Sub-pixel Accuracy Research Articles

Displacement detection with sub-pixel accuracy and high spatial resolution using deep learning.

The purpose of this study was to detect two dimensional and sub-pixel displacement with high spatial resolution using an ultrasonic diagnostic apparatus. Conventional displacement detection methods assume neighborhood uniformity and cannot achieve both high spatial resolution and sub-pixel displacement detection. A deep-learning network that utilizes ultrasound images and output displacement distribution was developed. The network structure was constructed by modifying FlowNet2, a widely used network for optical flow estimation, and a training dataset was developed using ultrasound image simulation. Detection accuracy and spatial resolution were evaluated via simulated ultrasound images, and the clinical usefulness was evaluated with ultrasound images of the liver exposed to high-intensity-focused ultrasound (HIFU). These results were compared to the Lucas-Kanade method, a conventional sub-pixel displacement detection method. For a displacement within ± 40µm (± 0.6 pixels), a pixel size of 67µm, and signal noise of 1%, the accuracy was above 0.5µm and 0.2µm, the precision was above 0.4µm and 0.3µm, and the spatial resolution was 1.1mm and 0.8mm for the lateral and axial displacements, respectively. These improvements were also observed in the experimental data. Visualization of the lateral displacement distribution, which determines the edge of the treated lesion using HIFU, was also realized. Two-dimensional and sub-pixel displacement detection with high spatial resolution was realized using a deep-learning methodology. The proposed method enabled the monitoring of small and local tissue deformations induced by HIFU exposure.

Real-Time Deformation Measurements Using Single Image Photogrammetry

Most photogrammetric measurements are currently based on image acquisition in the field and subsequent processing in office environment with certain temporal delay. However, in some cases it is necessary to process the data real-time, or at least in-situ. Bridge load testing is an example of measurement processing directly at the place of imaging, where almost immediate information about the current state or change of the object is required. An algorithm is developed for these purposes, including a camera controlling software and a MATLAB code that identifies and quantifies the shifts of the observed points in the image plane. The observed points are in the shape of black disks on a white background. Using a horizontal camera position individual epochs are captured. Each image is immediately transferred to a computer via Wi-Fi. The MATLAB code then loads the image and binarizes it. Binarization of the image is performed by the Canny edge detector. Using normalized 2-D cross-correlation, the algorithm determines the approximate coordinates based on a target template. A function performs least squares ellipse fitting and determines the center of the target in sub-pixel accuracy, the semi-major axis, the semi-minor axis and the rotation angle of the ellipse. The target detection is executed in a while cycle loop, which compares the point coordinates from each epoch to the initial state, thus quantifying the deformations in pixels. If the next image is not yet available, the loop restarts. The deformations are calculated based on the known scale of each target. This paper presents a detailed description of the development of the algorithm, the results achieved and the proposed improvements going forward.

A fast non-iterative method for the object to image space best scanline determination of spaceborne linear array pushbroom images

The back-projection of three-dimensional (3D) object coordinates append onto the two-dimensional (2D) image space is the principal process of several photogrammetric tasks. Unlike frame-type images, each scanline of linear array images has six exterior orientation parameters (EOPs) at the exposure. Consequently, it is not possible to directly convert 3D object coordinates to 2D image coordinates by the Collinearity Equation (CE) unless precise EOPs have been determined for each scanline. Therefore, determining the best scanline is a pre-requisite step for the object-to-image transformation. Previous best scanline determination (BSD) methods utilized iterative procedures, becoming time-consuming and inefficient for near-real-time applications. This paper introduces a novel non-iterative three-stage methodology for the BSD of spaceborne linear pushbroom images, recording the Earth’s surface information. First, the approximate times of exposure of simulated control points (SCOPs) were computed. Afterwards, two separate approaches: (1) artificial neural networks (ANN) and (2) optimized global polynomial (OGP) were employed to model the relationship between approximate and exact exposure times. Finally, the best scanline of each unknown point was determined by refining the approximate exposure time using one of the models adopted in the previous step, regardless of the iterative procedure. The proposed method was applied to eight different images acquired by six sensors, and eight million simulated check points (SCPs) per image were utilized for statistical assessments. The achieved root mean square errors (RMSEs) of the proposed BSD method in eight images varied between 0.20 and 0.46 (pixel), demonstrating the proposed method’s potential to obtain desirable sub-pixel accuracy. Additionally, the experimental results revealed that the proposed method outperformed other well-known algorithms such as the Newton-Raphson (NR), the Bisecting Window Search (BWS), and the Sequential Search (SS) algorithms. Both proposed approaches significantly reduced over 95% computation time, suggesting the applicability of the proposed workflow for near-real-time photogrammetric tasks.

