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The basic aproaches to image registration are surveyed. Three image models are presented as models of the subpixel problem. A variety of approaches to the analysis of subpixel analysis are presented using these models.
This work focuses on the characterization of natural, spatially variable, semivegetated landscapes using a linear, stochastic, canopy-soil reflectance model. A first application of the model was the investigation of the effects of subpixel and regional variability of scenes on the shape and structure of red-infrared scattergrams. Additionally, the model was used to investigate the inverse problem, the estimation of subpixel vegetation cover, given only the scattergrams of simulated satellite scale multispectral scenes. The major aspects of that work, including recent field investigations, are summarized.
A physically based linear stochastic geometric canopy soil reflectance model is presented for characterizing spatial variability of semivegetated landscapes at subpixel and regional scales. Landscapes are conceptualized as stochastic geometric surfaces, incorporating not only the variability in geometric elements, but also the variability in vegetation and soil background reflectance which can be important in some scenes. The model is used to investigate several possible mechanisms which contribute to the often observed characteristic triangular shape of red-infrared scattergrams of semivegetated landscapes. Scattergrams of simulated and semivegetated scenes are analyzed with respect to the scales of the satellite pixel and subpixel components. Analysis of actual aerial radiometric data of a pecan orchard is presented in comparison with ground observations as preliminary confirmation of the theoretical results.
A physically based linear stochastic geometric canopy soil reflectance model is presented for characterizing spatial variability of semivegetated landscapes at subpixel and regional scales. Landscapes are conceptualized as stochastic geometric surfaces, incorporating not only the variability in geometric elements, but also the variability in vegetation and soil background reflectance which can be important in some scenes. The model is used to investigate several possible mechanisms which contribute to the often observed characteristic triangular shape of red-infrared scattergrams of semivegetated landscapes. Scattergrams of simulated semivegetated scenes are analyzed with respect to the scales of the satellite pixel and subpixel components. Analysis of actual aerial radiometric data of a pecan orchard is presented in comparison with ground observations as preliminary confirmation of the theoretical results.
A stochastic-geometric landsurface reflectance model is formulated and tested for the parameterization of spatially variable vegetation and soil at subpixel scales using satellite multispectral images without ground truth. Landscapes are conceptualized as 3-D Lambertian reflecting surfaces consisting of plant canopies, represented by solid geometric figures, superposed on a flat soil background. A computer simulation program is developed to investigate image characteristics at various spatial aggregations representative of satellite observational scales, or pixels. The evolution of the shape and structure of the red-infrared space, or scattergram, of typical semivegetated scenes is investigated by sequentially introducing model variables into the simulation. The analytical moments of the total pixel reflectance, including the mean, variance, spatial covariance, and cross-spectral covariance, are derived in terms of the moments of the individual fractional cover and reflectance components. The moments are applied to the solution of the inverse problem: The estimation of subpixel landscape properties on a pixel-by-pixel basis, given only one multispectral image and limited assumptions on the structure of the landscape. The landsurface reflectance model and inversion technique are tested using actual aerial radiometric data collected over regularly spaced pecan trees, and using both aerial and LANDSAT Thematic Mapper data obtained over discontinuous, randomly spaced conifer canopies in a natural forested watershed. Different amounts of solar backscattered diffuse radiation are assumed and the sensitivity of the estimated landsurface parameters to those amounts is examined.
Landsat TM data have been used in conjunction with field spectrometer data to map the lithologic units associated with a series of gabbroic intrusions in the East Greenland Tertiary Igneous Province. The general lack of vegetation combined with the difficulty of access to these intrusions make them ideal candidates for lithologic mapping using remote sensing techniques. In addition, these bodies are of interest as possible precious metal ore deposits. The intrusions are spectrally distinct from the surrounding Precambrian gneisses; however, subpixel contamination by snow, oxide surface coatings, and lichen cover and severe topography limit the discrimination of lithologic units within the gabbro. The spectral nature of the surface contaminants was evaluated with a Barringer Hand Held Ratioing Radiometer (HHRR). These HHRR data indicate that bare rock exposures have distinct TM signatures for each lithologic unit but that even small amounts of subpixel contamination are enough to mask these differences because of the large differences between the TM signatures of the rocks and the contaminants.
