and second exposures, in order to achieve spatial overlap. A spatially overlapping pixel / frame is to be interpreted as the same content of a pixel / frame (e g. at least one scene, object, or feature) having the same (within a tolerance error) geolocation or coregistered pixel / frame coordinate in another pixel / frame. Two partially overlapping frames are to be interpreted as having one or more spatially overlapping pixels between the two frames.

[0055] When the same geographical area, object, or feature on the surface of the Earth in partially overlapping aerial or satellite exposures is captured at more than one spectral band, a correction surface may be determined for each spectral band, based on the intensity values of pixels from overlapping regions for each spectral band. For example, for additive radiometric inconsistencies, the color cast effect of each spectral band may be modeled as a correction surface which represents a two dimensional region on the image having pixels’ intensity values that are added to the corresponding pixels’ intensity values without color cast effect. Corresponding pixels between partially overlapping frames refer to the pixels within the overlapping region, in other words, to the pixels that in both frames include the same object, geographical area, or feature, on the surface of the Earth. These pixels may be determined using coregistered frames and / or orthorectified frames. A spectral band may be arranged as 1) a discrete filter band, in which the filter band allows the transmission of a wavelength range generally defined by a central wavelength, 2) a plurality of continuously variable filter bands, in which a transmitted wavelength continuously varies, or 3) a filter array or filter mosaic.

[0056] In some embodiments, the corrected exposures having a predetermined degree of overlap allow an imaging module to form an image by stitching together the corrected overlapping exposures.

[0057] Embodiments include determining or modeling one or more correction surfaces for a plurality of (i.e. two or more) partially overlapping frames based on at least one of intensity pixel values of samples of the same object, geographical area, or feature, on the surface of Earth present in the plurality of frames, and in overlapping regions of at least two partially overlapping frames with may be captured consecutively. Hie one or more correction surfaces may be also modeled based on the characteristics of the dominant underlying physical phenomena causing the radiometric inconsistencies and / or the type of spectral band (e.g. Red-Green Blue (RGB), Near-infrared (NIR), etc.). Firstly, a correspondence of spatially overlapping pixels between the at least two partially overlapping frames is determined, such that the spatially overlapping pixels have the same content. In order to detennine their correspondence, the at least two partially overlapping frames may be coregistered. In some instances, the at least two partially overlapping frames may be orthorectified and thecorrespondence may be determined based on the geolocation coordinates of the spatially overlapping pixels within the overlapping region. In some instances, the overlapping region and correspondence from frame to frame may be determined based on position and other telemetry from the imaging system and platform.

[0058] Determining the correction surfaces may further comprise determining, based on at least one of the intensity values of pixels within a frame, the intensity values of spatially overlapping pixels of partially overlapping frames, and the geolocation or coregistered coordinates of objects, features, or frames, a set of equations representing at least one dominant radiometric inconsistency present within a frame, the equations having one or more parameters; solving the set of equations to obtain one or more parameter values, which may be optimal parameter values; and determining, based on the one or more parameter values, one or more correction surfaces. The geolocation coordinates generally determine or estimate the geographic position or geographic coordinates of an object, feature, or landmark in a given map or geodetic datum. For determining the correction surfaces of one or more frames, the physical phenomena of the radiometric inconsistencies predominantly present in the one or more frames is determined. Additionally or alternatively, the variation of colorcast effect between partially overlapping frames or within a frame are also considered for determining the correction surfaces of one or more frames. Then, spatially overlapping pixels between partially overlapping frames and their geolocation or coregistered coordinates (i.e. pixel coordinates) are determined. Hie partially overlapping frames may be captured consecutively, that is, captured following one after the other in order, or may be captured at a later time, or having a different order, provided that the content is similar and there are portions of the frames that overlap. The partially overlapping frames may be part of a batch or subset of frames (batch and subset are terms used interchangeably throughout the Detailed Description) which have been preselected from a set containing multiple partially overlapping frames.

[0059] The set of equations are generally solved using the intensity value and pixel coordinates of the pixels within the plurality of frames and the spatially overlapping pixels between partially overlapping frames. Given that the geolocation or coregistered pixel coordinates may have different orders of magnitude between frames, and the coordinates are part of the information used to solve the equations, it is preferable to centralize and normalize the coordinates. In some embodiments, the set of equations may be a linear system of equations relating the intensity value and pixel coordinates of the spatially overlapping pixels and the parameters defining the correction surfaces. However, in some embodiments, the set of equations may be a nonlinear system of equations. There are several fonns of determining the spatially overlapping pixels. For example, the spatially overlapping pixels may be determined using the pixel coordinates of coregistered, georeferenced and / or orthorectified frames.

[0060] The method further comprises correcting the frames using the modeled one or more correction surfaces. In the case of correction surfaces modeling additive radiometric inconsistencies (additive correction surfaces), the frames may be corrected by subtracting the additive correction surfaces from the frames. In some instances, the correction surfaces modeling radiometric inconsistencies which are not additive may be modeled asadditive. For example, the correction of frames using multiplicative correction surfaces representing multiplicative radiometric inconsistencies may be converted to additive correction surfaces by applying a logarithmic transformation to the data (i.e. frame), in order to then subtract the correction surfaces from the frames.

[0061] By operating in this maimer, multiple partially overlapping exposures may be captured and the radiometric inconsistencies are corrected. The corrected exposures having a determined amount of overlap enable the exposures to eliminate or reduce the color cast effect, and enables to stitch together the corrected exposures to form an image of arbitrary length and / or width. When a multi-band optical filter is used and the radiometric inconsistencies are corrected for the spectral bands, each segment of the image may be exposed through all bands of the multi-band optical filter during successive exposures to form an image of arbitrary’ length and / or width at a spectral band, with minimal or no color cast effect.

[0062] As explained elsewhere in the Detailed Description, the plurality of partially overlapping frames may be divided in batches and frames from different batches may be used as look-ahead or look-behind frames to improve consistency, especially in instances in which the content of a frame affects the radiometric inconsistencies frame by frame, as in additive radiometric inconsistencies. Optionally, this type of “superposition” between batches may be created with the aim of linking the batches, so that the frames between one batch and the next are not independent from each other in the sense that no radiometric inconsistencies are introduced or maintained between batches. In this manner the transition between batches is smoother. The decision on whether or not to create the superposition between batches may depend on the degree of variation of the colorcast effect between partially overlapping frames. For example, for frames captured at the NIR spectral band, the superposition between batches is not necessary because the colorcast effect varies more gradually and steadily than the size of the batches, in other w ords, the colorcast effect within the batches shows little variation compared to the variation shown within all the frames.