Learning an epipolar shift compensation for light field image super-resolution

Light field imaging has drawn broad attention since the advent of practical light field capturing systems that facilitate a wide range of applications in computer vision. However, existing learning-based methods for improving the spatial resolution of light field images neglect the shifts in the sub-pixel domain that are widely used by super-resolution techniques, thus, fail in recovering rich high-frequency information. To fully exploit the shift information, our method attempts to learn an epipolar shift compensation for light field image super-resolution that allows the restored light field image to be angular coherent with the enhancement of spatial resolution. The proposed method first utilizes the rich surrounding views along some typical epipolar directions to explore the inter-view correlations. We then implement feature-level registration to capture accurate sub-pixel shifts of central view, which is constructed by the compensation module equipped with dynamic deformable convolution. Finally, the complementary information from different spatial directions is fused to provide high-frequency details for the target view. By taking each sub-aperture image as a central view, our method could be applied for light field images with any angular resolution. Extensive experiments on both synthetic and real scene datasets demonstrate the superiority of our method over the state-of-the-art qualitatively and quantitatively. Moreover, the proposed method shows good performance in preserving the inherent epipolar structures in light field images. Specifically, our LFESCN method outperforms the state-of-the-art method with about 0.7 dB (PSNR) on average.

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.

Reflectance Imaging Spectroscopy (RIS) for Operation Night Watch: Challenges and Achievements of Imaging Rembrandt's Masterpiece in the Glass Chamber at the Rijksmuseum.

Visible and infrared reflectance imaging spectroscopy is one of the several non-invasive techniques used during Operation Night Watch for the study of Rembrandt’s iconic masterpiece The Night Watch (1642). The goals of this project include the identification and mapping of the artists’ materials, providing information about the painting technique used as well as documenting the painting’s current state and ultimately determining the possible conservation plan. The large size of the painting (3.78 m by 4.53 m) and the diversity of the technical investigations being performed make Operation Night Watch the largest research project ever undertaken at the Rijksmuseum. To construct a complete reflectance image cube at a high spatial resolution (168 µm2) and spectral resolution (2.54 to 6 nm), the painting was imaged with two high-sensitivity line scanning hyperspectral cameras (VNIR 400 to 1000 nm, 2.54 nm, and SWIR 900 to 2500 nm, 6 nm). Given the large size of the painting, a custom computer-controlled 3-D imaging frame was constructed to move each camera, along with lights, across the painting surface. A third axis, normal to the painting, was added along with a distance-sensing system which kept the cameras in focus during the scanning. A total of 200 hyperspectral image swaths were collected, mosaicked and registered to a high-resolution color image to sub-pixel accuracy using a novel registration algorithm. The preliminary analysis of the VNIR and SWIR reflectance images has identified many of the pigments used and their distribution across the painting. The SWIR, in particular, has provided an improved visualization of the preparatory sketches and changes in the painted composition. These data sets, when combined with the results from the other spectral imaging modalities and paint sample analyses, will provide the most complete understanding of the materials and painting techniques used by Rembrandt in The Night Watch.