The effect of some systematic errors for high-precision time-series spaceborne photometry and astrometry has been investigated with a CCD as the detector. The 'pixelization' of the images causes systematic error in astrometric measurements. It is shown that this pixelization noise scales as image radius r exp -3/2. Subpixel response gradients, not correctable by the 'flat field', and in conjunction with telescope pointing jitter, introduce further photometric and astrometric errors. Subpixel gradients are modeled using observed properties of real flat fields. These errors can be controlled by having an image span enough pixels. Large images are also favored by CCD dynamic range considerations. However, magnified stellar images can overlap, thus introducing another source of systematic error. An optimum image size is therefore a compromise between these competing factors.
A sophisticated 3D laser radar sensor simulation, developed and applied to the task of autonomous hazard detection and avoidance, is presented. This simulation includes a backward ray trace to sensor subpixels, incoherent subpixel integration, range dependent noise, sensor point spread function effects, digitization noise, and AM-CW modulation. Specific sensor parameters, spacecraft lander trajectory, and terrain type have been selected to generate simulated sensor data.
In many remote sensing studies of geophysical fields such as clouds, land cover, or sea ice characteristics, the fractional area coverage of the field in an image is estimated as the proportion of pixels that have the characteristic of interest (i.e., are part of the field) as determined by some thresholding operation. The effect of sensor field-of-view on this estimate is examined by modeling the unknown distribution of subpixel area fraction with the beta distribution, whose two parameters depend upon the true fractional area coverage, the pixel size, and the spatial structure of the geophysical field. Since it is often not possible to relate digital number, reflectance, or temperature to subpixel area fraction, the statistical models described are used to determine the effect of pixel size and thresholding operations on the estimate of area fraction for hypothetical geophysical fields. Examples are given for simulated cumuliform clouds and linear openings in sea ice, whose spatial structures are described by an exponential autocovariance function. It is shown that the rate and direction of change in total area fraction with changing pixel size depends on the true area fraction, the spatial structure, and the thresholding operation used.
Biomass burning is a significant source of many trace gases in the atmosphere. Up to 25% of the total anthropogenic carbon dioxide added to the atmosphere annually is from biomass burning. However, this gaseous emission from fires is not directly detectable from satellite. Infrared radiance from the fires is. In order to see if infrared radiance can be used as a tracer for these emitted gases, we made laboratory measurements to determine the correlation of emitted carbon dioxide, carbon monoxide and total burned biomass with emitted infrared radiance. If the measured correlations among these quantities hold in the field, then satellite-observed infrared radiance can be used to estimate gaseous emission and total burned biomass on a global, daily basis. To this end, several types of biomass fuels were burned under controlled conditions in a large-scale combustion laboratory. Simultaneous measurements of emitted spectral infrared radiance, emitted carbon dioxide, carbon monoxide, and total mass loss were made. In addition measurements of fuel moisture content and fuel elemental abundance were made. We found that for a given fire, the quantity of carbon burned can be estimated from 11 (micro)m radiance measurements only within a factor of five. This variation arises from three sources, 1) errors in our measurements, 2) the subpixel nature of the fires, and 3) inherent differences in combustion of different fuel types. Despite this large range, these measurements can still be used for large-scale satellite estimates of biomass burned. This is because of the very large possible spread of fire sizes that will be subpixel as seen by Moderate Resolution Imaging Spectroradiometer (MODIS). Due to this large spread, even relatively low-precision correlations can still be useful for large-scale estimates of emitted carbon. Furthermore, such estimates using the MODIS 3.9 (micro)m channel should be even more accurate than our estimates based on 11 (micro)m radiance.