[0063] FIG. 1 shows a block diagram of an example of system 100 for correcting radiometric inconsistencies on images according to embodiments of present disclosure including a satellite 102 such as a low Earth orbit (LEO) satellite. The satellite 102 includes one or more payloads, where in many cases one of the payloads will include an imaging system 104. The imaging system 104 may include one or more cameras. The imaging system 104 may include sensors, such as light-sensitive sensors or pixel sensors, such as for example semiconductor components suitable to implement at least one charge coupled device (CCD), at least one complementary metal oxide semiconductor (CMOS) sensor, and / or other suitable sensor architecture suitable for capturing frames or exposures. The system 100 further comprises memory' 106 which may store program instructions and program modules that are loadable and executable on one or more processor(s) 108, and control module 110. The control module 110 may perform some or all of the control functions associated w ith capturing frames or exposures in accordance with embodiments of the present disclosure. The control module 110 is executable by the one or more processors 108 to control the imaging system 104, such as through one or more input / output interfaces.Additionally, the control module 110 may perform or otherwise control various functions of the imaging system 104 to control exposure times, synchronize the exposure capture, determine sensor, orbit or image parameters or the like, store image data on the memory 106, and so forth. The memory 106, one or more processor(s) 108 and control module 110 may be all or partially on-board satellite 102. In some embodiments, some of the components of the system 100 may be ground-based or on-board a separate aircraft or spacecraft, with such ground-based or separate aircraft or spacecraft in communication with the satellite 102.

[0064] Memory' 106 may store program instructions and program modules that are loadable and executable on one or more processor(s) 108, as well as data generated during execution of, and / or usable in conjunction with, these programs, such as image data, images, and so forth. Depending on the configuration and type of computing device used, memory’ 106 of system 100 may include volatile memory (such as random access memory (RAM)) and / or non-volatile memory (such as read-only memory (ROM), flash memory, etc.). Memory 106 may also include additional removable storage and / or non-removable storage including, but not limited to. flash memory, magnetic storage and / or optical storage, and / or tape storage that may provide non-volatile storage of computer- readable instructions, data structures, program modules, and other data for the system 100. Memory 106 is an example of non-transitory computer-readable media. Non-transitory computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any process or technology for storage of infonnation such as computer-readable instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, phase change memory (PRAM), static random-access memory (SRAM), dynamic random -access memory (DRAM), other types of RAM, ROM, electrically erasable programmable read-only memory? (EEPROM), flash memory' (such as NAND flash memory' such as may be included in one or more nonvolatile memory' cards, and including flash with both single-level and multi-level cell technologies) or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to store information for access by a computing device.

[0065] Memory' 106 includes control module 110 and an imaging module 112. The imaging module 112 performs various image processing functions of the system 100. including tone mapping to generate high dynamic range (HDR) images, a resolution enhancement algorithm to produce high-resolution images, and a stitching algorithm to generate images from multiple partially overlapping exposures, as well as other processing functions, such as blur removal, artifact removal, color enhancement, cropping, image conversion, image compression, data encry ption, and so forth. The control module 110 may be further configured to control the imaging system to capture one or more exposures and correct the radiometric inconsistencies on the exposures with the processes described throughout this Detailed Description. FIG. 2 shows an example of an image of arbitrary length fomied with partially overlapping frames captured by a satellite having color cast artifacts due to radiometric inconsistencies. The radiometric inconsistency corrections may be performed bythe control module 110, or may be shared between the imaging module 112 and the control module 110. In some embodiments, the radiometric correction and / or image processing workflows may be shared between multiple satellites within a constellation, or between a satellite and a ground-based station. It should be appreciated that not all of the modules need be present in every embodiment, that additional modules may be present for other purposes, and that several modules may be present for one or many of the purposes described. The modules stored within the memory 106, in many instances, provide for control of other systems and hardware on board the satellite.

[0066] In some embodiments, some or all of the functions of the control module 110, and / or the imaging module 112 may be implemented as logic functions on the one or more processors 108. For example, in some embodiments, the one or more processors 108 may include a central processing unit (CPU), a graphics processing unit (GPU), an application-specific integrated circuit (ASIC), a programmable logic device, such as a field programmable gate array (FPGA), a digital signal processor (DSP), a tensor processing unit (TPU), any combination of these, or any other logic circuit to perform various functions, including various control functions of the control module 110. The one or more processors 108 are processors that control the system or apparatus, such as the satellite 102, but in many instances may be the same processors dedicated to the imaging system 104.

[0067] Some embodiments of the imaging systems and apparatus described herein may be employed to take images of a celestial body, such as images of the Earth, from satellites, such as satellites in Tow Earth Orbit (LEO). LEO satellites orbit at speeds relative to a stationary point on the Earth that make motion blur an important issue. In satellite embodiments, the imaging system 104 includes a telescope and the pixel sensors may be placed after the telescope, such as at the focal plane of the telescope.

[0068] Tire present disclosure describes different exemplary embodiments of correcting or reducing radiometric inconsistencies or errors. However, all the examples have in common that correction surfaces are determined for the aerial or spatial exposures, then subtracted or divided from the aerial or spatial exposures so that an image or video of arbitrary length / width may be formed.Example Operations

[0069] FIGs. 3 and 4 depict flow graphs that show example processes in accordance with various embodiments. The operations of the processes are illustrated in individual blocks and summarized with reference to those blocks. Tire processes are illustrated as a logical flow graph, each operation of which may represent a set of operations that can be implemented in hardware, software, or a combination thereof. In the context of software, the operations represent computer-executable instructions stored on one or more computer storage media that, when executed by one or more processors, enable the one or more processors to perform the recited operations. Generally, computer-executable instructions include routines, programs, objects, modules, components, data structures, and the like that perform particular functions or implement particular abstract data types. In the context of hardware, the operations may be carried out in an integrated circuit, suchas in an application specific integrated circuit (ASIC), a programmable logic device, such as a field programmable gate array (FPGA), graphics processing unit (GPU), tensor processing unit (TPU), or central processing units (CPUs). Other examples of hardware may be used with the embodiments described herein and arc contemplated herein as providing the features and benefits described. The order in which the operations arc described is not intended to be construed as a limitation, and any number of the described operations can be combined in any order, separated into sub-operations, and / or performed in parallel to implement the process. Processes according to various embodiments of the present disclosure may include only some or all of the operations depicted in the logical flow graph. Moreover, the operations may be carried out by a single system, such as onboard a spacecraft or on the ground systems, or may be shared between multiple systems located onboard the spacecraft or ground-based systems.