A monocular vision-based decoupling measurement method for plane motion orbits

The plane motion that composed of dynamic displacement and angle is the basis of six-degree-of-freedom motion, and its accurate measurement is especially important for the applications of inertial navigation, pose estimation, and bridge structural healthy analysis. Currently, the commonly used measurement strategies include the laser interferometry, grating ruler-based method, and sensor-based method. However, they are always difficult to accomplish the high-accuracy and efficiency measurement in a broad low-frequency range due to the limitation of their performances. In this study, a monocular vision-based method is investigated to measure the plane motion, which can get the displacement and angle as well as orbit simultaneously by using the Zernike moment method with sub-pixel accuracy and decoupling model. The measurement uncertainties of dynamic displacement and angle are 0.266% and 0.098°, and the resolutions can highly reach to 0.1 um and 0.0001°, respectively. Comparison experiments with the laser interferometry and circular grating method demonstrate the investigated method can accomplish high-accuracy displacement and angle measurements in the ranges of 0.05–20 Hz and 0.001–10 Hz. Meanwhile, the different plane motion orbits can also be measured by the investigated method.

Positioning error calibration for two-dimensional precision stages via globally optimized image registration

Positioning errors are a primary performance indicator of precision stages. Calibration of stage positioning errors usually requires expensive, specialised instruments or artefacts. In this paper, we introduce a simple and cost-effective, machine vision-based method for stage error calibration. The novelty is that we used an arbitrarily textured plane, for example an array of coins, as the imaging target, as opposed to costly precision machined artefacts. Positioning errors were extracted from overlapped texture images using a fast and globally optimised feature-matching algorithm. A computer simulation demonstrates that the method is accurate and numerically stable in terms of sensing noise. Trials with a coordinate measuring machine reveal that the method can achieve sub-pixel accuracy, with a maximum measurement error of approximately 3 μm within a 100 mm range.

Hybrid FPGA-CPU pupil tracker.

An off-axis monocular pupil tracker designed for eventual integration in ophthalmoscopes for eye movement stabilization is described and demonstrated. The instrument consists of light-emitting diodes, a camera, a field-programmable gate array (FPGA) and a central processing unit (CPU). The raw camera image undergoes background subtraction, field-flattening, 1-dimensional low-pass filtering, thresholding and robust pupil edge detection on an FPGA pixel stream, followed by least-squares fitting of the pupil edge pixel coordinates to an ellipse in the CPU. Experimental data suggest that the proposed algorithms require raw images with a minimum of ∼32 gray levels to achieve sub-pixel pupil center accuracy. Tests with two different cameras operating at 575, 1250 and 5400 frames per second trained on a model pupil achieved 0.5-1.5 μm pupil center estimation precision with 0.6-2.1 ms combined image download, FPGA and CPU processing latency. Pupil tracking data from a fixating human subject show that the tracker operation only requires the adjustment of a single parameter, namely an image intensity threshold. The latency of the proposed pupil tracker is limited by camera download time (latency) and sensitivity (precision).

Refocusing and locating effect of fluorescence scattering field* *Project supported by the National Key Research and Development Program of China (Grant No. 2019YFC0119800), the Youth Talent Support Program of Universities of Hebei Province, China (Grant No. BJ2021038), the National Natural Science Foundation of China (Grant No. 12004265), the Natural Science Foundation of Hebei Province, China (Grant No. A2020210001), and the

Optical imaging deep inside scattering medium has always been one of the challenges in the field of bioimaging, which significantly drawbacks the employment of con-focal microscopy system. Although a variety of feedback techniques, such as acoustic or nonlinear fluorescence-based schemes have realized the refocusing of the coherent light, the problems of non-invasively refocusing and locating of linearly-excited fluorescent beads inside the scattering medium have not been thoroughly explored. In this paper, we linearly excited the fluorescent beads inside a scattering medium by using our homemade optical con-focal system, collected the fluorescence scattering light as the optimized target, and established a theoretical model of target contrast enhancement, which is consistent with the experimental data. By improving both the cost function and variation rate within the genetic algorithm, we could refocus the fluorescence scattering field while improving the contrast enhancement factor to 12.8 dB. Then, the positions of the fluorescent beads are reconstructed by subpixel accuracy centroid localization algorithm, and the corresponding error is no more than 4.2 μm with several fluorescent beads within the field of view. Finally, the main factors such as the number of fluorescent beads, the thickness of the scattering medium, the modulating parameter, the experimental noise and the system long-term stability are analyzed and discussed in detail. This study proves the feasibility of reconstructing fluorescent labeled cells inside biological tissues, which provides certain reference value for deep imaging of biological tissues.