Spatially-distributed soil moisture observations have applications spanning a wide range of spatial resolutions from the very local needs of individual farmers to the progressively larger areas of interest to weather forecasters, water resource managers, and global climate modelers. To date, the most promising approach for space-based remote sensing of soil moisture makes use of passive microwave emission radiometers at L-band frequencies (1-2 GHz). Several soil moisture-sensing satellites have been proposed in recent years, with the European Space Agency's Soil Moisture Ocean Salinity (SMOS) mission scheduled to be launched first in a couple years. While such a microwave-based approach has the advantage of essentially allweather operation, satellite size limits spatial resolution to 10's of km. Whether used at this native resolution or in conjunction with some type of downscaling technique to generate soil moisture estimates on a finer-scale grid, the effects of subpixel spatial variability play a critical role. The soil moisture variability is typically affected by factors such as vegetation, topography, surface roughness, and soil texture. Understanding and these factors is the key to achieving accurate soil moisture retrievals at any scale. Indeed, the ability to compensate for these factors ultimately limits the achievable spatial resolution and/or accuracy of the retrieval. Over the last 20 years, a series of airborne campaigns in the USA have supported the development of algorithms for spaceborne soil moisture retrieval. The most important observations involved imagery from passive microwave radiometers. The early campaigns proved that the retrieval worked for larger and larger footprints, up to satellite-scale footprints. These provided the solid basis for proposing the satellite missions. More recent campaigns have explored other aspects such as retrieval performance through greater amounts of vegetation. All of these campaigns featured extensive ground truth collection over a range of grid spacings, to provide a basis for examining the effects of subpixel variability. However, the native footprint size of the airborne L-band radiometers was always a few hundred meters. During the recently completed (November, 2005) National Airborne Field Experiment (NAFE) campaign in Australia, a compact L-band radiometer was deployed on a small aircraft. This new combination permitted routine observations at native resolutions as high as 60 meters, substantially finer than in previous airborne soil moisture campaigns, as well as satellite footprint areal coverage. The radiometer, the Polarimetric L-band Microwave Radiometer (PLMR) performed extremely well and operations included extensive calibration-related observations. Thus, along with the extensive fine-scale ground truth, the NAFE dataset includes all the ingredients for the first scaling studies involving very-high-native resolution soil moisture observations and the effects of vegetation, roughness, etc. A brief overview of the NAFE will be presented, then examples of the airborne observations with resolutions from 60 m to 1 km will be shown, and early results from scaling studies will be discussed.
This paper describes a vision-guided manipulation algorithm that improves arm end-effector positioning to subpixel accuracy and meets the highly restrictive imaging and computational constraints of a planetary robotic flight system. Analytical, simulation-based, and experimental analyses of the algorithm's effectiveness and sensitivity to camera and arm model error is presented along with results on several prototype research systems and 'ground-in-the-loop' technology experiments on the Mars Exploration Rover (MER) vehicles. A computationally efficient and robust subpixel end-effector fiducial detector that is instrumental to the algorithm's ability to achieve high accuracy is also described along with its validation results on MER data.
In developing software for independent verification and validation (IVV) of the Image Navigation and Registration (INR) capability for the Geostationary Operational Environmental Satellite R Series (GOES-R) Advanced Baseline Imager (ABI), we have encountered an image registration artifact which limits the accuracy of image offset estimation at the subpixel scale using image correlation. Where the two images to be registered have the same pixel size, subpixel image registration preferentially selects registration values where the image pixel boundaries are close to lined up. Because of the shape of a curve plotting input displacement to estimated offset, we call this a stair-step artifact. When one image is at a higher resolution than the other, the stair-step artifact is minimized by correlating at the higher resolution. For validating ABI image navigation, GOES-R images are correlated with Landsat-based ground truth maps. To create the ground truth map, the Landsat image is first transformed to the perspective seen from the GOES-R satellite, and then is scaled to an appropriate pixel size. Minimizing processing time motivates choosing the map pixels to be the same size as the GOES-R pixels. At this pixel size image processing of the shift estimate is efficient, but the stair-step artifact is present. If the map pixel is very small, stair-step is not a problem, but image correlation is computation-intensive. This paper describes simulation-based selection of the scale for truth maps for registering GOES-R ABI images.
In developing software for independent verification and validation (IVV) of the Image Navigation and Registration (INR) capability for the Geostationary Operational Environmental Satellite R Series (GOES-R) Advanced Baseline Imager (ABI), we have encountered an image registration artifact which limits the accuracy of image offset estimation at the subpixel scale using image correlation. Where the two images to be registered have the same pixel size, subpixel image registration preferentially selects registration values where the image pixel boundaries are close to lined up. Because of the shape of a curve plotting input displacement to estimated offset, we call this a stair-step artifact. When one image is at a higher resolution than the other, the stair-step artifact is minimized by correlating at the higher resolution. For validating ABI image navigation, GOES-R images are correlated with Landsat-based ground truth maps. To create the ground truth map, the Landsat image is first transformed to the perspective seen from the GOES-R satellite, and then is scaled to an appropriate pixel size. Minimizing processing time motivates choosing the map pixels to be the same size as the GOES-R pixels. At this pixel size image processing of the shift estimate is efficient, but the stair-step artifact is present. If the map pixel is very small, stair-step is not a problem, but image correlation is computation-intensive. This paper describes simulation-based selection of the scale for truth maps for registering GOES-R ABI images.