[0070] FIG. 3 is a flow diagram showing an example overview process 300 for correcting radiometric inconsistencies on a plurality of frames (two or more) according to embodiments of present disclosure. The process is based on a system of equations describing correction surface models used to calculate one or more correction surfaces. For a set of partially overlapping frames, at 302, one or more correction surface models are determined. The one or more correction surfaces models may be determined based on radiometric inconsistencies based on at least one of the dominant underlying phenomena generating the radiometric inconsistencies, the type of spectral band (e.g. RGB, NIR, etc.), the number of spectral bands, tire pixel coordinate system, the characteristics of the imaging system, intensity differences between spatially overlapping pixels of partially overlapping frames (which may be captured consecutively), or any effect causing the radiometric inconsistencies. The one or more correction surfaces may be also or alternatively determined based on intensity pixel values of samples of the same object, geographical area, or feature on the surface of Earth present in overlapping regions of at least two partially overlapping frames of the plurality of frames. The plurality of frames may be frames stored in a memory or any physical medium which can be used to store information and which can be accessed by processors. The memory and / or the processors may be on the ground or on-board a moving platform such as an airplane, a balloon, a drone or a satellite. In some embodiments, the plurality or set of frames may be captured by an imaging system on-board an aerial or satellite platform such as a push-frame camera. The memory and the processors may be all on board the aerial or satellite platform so that the image processing, including the radiometric correction, is perfomied on board the aerial or satellite platform. Depending on the underlying phenomena, the correction surfaces characterizing the radiometric inconsistencies may be modeled as additive correction surfaces, multiplicative correction surfaces, or other types of correction surfaces.

[0071] It is possible to determine a mathematical model (also referred to as model) for determining the parametric correction surfaces (correction surface and parametric corrections surface are terms used interchangeably) based on the underlying dominant physical phenomena causing the radiometric inconsistencies within the frames. For example, a model may be additive if the underlying dominant physicalphenomenon causing the radiometric inconsistencies seems to be stray light, or multiplicative if the underlying dominant physical phenomenon causing the radiometric inconsistencies seems to be a vignetting-like effect. The underlying dominant phenomena may be determined based on the characteristics of the imaging system, the partially overlapping frames, and / or the overlapping zones or regions of partially overlapping frames. For example, the underlying dominant phenomena of radiometric inconsistencies may depend on the light intensity expected on the sensor, the variation of colors within spatially overlapping pixels of partially overlapping frames, the patterns found on images which van’ from one frame to another or vary within the plurality of partially overlapping frames, any combination of these, and so forth.

[0072] Tire dominant phenomena causing or underlying the radiometric inconsistencies (color cast phenomena) between the partially overlapping frames may be determined by analyzing some or all the frames of the set of partially overlapping frames, wherein the partially overlapping frames were captured by imaging systems onboard satellites belonging to the same constellation in which the imaging systems are similar, since the underlying physical phenomenon causing the radiometric inconsistencies is expected to be the same for all imaging systems of the satellites of the same constellation, and may be omitted for subsequent set of frames captured by similar imaging systems. However, when the imaging systems from which sets of partially overlapping frames have not been characterized or are expected to be different among them, it is preferable to analyze all the sets of partially overlapping frames (even the subsequent ones), to determine the dominant phenomena causing or underlying the radiometric inconsistencies. By determining the dominant phenomena causing or underlying the radiometric inconsistencies it is possible to determine the more suitable model for correcting the radiometric inconsistencies.

[0073] A set or system of equations may be determined to model the correction surfaces. The set of equations may include correction terms, which are mathematical expressions that model the correction surfaces and are used to eliminate the radiometric inconsistencies contained in the frames, and data fitting or regularization terms, which are mathematical expressions used in conjunction with the correction terms that are variable and depend on the type of radiometric inconsistencies. The correction surfaces may be modeled as polynomials of arbitrary order wherein the order of the polynomial is a parameter to the method, and should be selected based on the characteristics of the underlying physical phenomena causing the radiometric inconsistencies. The order of the polynomial generally dominates the shape of the correction surface and is generally chosen as the lower order that better represents the shape of the correction surface . For example, an order of 5 may be used for NearInfrared (NIR) frames in which the obtained correction surfaces better represent the color cast effect. A polynomial of order 2 may better represent the additive radiometric inconsistencies present in RGB frames, in which the color cast effect is generally due to stray light and depends on the content of the frame.

[0074] Tire set of equations (correction and data fitting / regularization), and the number of parametric correction surfaces modeled may be determined, depending on the underlying physical phenomena of the radiometric inconsistencies and on whether or not the radiometric inconsistencies vary frame by frame or withina frame. A parametric correction surface may be modeled for all frames, a parametric correction surface may be modeled for each frame, or a parametric correction surface may be modeled for all frames of a batch. For example, in the case of additive radiometric inconsistency, in which the color cast effects may depend on the individual content of the scenes within the frame, a correction surface may be modeled for each frame. In instances in which the radiometric inconsistencies (i.e. color cast effect) vary frame by frame or within a frame, for example influenced by the content of the frames, one correction surface may be modeled for each frame. For example, in RGB frames the dominant physical cause underlying the radiometric inconsistencies seems to be stray light and the additive effects of the stray light may depend on the individual content of the frame. Hence, for RGB frames, the plurality of partially overlapping frames may be divided in batches, and one correction surface may be modeled for each frame, so that there are as many additive correction surfaces as frames. Yet, a first correction surface may be used to correct a first group of frames within a batch, a second correction surface may be used to correct a second group of frames within a batch, and so forth. Overlapping zones or overlapping regions between partially overlapping frames are also considered in the determination of the correction surfaces. As explained elsewhere in the Detailed Description, when the frames are divided in batches, frames from different batches may be used as look-ahead or look-behind frames to improve consistency. For example, the batches may be linked by computing an extra corrected frame from one batch, which will be used in the following batch as a look-ahead constraint to improve consistency between the two batches. This is repeated for all subsequent batches of the plurality of frames. Similarly, where the radiometric inconsistencies are found not to vary (within a variation threshold tolerance), the same correction surface may be modeled for all frames. For example, in the case of NIR frames, the underlying phenomenon of the radiometric inconsistencies that dominates seems to be a multiplicative vignetting-like effect that does not vary noticeably from frame to frame. Hence, for NIR frames one correction surface may be modeled for all the frames, and the plurality of frames may or may not be divided in batches. Similarly, if divided in batches, a first correction surface may be used to correct a first group of frames within a batch, a second correction surface may be used to correct a second group of frames within a batch, and so forth. In some instances, the multiplicative compensation of inconsistencies may be changed to additive by first applying a logarithmic transform to the image data (frames), solving tire problem using the additive formulation, and then reversing the transform. In the case of a multiplicative model, a regularization to enforce the solution surface to be close to a desired scalar (e.g. 1) is found to prevent drift of the color cast solutions. Optionally, as a post-processing step, the correction surface may be normalized to a desired scale, in a non-limiting example it may be normalized to have mean I .