Fast two-step phase-shifting method for measuring the three-dimensional contour of objects

A two-step phase-shifting method is proposed. The method realized the rapid measurement of the three-dimensional (3D) contour of some objects using mean envelope denoising based on the striped structured light. First, Butterworth low-pass pre-filtering in the frequency domain was performed on the two deformed fringe images containing the height information of the objects. It reduced the influence of higher harmonics. Then the peak and valley values of fringes with sub-pixel accuracy were obtained through numerical interpolation and point-by-point comparison. Furthermore, the mean envelope was accurately obtained and removed. After removing the mean envelope, the rectangular low-pass filtering was used to thoroughly filter out the remaining background signal. Finally, the fast reconstructions of the 3D contour of the objects were realized. The 3D contour reconstructions of the objects were simulated and experimentally measured using the method proposed. The calculation speed and accuracy were compared with the traditional four-step phase-shifting method and other two-step phase-shifting methods. The method has the advantages of fast calculation speed and high calculation accuracy. It is a valuable method for quickly measuring the 3D contour of some objects.

Sub-pixel accuracy evaluation of FY-3D MERSI-2 geolocation based on OLI reference imagery

ABSTRACT The geolocation quality of satellite observation datasets is causally related to the credibility of operational products. The twice-daily global Earth observations provided by FY-3D/MERSI-2 (FengYun-3D/MEdium Resolution Spectral Imager II) have been used to generate various remote sensing application products, but their geolocation performance has not yet been documented, while the comprehensive analysis of geometric accuracy provides important guidance for improving geolocation accuracy and data application in the future. In this paper, a combination of phase-only correlation and anomaly isolation techniques was used to design a robust algorithm of sub-pixel geolocation displacement detection for MERSI-2 data with 1 km spatial resolution. Utilizing MERSI-2 data from three typical regions and monthly Landsat 8 OLI (Operational Land Imager) data synthesized by Google Earth Engine (GEE), an exhaustive presentation of how the developed method quantifies the geometric displacements of the Level 1 dataset to along-track and cross-track directions is described, ultimately revealing the deterioration of MERSI-2 on-orbit geolocation performance. During the 17 months of official operational products, the geolocation error increases by a factor of 1.13 in along-track direction and 1.56 in cross-track direction. But approximately 70% of the geometric displacements remain within ±300 m in both along-track and cross-track directions, while about 92% are within ±500 m. This method reliably ascertains that the geolocation accuracy of MERSI-2 matches within 1/2 Instantaneous Field of View (IFOV).

An online visual measurement method for workpiece dimension based on deep learning

Image preprocessing and edge detection are the two most critical steps when applying machine vision to measure workpiece dimension in industrial field. The surface of the workpiece is usually covered with interference regions, which makes edge detection difficult. Aiming at the problem, the Full Convolutional Network (FCN) model is used to detect interference regions of workpiece images, and then interference regions are processed by the directional texture repair method. To avoid the influence of workpiece surface texture after rough machining, a method based on Holistically-nested Edge Detection (HED) model for rough edge detection of workpiece images is proposed. The edge is obtained by HED, and then it is post-processed based on the non-maximum value suppression and double threshold segmentation methods in the Canny operator to obtain a refined edge image. In order to further improve the accuracy of the dimension measurement, sub-pixel level edge detection accuracy is achieved by cubic spline interpolation. Finally, the method is validated by a shaft workpiece. The measuring accuracy of the outer diameter of the workpiece can reach 0.02 mm, which can effectively meet the requirements of fast semi-finishing inspection. This research provides a common workpiece dimension measurement method in industrial field and methodological guidance for the application of deep learning in industrial inspection.