Edge-Directed Radial Basis Functions (EDRBF) are used to compute super resolution(SR) image from a given set of low resolution (LR) images differing in subpixel shifts. The algorithm is tested on remote sensing images and compared for accuracy with other well-known algorithms such as Iterative Back Projection (IBP), Maximum Likelihood (ML) algorithm, interpolation of scattered points using Nearest Neighbor (NN) and Inversed Distance Weighted (IDW) interpolation, and Radial Basis Functin(RBF) . The accuracy of SR depends on various factors besides the algorithm (i) number of subpixel shifted LR images (ii) accuracy with which the LR shifts are estimated by registration algorithms (iii) and the targeted spatial resolution of SR. In our studies, the accuracy of EDRBF is compared with other algorithms keeping these factors constant. The algorithm has two steps: i) registration of low resolution images and (ii) estimating the pixels in High Resolution (HR) grid using EDRBF. Experiments are conducted by simulating LR images from a input HR image with different sub-pixel shifts. The reconstructed SR image is compared with input HR image to measure the accuracy of the algorithm using sum of squared errors (SSE). The algorithm has outperformed all of the algorithms mentioned above. The algorithm is robust and is not overly sensitive to the registration inaccuracies.
This paper describes a vision-guided manipulation algorithm that improves arm end-effector positioning to subpixel accuracy and meets the highly restrictive imaging and computational constraints of a planetary robotic flight system. Analytical, simulation-based, and experimental analyses of the algorithm's effectiveness and sensitivity to camera and arm model error is presented along with results on several prototype research systems and ground-in-the-loop technology experiments on the Mars Exploration Rover (MER) vehicles. A computationally efficient and robust subpixel end-effector fiducial detector that is instrumental to the algorithm's ability to achieve high accuracy is also described along with its validation results on MER data.
The 4 April 2010 M w 7.2 El Mayor-Cucapah (EMC) earthquake in Baja, California, and Sonora, Mexico, had primarily right-lateral strike-slip motion and a minor normal-slip component. The surface rupture extended about 120 km in a NW-SE direction, west of the Cerro Prieto fault. We use geodetic measurements including near- to far-field GPS, interferometric synthetic aperture radar (InSAR), and subpixel offset measurements of radar and optical images to characterize the fault slip during the EMC event. We use dislocation inversion methods and determine an optimal nine-segment fault geometry, as well as a subfault slip distribution from the geodetic measurements. With systematic perturbation of the fault dip angles, randomly removing one geodetic data constraint, or different data combinations, we are able to explore the robustness of the inferred slip distribution along fault strike and depth. The model fitting residuals imply contributions of early postseismic deformation to the InSAR measurements as well as lateral heterogeneity in the crustal elastic structure between the Peninsular Ranges and the Salton Trough. We also find that with incorporation of near-field geodetic data and finer fault patch size, the shallow slip deficit is reduced in the EMC event by reductions in the level of smoothing. Finally, these results show that the outcomes of coseismic inversions can vary greatly depending on model parameterization and methodology.
X-ray imaging offers unique possibilities for Digital Image Correlation (DIC), opening the door for full-field deformation measurements of a test article in complex environments where optical DIC suffers severe biases or is impossible. While X-ray DIC has been performed in the past with standard DIC codes designed for optical images, the path-integrated nature of X-ray images places constraints on the experimental setup, predominantly that only a single surface of interest moves/deforms. These requirements are difficult to realize for many practical situations and limit the amount of information that can be garnered in a single test. Other X-ray based diagnostics such as Digital Volume Correlation (DVC) and Projection DVC (P-DVC) overcome these obstacles, but DVC is limited to quasi-static tests, and both DVC and P-DVC necessitate high-resolution computed tomography (CT) scan(s) and often require a potentially invasive pattern throughout the volume of the specimen. Here this work presents a novel approach to measure time-resolved displacements and strains on multiple surfaces from a single series of 2D, path-integrated (PI) X-ray images, called PI-DIC. The principle of optical flow or conservation of intensity—the foundation of DIC—was reframed for path-integrated images, for an exemplar setup comprised of two plates moving and deforming independently. Synthetic images were generated for rigid translations, rigid rotations, and uniform stretches, where each plate underwent a unique motion/deformation. Experimental specimens were fabricated (either an aluminum plate with tantalum features or a plastic plate with steel features) and the two specimens were independently translated. PI-DIC was successfully demonstrated with the synthetic images and validated with the experimental images. Prescribed displacements were recovered for each plate from the single set of path-integrated, deformed images. Errors were approximately 0.02 px for the synthetic images with 1.5% image noise, and 0.05 px for the experimental images. These results provide the foundation for PI-DIC to measure motion and deformation of multiple, independent surfaces with subpixel accuracy from a single series of path-integrated X-ray images.