[0075] The following example illustrates correction terms (Eqs. 1 and 2) and data fitting or regularization terms (Eq. 3) for modeling correction surfaces for two partially overlapping RGB frames in which the underlying phenomena causing the radiometric inconsistencies is additive. Tire following linear system ofequations may be determined based on an additive model for two partially overlapping frames satisfying Eq. 1 within the overlapping zone:

[0076] Il— Si= Ij— Sj Eq. 1

[0077] Wherein, / , refers to the first frame I, lj refers to the second frame / partially overlapping the first frame z, Stmodels the radiometric error surface (correction surface) for the frame / (. and Sj models the radiometric error surface (correction surface) for the frame Ij. This is done for the overlapping zones of the subsequent partially overlapping frames of the set of partially overlapping frames. In this example, the linear system of equations equals the corrected images (7;— S,) with an identity matrix. However, in some instances, the matrix relating both terms may be different than the identity matrix and the sets of equations that model the correction surfaces may be nonlinear.

[0078] Tire equations for modeling the shape of the correction surfaces use polynomials of order 2 wherein a, through fi are the unknown variable coefficients, and xtand ytare the known pixel coordinates of the spatially overlapping pixels of the partially overlapping frame / (and n7through fy are the unknown variable coefficients, and Xj and y7are the known pixel coordinates of the spatially overlapping pixels of the partially overlapping frame Ij. The number of equations S depends on the number of correction surfaces to be modeled.

[0081] Optionally, the pixel coordinates of the spatially overlapping pixels may be centered and / or nonnalized, and may be image coordinates of each specific frame or a common set of coordinates across all frames. By normalizing the coordinates and intensities of the pixels, the numerical stability of the linear equation system may be improved. It should be understood that in the example above, the equations for two frames are illustrated, however this should be extended to the plurality of frames, which may or may not be divided in batches.

[0082] Depending on the type of dominant radiometric inconsistencies, one or more data fitting or regularization terms may be set. The data fitting / regularization terms may be set based on the characteristic values of the spatially overlapping pixels, or on the underlying phenomena causing the radiometric inconsistencies (e.g. on the linear equation system). For example, fortwo partially overlapping RGB frames ( / (and Ij) in which the underlying phenomena causing the radiometric inconsistencies is stray light (i.e. additive), the data fitting term may be set as:

[0083] A(7i - S = A. min(Ji, Ij)

[0084] A(77- Sj) = A. min(IbIj) Eq. 3

[0085] The data fitting / regularization term is set in this example to mean that the intensity value of the corrected pixel is equal to the minimum intensity value amongst the pixels of frames I and j. This is because the intensity pixel value that is considered the more reliable one is the minimum intensify pixel value between thetwo pixels, because unintended light is being added to the captures. It should be understood that other expressions for the data fitting term may be used instead of or in addition to fitting to the minimum value, such as fitting to the maximum value, the mean value, or any other value more suitable to be used depending on the dominant or predominant physical cause of the radiometric inconsistency. For instance, the data fitting term fitting to a minimum value may be replaced or complemented by an extra regularization tenn which determines that the values of a multiplicative correction surface should be close to a desired number, such as 1.

[0086] In the data fitting term expression of Eq. 3, A is a scalar parameter used to determine the strength of the minimum value of the fitting term. Generally, the value of A is a positive number above 1, and is set to have the maximum possible value that does not interfere with the results of the correction surface. In general, there is a trade off taken into consideration while setting the appropriate value for A. For example, for the fitting tenn of the additive radiometric inconsistencies above (RGB frames), the higher the value of A the more the corrected value will resemble the raw data (captured frame), but this may lower the correction effect without reducing or eliminating the color cast. On the contrary, the lower the value of A, the more the correction surface will resemble the captured frame, hence the color cast will be eliminated but the frame content may be eliminated as well. In addition, the value of A may take into consideration the number of pixels in the overlapping zones so that in instances in which there are different numbers of spatially overlapping pixels in the different overlapping zones this does not affect the process. Similarly, for two partially overlapping NIR frames in which the underlying phenomena causing the radiometric inconsistencies is a vignetting-like effect and the correction surfaces may be modeled as multiplicative correction surfaces, the fitting term may be set as the maximum value instead of the minimum shown above, or may be set as AS, = Atand ASj = Atwherein Atis a fixed number. This illustrates that the data fitting term may be selected to better fit the physical causes of the colorcast and the characteristics sought for the correction surfaces. For example, it can be determined by fixing values in areas of the sensor known to not be affected by inconsistencies or any other variation that conforms best with the known causes or characteristics of the inconsistencies. In any case, even though the values of the corrected frame have to reduce the radiometric inconsistencies of the captured frames, these values cannot be so different from the measured values of the captured frames since the radiometric fidelity has to be maintained.

[0087] At 304, a correction surface model from the one or more correction surface models is selected. Once different correction surfaces are modeled for different dominant phenomena causing radiometric inconsistencies, it is possible to select the more suitable model for correcting tire radiometric inconsistencies of the set of partially overlapping frames. In some implementations, a relation may be established between the type of spectral band and the correction surface model. Hence, the correction surface model may be selected depending on the type of spectral band. For example, it may be determined that for frames captured in RGB spectral band or in the red spectral band, the correction surface model is additive, and for frames captured in the NIR spectral band or blue spectral band, the correction surface model is multiplicative. This step is optional.

[0088] At 306 the set of frames is divided into one or more batches (subsets) of partially overlapping frames. In some instances, the batches have the same number of partially overlapping frames, but it may be different. The size of the batch (i.e. the number of frames per batch) may be determined based, at least in part, on the total number of frames, the computing power of the control module of the system, or the quality of the frames. In some instances, the number of frames in a batch may be truncated. For example, if the number of frames per batch is N, this number may be lower than N and the batch may be truncated. Hence, if it was detenuined that each batch of the set of frames should have 5 frames, but in the sequence of consecutive partially overlapping frames there was a batch in which there were some (portions or whole) frames having the quality or resolution below7a predetermined threshold or it was not possible to coregister or geolocate them, that batch w7ould have less than 5 frames, and a new batch w ould be started even though that batch had less than 5 frames. By operating in this manner, it is guaranteed that within the batch all the frames of the batch have the desired degree of overlap between partially overlapping frames.

[0089] Additionally or alternatively, when the frames are divided in batches, frames from different batches may be used as look-ahead or look -behind frames to improve consistency. A look-ahead frame refers to a frame that follows the batch and a look-behind frame refers to a frame that precedes the batch. For instance, for a given batch, the last corrected frame of the previous batch can be included in the system of equations to maximize consistency with the previously corrected batch. This frame is already corrected and no correction surface is calculated for it. This is useful to find the most consistent correction for frames between batches, and the frame acts as a look-behind frame. Additionally or alternatively, in the given batch, the following frame (i.e. the first frame of the next batch) may be also included in the system of equations to maximize consistency with the following batch. This frame is not corrected, since it has not been processed yet. A correction surface is calculated for it, but the correction is not applied (a correction for this frame will be calculated and applied on the next batch). This is useful to find the most consistent correction for frames strictly within the batch and acts as a look-ahead frame.