Pixel-wise in situ calibration method for high accuracy infrared thermography of moving targets

We present a calibration method for the measurement of temperature using infrared cameras that enables high-accuracy thermography of moving targets with locally varying emissivity. Correlation-based image matching techniques are applied to calculate position-dependent calibration functions with sub-pixel accuracy. The calibration method is described in detail and demonstrated using an experimental setup consisting of a rotating cube. The measurement uncertainty is analysed in comparison to a conventional pixel-wise in situ method used for non-moving measurements. An analysis is carried out for varying levels of sub-pixel resolution and within different regions of the field of view. The results show that the measurement uncertainty decreases with increasing sub-pixel resolution and is comparable to levels obtained with a pixel-wise in situ calibration applied on a non-moving target. The error introduced by the motion of the sample was reduced by 75% on a high emissivity surface and by 96% within an area of the field of view, which experienced significant emissivity changes due to the motion of the sample.

Pixel-level mapping method in high dynamic range imaging system based on DMD modulation

In order to build pixel-to-pixel correspondence between the CCD camera and digital micromirror device (DMD) in high dynamic range (HDR) imaging system, we proposed an absolute phase mapping method based on the first partial derivatives of phase-shifted composite fringes in this paper. Compared with the conventional phase mapping method, the needed fringe patterns of our method are reduced by one time, which improves the mapping efficiency. Meanwhile, experimental results show the proposed method has an accuracy improvement over the existing methods. The root mean square error is within 0.11 pixels in both the horizontal and vertical directions, reaching the sub-pixel mapping accuracy and indicating the superiority of our method. Finally, we combined the proposed mapping method with the imaging system and achieved high dynamic range imaging by photographing the surface of highlighted object, which verified the validity and practicability of our method.

Image processing pipeline for the detection of blood flow through retinal vessels with subpixel accuracy in fundus images

Background and ObjectiveBlood flow detection through the retinal vessels is an essential step in diagnosing several eye diseases. It manifests itself as changes in vessel diameter in consecutive phases of blood flow. Previous studies focused mainly on determining retinal vessel diameter by the manual demarcation of vessel edges, which is time-consuming. As a result, only a few selected vessels were considered, which is not reliable. Such measurements are also prone to human errors and operator subjectivity, which additionally decreases their reliability. For these reasons, this paper proposes an automated pipeline to analyze the blood flow through retinal vessels. MethodsConvolutional neural networks were used for optic disc and vessel detection and full width at half maximum analysis used for vessel width assessment at the subpixel level. Measurements of the diameter were performed for five phases of the blood flow to all vessels at a particular distance derived from the optic disc size. We tested the approach on fundus images of five patients, with both eyes examined in each participant. The threshold for the detections of blood flow was when the retinal diameter vessel measurements were above the camera's resolution as compared among all 5 phases of blood flow. ResultsA total of 205 large caliber blood vessels were analyzed with blood flow detected in 18 retinal blood vessels. Conclusions Average vessel diameters derived from manual and automatic measurements differed on average by 4.96%. Average relative errors for single vessel measurements along the vessels range from 4.21 to 11.85%, with a global average at the level of 8%. Therefore, the measurements can be considered as accurate and in a high agreement between the expert and algorithm

A Scale and Rotational Invariant Key-point Detector based on Sparse Coding

Most popular hand-crafted key-point detectors such as Harris corner, SIFT, SURF aim to detect corners, blobs, junctions, or other human-defined structures in images. Though being robust with some geometric transformations, unintended scenarios or non-uniform lighting variations could significantly degrade their performance. Hence, a new detector that is flexible with context change and simultaneously robust with both geometric and non-uniform illumination variations is very desirable. In this article, we propose a solution to this challenging problem by incorporating Scale and Rotation Invariant design (named SRI-SCK) into a recently developed Sparse Coding based Key-point detector (SCK). The SCK detector is flexible in different scenarios and fully invariant to affine intensity change, yet it is not designed to handle images with drastic scale and rotation changes. In SRI-SCK, the scale invariance is implemented with an image pyramid technique, while the rotation invariance is realized by combining multiple rotated versions of the dictionary used in the sparse coding step of SCK. Techniques for calculation of key-points’ characteristic scales and their sub-pixel accuracy positions are also proposed. Experimental results on three public datasets demonstrate that significantly high repeatability and matching score are achieved.