[0090] For each batch, at 308, a zone of spatially overlapping pixels (overlapping pixel zone) between two partially overlapping frames is determined. In some instances, the partially overlapping frames may be coregistered and / or orthorectified using their geographical location coordinates (obtaining coregistered or geolocation coordinates) in order to determine a correspondence of spatially overlapping pixel content between them. In some instances, it is possible to use orthorectified frames in which all frames have the same coordinate reference system (CRS), ground sampling distance (GSD), and their pixel grids are aligned. This means that given the pixel coordinate in one frame, the pixel corresponding to the same geographic coordinate in another frame can be directly identified even though they do not have the same pixel coordinates, and there is no resampling needed. Another option that does not include orthorectification would be to coregister frames and warping them to match the grid of another frame. In some instances, if the set of frames is divided in batches, the option may be to coregister frames and warping them to match the grid of the frame in the center of a batch.The coregistration may be performed using known techniques in the art, such as intensity-based or featurebased techniques. Tn other words, the correspondence of spatially overlapping pixels may be obtained as a byproduct of the orthorectification of the frames, or by explicitly registering the frames of the sequence with respect to a reference frame (usually the center frame of a subset of frames).

[0091] In some instances, the spatially overlapping pixel zone or overlapping region is detennined as having a degree of overlap between partially overlapping frames above a predetermined threshold. In some instances, the predetermined threshold of overlap between frames may be determined based on the minimum degree of overlap necessary to stitch together the partially overlapping frames to compose an image of arbitrary length and / or width. The frame may include one or more spectral bands. In instances in which the frames include two or more spectral bands, the degree of overlap between partially overlapping frames may be determined based on the degree of overlap between the corresponding two or more spectral bands of the partially overlapping frames and the number of spectral bands. For example, the subset, also referred to as batch, may have N partially overlapping frames wherein each frame has M spectral bands, where N and M are each an integer number. The degree of overlap between corresponding spectral bands may be the same or different for each band, and may be detennined as a predetermined number of spatially overlapping pixels, or as a percentage with respect to the size of the spectral band. Tire degree of overlap between partially overlapping frame s / spectral bands captured by a satellite is generally constant during data collection. However, in some instances the degree of overlap between partially overlapping frames / spectral bands of a batch may be different from the degree of overlap of the frames / spectral bands of another batch of the set of frames. For example, the degree of overlap between frames may slightly change due to covering maneuvers of the satellite. It should be noted however this is merely an example and several forms of determining the degrees of overlap are also within the scope of present disclosure.

[0092] Optionally, at 310, downsampling may be performed, where the spatial resolution may be reduced. Some or all pixel intensity values in the spatially overlapping pixel zone of at least two partially overlapping frames may be combined to reduce or minimize the effects of registration errors between frames, object motions and noise. Several techniques known in the art of image processing may be used. For example, binning may be applied to a frame by which the pixel intensity values of a group or cluster of adjacent pixels throughout a frame may be combined into a single pixel intensity value, providing at least the advantages of reducing memory consumption and hastening the overall method. For instance, for a square of 10x10 pixels, an average intensity value may be calculated based on the intensity values of all the pixels of the square, so that all the pixels of the square are assigned the calculated average intensity value. Binning with a factor of lOx for satellite imagery of 1 m may be applied. This step provides a more robust solution and reduces the registration errors between frames since the same object may not be in the same place from one frame to another because the object might have actually moved or because there were errors in the satellite position or calibration.

[0093] Optionally, at 312, filtering may be performed, where unreliable information contained in the spatially overlapping pixel zone of at least two partially overlapping frames may be discarded. For example, some or all the spatially overlapping pixels of the overlapping zone that are saturated, meaning that the incident light at the pixel causes the camera sensor to respond at its maximum value, or underexposed, meaning that the incident light at the pixel causes the camera sensor to respond at its minimum value, are masked out to consider only reliable information in the system. Similarly, some or all the spatially overlapping pixels at the borders of the overlapping zone may be also masked out to prevent or reduce undesirable artifacts. Also pixels having intensity values different than a predetermined threshold, which may have an intensity value much higher than the intensity value expected due to a colorcast effect, may be disregarded from the equations to be solved to find the correction surfaces.

[0094] At 314, characteristic values of the spatially overlapping pixels are determined. Hie characteristic values may be the intensity (I) of the pixels and the pixel coordinates. The frames may be georeferenced so that geographical information is added to the frames, generally by assigning geographic coordinates (such as x and y coordinates) in a given coordinate system to a set of pixels on the frame. Additionally, the frames may be orthorectified for removing image distortions or displacements generally caused by sensor tilt or topographic relief.

[0095] At 316, one or more parameter values are obtained, which may be optimal. Generally, the parameters are obtained by solving a generic optimization problem. The equations of the linear equation system including the correction terms and the data fitting / regularization terms obtained at 302 (and optionally selected at 304) are solved, based on the pixel values (e.g. xt, yi) of the pixels of the frames and the spatially overlapping pixels within the overlapping zones or regions, to determine the (optimal) parameter values used for building the one or more correction surfaces. In an overdetermined linear system of equations, the different equations (or constraints) are not perfectly satisfied, because each equation has a different goal. After optimization they reach a balance that minimizes a weighted error. Parameters like A allow to modify the weight of some parts of the error and steer the system to fit more or less certain constraints. When the frames are divided in batches, a single system may be evaluated for all the frames in a batch, which means that tire optimal parameter values of the correction surfaces for each of these frames is jointly estimated. As explained elsewhere, look-bchind and look-head frames may be used to improve consistency between batches, so that there is consistency between frames of a batch and also between batches.

[0096] At 318, one or more correction surfaces are built, based on the (optimal) parameter values calculated at 316. As explained elsewhere throughout the Detailed Description, after the (optimal) parameter values are found by solving the set of equations (also referred as equation system) and the correction surfaces built at 318, at 320, the frames are corrected. Tire corrected frames may be obtained by subtracting or dividing tire correction surface value from each corresponding pixel in the frame. The corrected intensity pixel value of a frame may be obtained by subtracting or dividing the corresponding intensity pixel value of the correction surface fromthe intensity pixel value of the original frames (e.g. the frames captured by a satellite). In instances where there is a single correction surface modeling the radiometric inconsistencies of all the frames, the same correction surface divides each of the frames to obtain corrected frames. Alternatively, the same correction surface may be subtracted from all frames but in logarithmic form. For example in NIR images, the underlying phenomenon is a vignetting-like effect, so one correction surface, modeled based on a multiplicative model, is modeled for all the frames. If there are M frames, the correction surface may divide each of the M frames, or if the values are in logarithmic form the correction surface may be subtracted from each of the M frames. On the contrary, in instances where a correction surface is modeled for each frame, as in RGB images, a correction surface obtained for a frame (from the plurality of correction surfaces that were determined, one for each frame) is subtracted from its corresponding frame to obtain corrected frames. In instances in which the plurality of frames was separated in batches of N frames, there are N corresponding correction surfaces in such a way that each correction surface is subtracted from its corresponding frame of the batch.

[0097] The corrected frames and / or the formed image may be stored in memory' on-board the aerial or satellite platform for further processing, for transmission to another location, or for performing image analysis. In some instances, the exposures are taken by the imaging system of an aerial or satellite platform and the image processing is perfonned on memory and processors on the ground.

[0098] Optionally, at 322, the perception of quantization errors are reduced to make the quantization distortions less perceivable for the target or output dynamic range. Uris is necessary in instances in which new color cast effects may be introduced due to inconsistencies introduced by quantization errors which appear generally when the bit depth of a signal is being reduced. Examples in which quantization may be necessary' are when the correction surfaces and the corrected frames are calculated in float and the frames are outputted to 8 bits. Since the correction surfaces and corrected frames are calculated in float, when mapping down to an 8 bit representation the half-value level lines of the correction surfaces may become visible as new apparent color cast artifacts. This may be the case of some satellite applications. However, in instances in which the satellite may capture frames at a higher dynamic range and make calculations at higher dynamic range without the necessity of reducing the bit depth of a signal or reducing the bit depth but at higher dy namic ranges, this step may be omitted since the quantization errors, artifacts, or distortions will be less perceivable. Dithering or a similar algorithm may be used to hide or make less perceivable quantization artifacts or distortions in the corrected figures. Dithering is a form of noise used to randomize quantization errors that allows to hide artifacts or distortions that may be the result of multiplying quantized values. In this manner, artifacts that are the result of equalizing quantized images are hidden or made less perceivable.

[0099] Optionally, at 324, based at least in part on the corrected frames, an image of arbitrary width and / or length is formed. For example, an imaging module may process the corrected frames to generate an image with minimum or none radiometric inconsistencies, such as by stitching together tire plurality of overlapping corrected frames to form an image of the scene. The processing may include utilizing the overlapping correctedframes from some or all the subsets. Corrected frames from partially overlapping corrected frames, which may be captured consecutively, are stitched together. A sufficient number of corrected frames may be obtained to generate an image of any length or width. A stitching algorithm is utilized in some embodiments to generate a final image (or video frame) from the plurality of partially overlapping corrected frames.

[0100] Once the color cast effect has been corrected from the frames, or as an initial step to evaluate the initial color cast effect before correction, additionally or alternatively, it is possible to measure the color cast correction on frames. The color cast metric provides a measurement of the degree of color cast present on the image, which may be used after the color cast correction has been applied, in order to learn how much color cast effect is present after the color cast correction. FIG. 4 is a flow diagram showing an example ovendew process according to embodiments of present disclosure for measuring the color cast effect on frames, providing a color cast metric. At 402 a pair of partially overlapping frames are selected. In some instances, the frames may be selected from a stripe 502 captured by a satellite, which was divided in tiles 504, as illustrated in FIG. 5, or the frames may be obtained from a database, received, or the like. Optionally, at 404 the pixel intensity values of the two partially overlapping frames are combined to reduce or minimize noise (e g. downsampling with filtering). Several techniques known in the art of image processing may be used. For example, binning may be applied to the frames, by which the pixel intensity values of a group or cluster of adjacent pixels throughout a frame may be combined into a single pixel intensity value. For instance, the two partially overlapping frames may be binned by a factor of 10. At 406, the overlap between the two partially overlapping frames is detennined, defining an overlapping region. Methods as explained elsewhere in the Detailed Description may be used to determine the overlapping region. At 408, a difference between the intensity pixel values within the overlapping region for the two partially overlapping frames is computed pixelwise, and at 410 the difference is normalized by the average of the pixel value for both frames. At 412 a filter is applied, for example a Gaussian filter. This process may be repeated for all the frames contained in a tile to obtain the difference map 414. For a tile, the difference map 414 shows an image formed by stripes in which each stripe represents the overlapping regions of different pairs of partially overlapping frames and shows the difference between the intensity pixel values (determined at 408) normalized by the average of the pixel value for both frames (determined at 410), pixel by pixel, within the overlapping region. It is possible to obtain a color cast metric for the tile, computing statistical values over the differences between the values, pixel by pixel. Tire difference map 414 may be saved as a debugging tool to visualize and understand the residuals of the correction. The actual metric may report statistical results per tile from the difference (visual) map. for example, the mean, the circular error at the 90th percentile (CE90) for the whole overlap, and also for the '‘transition” area which is a thinner overlap defined by configuration.

[0101] Additionally, the tiles may be divided per spectral band and the process may be implemented by spectral band, as illustrated in FIG. 6, which shows original band 602 showing a non uniform intensity response through the image, leading to sharp intensity steps when the frames are stitched (a color cast effect), the green band 604,the blue band 606, the red band 608, and the NIR band 610, each one showing different transition percentage differences.

[0102] Similarly, it is possible to compute statistical values, such as the mean difference for each spectral band, independently, taking into consideration the values of the tiles to obtain color cast metrics for the tiles for each spectral band. Uris illustrated in FIG. 7. in which the stripe 702 divided in tiles shows the metric for each tile for the blue band, the stripe 704 divided in tiles shows the metric for each tile for the red band, the stripe 706 divided in tiles shows the metric for each tile for the green band, and the stripe 708 divided in tiles shows the metric for each tile for the NIR band. For example, if there is a portion of the capture in the red band that has no color cast, then the values on the difference map will be zero (or minimum threshold value), meaning that a pixel from the red band of a first frame sensing a point on the Earth has the same intensity value as a pixel from the red band of a second frame sensing the same point on the Earth (ignoring noise for this example), wherein the red band of the first frame and the red band of the second frame are partially overlapping bands. When the values of the difference maps (for the whole frame of for each of the spectral bands) are different than zero (or minimum threshold value), there is color cast between the frames, meaning that there is an offset value evident by the different pixel intensity values of the same point on the Earth in the overlapped pixels of two different partially overlapping frames. For the example above, this means that a pixel from the red band of a first frame sensing a point on the Earth has a different intensity value compared to a pixel from the red band of a second frame sensing the same point on the Earth, wherein the red band of the first frame and the red band of the second frame are partially overlapping bands. The advantage of having the difference map is that it is possible to identify the portions having more color cast or less color cast within the overlapping region of the two partially overlapping frames. Based on the difference map, and on statistical values computed based on the difference map, it is also possible to determine whether or not what is identified as color cast is in fact color cast or a moving object. For example, a ship might be expected to appear on the same position on the Earth in the two partially overlapping frames, however, since the ship moved, the intensity value of the spatially overlapping pixel would be different since the same ship appeared on a different position in the two partially overlapping frames. In this situation, the change in the pixel intensity value is not due to a color cast effect but it is due to the movement of the ship. By computing statistical values on the difference map it is possible to identify that the difference on the pixel intensity value was due to the movement of the ship and not due to a color cast effect.