Automatic Sub-Pixel Co-Registration of Remote Sensing Images Using Phase Correlation and Harris Detector

In this paper, we propose a new approach for sub-pixel co-registration based on Fourier phase correlation combined with the Harris detector. Due to the limitation of the standard phase correlation method to achieve only pixel-level accuracy, another approach is required to reach sub-pixel matching precision. We first applied the Harris corner detector to extract corners from both references and sensed images. Then, we identified their corresponding points using phase correlation between the image pairs. To achieve sub-pixel registration accuracy, two optimization algorithms were used. The effectiveness of the proposed method was tested with very high-resolution (VHR) remote sensing images, including Pleiades satellite images and aerial imagery. Compared with the speeded-up robust features (SURF)-based method, phase correlation with the Blackman window function produced 91% more matches with high reliability. Moreover, the results of the optimization analysis have revealed that Nelder–Mead algorithm performs better than the two-point step size gradient algorithm regarding localization accuracy and computation time. The proposed approach achieves better accuracy than 0.5 pixels and outperforms the speeded-up robust features (SURF)-based method. It can achieve sub-pixel accuracy in the presence of noise and produces large numbers of correct matching points.

Visual Object Tracking using Surface Fitting for Scale and Rotation Estimation

Since correlation filter appeared in the field of object tracking, it plays an increasingly vital role due to its excellent performance. Although many sophisticated trackers have been successfully applied to track the object accurately, very few of them attaches importance to the scale and rotation estimation. In order to address the above limitation, we propose a novel method combined with Fourier-Mellin transform and confidence evaluation strategy for robust object tracking. In the first place, we construct a correlation filter to locate the target object precisely. Then, a log-polar technique is used in the Fourier-Mellin transform to cope with the rotation and scale changes. In order to achieve subpixel accuracy, we come up with an efficient surface fitting mechanism to obtain the optimal calculation result. In addition, we introduce a confidence evaluation strategy modeled on the output response, which can decrease the impact of image noise and perform as a criterion to evaluate the target model stability. Experimental experiments on OTB100 demonstrate that the proposed algorithm achieves superior capability in success plots and precision plots of OPE, which is 10.8% points and 8.6% points than those of KCF. Besides, our method performs favorably against the others in terms of SRE and TRE validation schemes, which shows the superiority of our proposed algorithm in scale and rotation evaluation.

Multithreading Based Parallel Processing for Image Geometric Coregistration in SAR Interferometry

Within the framework of multi-temporal Synthetic Aperture Radar (SAR) interferometric processing, image coregistration is a fundamental operation that might be extremely time-consuming. This paper explores the possibility of addressing fast and accurate SAR image geometric coregistration, with sub-pixel accuracy and in the presence of a complex 3-D object scene, by exploiting the parallelism offered by shared-memory architectures. An efficient and scalable processor is proposed by designing a parallel algorithm incorporating thread-level parallelism for solving the inherent computationally intensive problem. The adopted functional scheme is first mathematically framed and then investigated in detail in terms of its computational structures. Subsequently, a parallel version of the algorithm is designed, according to a fork-join model, by suitably taking into account the granularity of the decomposition, load-balancing, and different scheduling strategies. The developed parallel algorithm implements parallelism at the thread-level by using OpenMP (Open Multi-Processing) and it is specifically targeted at shared-memory multiprocessors. The parallel performance of the implemented multithreading-based SAR image coregistration prototype processor is experimentally investigated and quantitatively assessed by processing high-resolution X-band COSMO-SkyMed SAR data and using two different multicore architectures. The effectiveness of the developed multithreaded prototype solution in fully benefitting from the computing power offered by multicore processors has successfully been demonstrated via a suitable experimental performance analysis conducted in terms of parallel speedup and efficiency. The demonstrated scalable performance and portability of the developed parallel processor confirm its potential for operational use in the interferometric SAR data processing at large scales.