[0103] In a non-limiting example, a satellite may capture image data as a plurality of partially overlapping frames which may be stitched to form an image of arbitrary length which, depending on the acquisition mode, may be referred to as a stripe. In order to learn how much color cast effect is present on the stripe, the process described in FIG. 4 may be used, and a difference map obtained. The stripe may be divided in tiles, to simplify the calculations, and the color cast metric may be computed for each tile and, if the stripe is captured at different spectral bands, the color cast metric may, in addition or alternatively, be computed for each spectral band. Additionally or alternatively, statistical values for the difference map may be computed, for instance, tocharacterize images. For example, based on the difference map of a stitched image, the mean, the CE90, or any other statistical value may be calculated: and based at least in part on the statistical values and predetermined threshold values, an image may be characterized as problematic or not, in terms of amount or degree of color cast.

[0104] In another non-limiting example, the control module on-board a satellite may direct an imaging device to capture a plurality of exposures (frames) with a predetermined degree of overlap between exposures and perfonu the methods / processes described in FIGs. 3 and 4. Alternatively, the control module on-board a satellite directs the imaging system to capture a plurality of exposures and some or all the steps of the processes described in FIGs. 3 and 4 may be performed on the ground or onboard another satellite. Yet, in other instances, the satellite receives frames either from the ground or from another satellite and is able to perform some or all the steps of the processes described in FIGs. 3 and 4.

[0105] As described for the process of computing color cast metrics, the color cast correction described in FIG. 3 may be performed on images (which may be stitched images) captured by manned or unmanned, aerial or space vehicles, such as satellites, acquired as spots or stripes, which may or may not be divided in tiles.

[0106] In general the processes described in the Detailed Description do not fix a frame as a reference and correct or adjust the radiometric inconsistencies of the other frames to equal tire radiometric values of the reference frame, like is done in color hannonization, midway transform or equalization methods. The advantage of the processes described throughout the Detailed Description is that what is being corrected are the radiometric inconsistencies that van' spatially between frames, modifying all frames, without requiring a reference frame and correcting the other frames to match the reference frame. The processes described in the Detailed Description allow to have a single equation system that can correct radiometric inconsistencies finding the correction surfaces simultaneously for all the overlapping zones providing the higher radiometric consistency possible between all frames (or batches if the plurality of frames are divided in batches). By operating in this manner, the solution provides a radiometric consistency between frames instead of modifying some frames without taking into consideration the subsequent frames.

[0107] Contrary to prior art forms of correcting radiometric inconsistencies which require specific technical information about the imaging devices / systems capturing the frames which may differ, in some instances significantly, among the capturing devices / systems, another advantage of the devices, systems and processes described in the Detailed Description is that it is possible to correct radiometric inconsistencies between frames captured by different image formation models, without being tied to any of them.

[0108] It is to be appreciated that embodiments of the methods and apparatuses discussed herein are not limited in application to the details of construction and the arrangement of components set forth in the description or illustrated in the accompanying drawings. Tire methods and apparatuses are capable of implementation in other embodiments and of being practiced or of being carried out in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are not intended to be limiting. Inparticular, acts, elements and features discussed in connection with any one or more embodiments are not intended to be excluded from a similar role in any other embodiment.

[0109] Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. Any references to embodiments or elements or acts of the systems and methods herein referred to in the singular may also embrace embodiments including a plurality of these elements, and any references in plural to any embodiment or element or act herein may also embrace embodiments including only a single element. The use herein of “including,” “comprising,” "having,” “containing,” “involving,” and variations thereof is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. References to “or” may be construed as inclusive so that any terms described using “or” may indicate any of a single, more than one, and all of the described terms. In the descriptions above and in the claims, phrases such as “at least one of’ or “one or more of’ may occur followed by a conjunctive list of elements or features. The term “and / or” may also occur in a list of two or more elements or features. Unless otherwise implicitly or explicitly contradicted by the context in which it is used, such a phrase is intended to mean any of the listed elements or features individually or any of the recited elements or features in combination with any of the other recited elements or features. For example, the phrases “at least one of A and B:” , “at least one of A or B:”, “one or more of A and B: ”, and “A and / or B' are each intended to mean "A alone, B alone, or A and B together.” A similar interpretation is also intended for lists including three or more items. For example, the phrases “at least one of A. B, and C:”, “at least one of A. B or C:”. “one or more of A. B, and C:” and "A, B, and / or C” are each intended to mean "A alone, B alone, C alone, A and B together, A and C together, B and C together, or A and B and C together.” In addition, use of the term “based on” above and in the claims is intended to mean “based at least in part on”, such that an unrecited feature or element is also permissible.Conclusion

[0110] The subject matter described herein can be embodied in systems, apparatus, methods, and / or articles depending on the desired configuration. Although the disclosure uses language that is specific to structural features and / or methodological acts, the invention is not limited to the specific features or acts described. Rather, the specific features and acts are disclosed as illustrative forms of implementing the subject matter described herein. The implementations set forth in the foregoing description do not represent all implementations consistent with the subject matter described herein. Instead, they are merely some examples consistent with aspects related to the described subject matter. Although a few variations have been described in detail above, other modifications or additions are possible. In particular, further features and / or variations can be provided in addition to those set forth herein. For example, the implementations described above can be directed to various combinations and subcombinations of the disclosed features and / or combinations and sub combinations of several further features disclosed above. In addition, the logic flows depicted in the accompanying figures and / or described herein do not necessarily require the particular order shown, or sequential order, to achieve desirable results. Other implementations may be within the scope of the following claims.

Claims

CLAIMSWhat is claimed is:

1. A system for correcting frame radiometric inconsistencies, the system comprising: a control module configured to: obtain a plurality of partially overlapping frames; determine radiometric inconsistencies between the plurality of partially overlapping frames; determine, based at least in part on the radiometric inconsistencies, one or more correction surfaces: and correct, based on the one or more correction surfaces, the plurality of partially overlapping frames to obtain corrected frames.

2. The system according to claim I, wherein the control module is configured to determine one or more correction surfaces by determining a set of equations representing at least one radiometric inconsistency present within at least one frame of the plurality of partially overlapping frames; wherein the set of equations include one or more parameters and is determined based on at least one of the intensity values of pixels within a frame, the intensity values of spatially overlapping pixels of partially overlapping frames, and the geolocation or coregistered coordinates of objects, features, or frames.

3. The system according to claim 1 or 2, wherein the control module is further configured to determine one or more correction surfaces based on at least one of intensity pixel values of samples of a same object, geographical area, or feature on the surface of Earth present in the plurality of partially overlapping frames, characteristics of dominant underlying physical phenomena causing the radiometric inconsistencies, spectral bands present in the plurality of partially overlapping frames, or a pixel coordinate system.

4. The system according to any one of the preceding claims, wherein the control module is configured to determine the one or more correction surfaces by: determining one or more spatially overlapping pixels between at least two partially overlapping frames; determining an intensity value and pixel coordinates of the one or more spatially overlapping pixels; solving, based on the intensity value and the pixel coordinates, the set of equations to obtain one or more parameter's values; and determining, based on the one or more parameter's values, the one or more correction surfaces.

5. Tire system according to any one of the preceding claims, wherein the control module is further configured to divide the plurality of partially overlapping frames into one or more batches.

6. The system according to claim 5, wherein the control module is configured to use frames from the plurality of partially overlapping frames from different batches as look -ahead or look -behind frames.

7. Tire system according to claim 5, wherein the control module is further configured to determine, based at least in part on a variability of the radiometric inconsistencies, one correction surface for the plurality of partially overlapping frames or for the plurality of partially overlapping frames within a batch, or one correction surface for each frame of the plurality of partially overlapping frames or for each frame of the plurality of partially overlapping frames within a batch.

8. Tire system according to any one of claims 2, 4-7, wherein the set of equations comprises one or more correction terms and one or more fitting or regularization terms, and the one or more parameter values are determined by solving the set of equations.

9. The system according to any one of the preceding claims, wherein the control module is configured to determine the one or more correction surfaces based on an additive correction surface model or a multiplicative correction surface model.

10. The system according to any one of the preceding claims, wherein to correct the plurality of partially overlapping frames, the control module is configured to subtract or divide intensity pixel values of the one or more correction surfaces from intensity pixel values of each of the plurality of partially spatially overlapping frames.

11. The system according to any one of the preceding claims, wherein the control module is further configured to combine, throughout some or all of the plurality of partially overlapping frames, pixel intensity values of one or more groups or clusters of adjacent pixels into a single pixel intensity value.

12. Tire system according to any one of the preceding claims, wherein the control module is further configured to discard unreliable information contained in spatially overlapping pixels by masking some or all the spatially overlapping pixels.

13. The system according to any one of the preceding claims, wherein the control module is further configured to apply a dithering technique to make less perceivable quantization artifacts or distortions in the corrected frames.

14. The system according to any one of the preceding claims, further comprising a spectral filter comprising a plurality of spectral bands, and wherein the control module is configured to determine at least one correction surface for each spectral band.

15. The system according to any one of the preceding claims, further comprising an imaging module configured to form an image or a video of arbitrary length by stitching together the corrected frames.

16. The system according to any one of the preceding claims, further comprising an imaging system; and wherein the control module is further configured to control the imaging system to capture the plurality of partially overlapping frames.

17. The system according to any one of the preceding claims, wherein the imaging system is all or partially on board a manned or unmanned aerial or space vehicle.

18. A computer-implemented method for correcting frame radiometric inconsistencies, the method comprising: for at least two partially overlapping frames: determining, based on the at least two partially overlapping frames, one or more correction surfaces: and correcting, based on the one or more correction surfaces, the at least two partially overlapping frames to obtain at least two corrected partially overlapping frames.

19. The method according to claim 18, further comprising: determining whether determined radiometric inconsistencies between the at least two partially overlapping frames vary, frame by frame or within a frame, above a variation threshold; determining a correction surface from the one or more correction surfaces for each frame if it is determined that the radiometric inconsistencies vary, frame by frame or within a frame, above the variation threshold; and determining a correction surface from the one or more correction surfaces for all frames of the at least two partially overlapping frames if it is determined that the radiometric inconsistencies do not vary, frame by frame or within a frame, above the variation threshold.

20. Tire method according to claim 18 or 19, wherein correcting the at least two partially overlapping frames comprises subtracting or dividing intensity pixel values of the one or more correction surfaces from intensity pixel values of each of the at least two partially overlapping frames.

21. The method according to any one of claims 18-20, wherein determining the one or more correction surfaces comprises: for the at least two partially overlapping frames: determining one or more spatially overlapping pixels between the at least two partially overlapping frames: determining an intensity value and pixel coordinates of the one or more overlapping pixels; solving, based on the intensity value and pixel coordinates of the one or more overlapping pixels, a set of equations to obtain one or more parameter values; and obtaining, based on the parameter values, the one or more correction surfaces.

22. The method according to any one of claims 18-21, wherein the set of equations comprises one or more correction terms and one or more fitting or regularization terms.

23. Tire method according to claim 21 or 22, wherein the set of equations is a linear system and the one or more correction surfaces comprises an additive correction surface model or a multiplicative correction surface model.

24. The method according to any one of claims 18 to 23, further comprising modeling the one or more correction surfaces as two-dimensional polynomials of arbitrary order, wherein the polynomial order is selected based on characteristics of tire underlying physical phenomena causing the radiometric inconsistencies.

25. The method according to any one of claims 18 to 24, wherein the at least two partially overlapping frames are part of a batch of a plurality of batches, wherein a plurality of partially overlapping frames are divided into the plurality of batches.

26. Tire method according to claim 25, wherein at least one partially overlapping frame from the plurality of partially overlapping frames from different batches is used as a look-ahead or look-behind frame.

27. The method according to any one of claims 18 to 26, further comprising forming an image or video of arbitrary7width or length by stitching together the at least two corrected partially overlapping frames.

28. A computer-implemented method for measuring frame radiometric inconsistencies, the method comprising: determining an overlapping region between at least two partially overlapping frames;calculating a difference between intensity pixel values within the overlapping region of the at least two partially overlapping frames: normalizing the difference to obtain a normalized difference; and filtering the normalized difference to obtain a difference map.

29. The method according to claim 28, wherein the at least two partially overlapping frames are part of a tile of an aerial or satellite image, and the steps are repeated for some or all the partially overlapping frames contained within the tile of the aerial or satellite image; and optionally for all the tiles of the aerial or satellite image.

30. The method according to claim 29, wherein one or more statistical values based on the difference map are computed for some or all the tiles of the aerial or satellite image.

31. Tire method according to any one of claims 28 - 30, wherein pixel intensity values of a group or cluster of adjacent pixels of the partially overlapping frames are combined into a single pixel intensity value.

Images