Sub-pixel Accuracy Research Articles

A Statistical Variable Selection Solution for RFM Ill-Posedness and Overparameterization Problems

Parameters of a rational function model (RFM), known as rational polynomial coefficients, are commonly redundant and highly correlated, leading to the problems of overparameterization and ill-posedness, respectively. In this paper, an innovative two-stage statistical method, called an uncorrelated and statistically significant RFM (USS-RFM), is presented to deal directly with these two problems. In the first stage, the proposed method employs a novel correlation analysis, which aims to exclude highly correlated coefficients. In the second stage, a new iterative significance test is applied to detect and remove unnecessary coefficients from the RFM. The proposed method is implemented on eight real data sets captured by Cartosat-1, GeoEye-1, Pleiades, Spot-3, and WorldView-3 platforms. The results are evaluated in terms of the positioning accuracy, model degrees of freedom, processing time, and figure condition analysis. Experimental results prove the efficiency of the proposed method, showing that it could achieve subpixel accuracy even for cases with five ground control points. The proposed USS-RFM is compared to an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm regularization (L1R) technique and a particle swarm optimization (PSO) algorithm in the terrain-dependent case of the RFM. The results demonstrate the superiority of the USS-RFM, which performs better than the alternative methods in terms of positioning accuracy by more than 50% on average. Moreover, the RFMs resulted from the USS-RFM demonstrate to have higher degrees of freedom and, as a result, higher level of reliability. From the perspective of processing time, USS-RFM and L1R are similar while both are much faster than PSO.

Automatic sub-pixel coastline extraction based on spectral mixture analysis using EO-1 Hyperion data

Many megacities (such as Shanghai) are located in coastal areas, therefore, coastline monitoring is critical for urban security and urban development sustainability. A shoreline is defined as the intersection between coastal land and a water surface and features seawater edge movements as tides rise and fall. Remote sensing techniques have increasingly been used for coastline extraction; however, traditional hard classification methods are performed only at the pixel-level and extracting subpixel accuracy using soft classification methods is both challenging and time consuming due to the complex features in coastal regions. This paper presents an automatic sub-pixel coastline extraction method (ASPCE) from high-spectral satellite imaging that performs coastline extraction based on spectral mixture analysis and, thus, achieves higher accuracy. The ASPCE method consists of three main components: 1) A Water-Vegetation-Impervious-Soil (W-V-I-S) model is first presented to detect mixed W-V-I-S pixels and determine the endmember spectra in coastal regions; 2) The linear spectral mixture unmixing technique based on Fully Constrained Least Squares (FCLS) is applied to the mixed W-V-I-S pixels to estimate seawater abundance; and 3) The spatial attraction model is used to extract the coastline. We tested this new method using EO-1 images from three coastal regions in China: the South China Sea, the East China Sea, and the Bohai Sea. The results showed that the method is accurate and robust. Root mean square error (RMSE) was utilized to evaluate the accuracy by calculating the distance differences between the extracted coastline and the digitized coastline. The classifier’s performance was compared with that of the Multiple Endmember Spectral Mixture Analysis (MESMA), Mixture Tuned Matched Filtering (MTMF), Sequential Maximum Angle Convex Cone (SMACC), Constrained Energy Minimization (CEM), and one classical Normalized Difference Water Index (NDWI). The results from the three test sites indicated that the proposed ASPCE method extracted coastlines more efficiently than did the compared methods, and its coastline extraction accuracy corresponded closely to the digitized coastline, with 0.39 pixels, 0.40 pixels, and 0.35 pixels in the three test regions, showing that the ASPCE method achieves an accuracy below 12.0 m (0.40 pixels). Moreover, in the quantitative accuracy assessment for the three test sites, the ASPCE method shows the best performance in coastline extraction, achieving a 0.35 pixel-level at the Bohai Sea, China test site. Therefore, the proposed ASPCE method can extract coastline more accurately than can the hard classification methods or other spectral unmixing methods.

Improvement of the visibility of concealed features in misregistered NIR reflectograms by deep learning

Features of Old Master paintings hidden under the upper layer of a painting are often studied using NIR reflectograms; however their interpretability can be reduced due to the visible content. In our previous work [3] we described the possibility of increasing the visibility of concealed features in NIR reflectograms from the painting surface. The method output, enhanced NIR reflectogram, is produced by extrapolating the VIS data to a NIR range reflectogram and subtracting it from the acquired data in the NIR spectral subband. As a result, separated information from the NIR domain is obtiained. This method has a severe limitation, because it requires precise image registration of the VIS and NIR spectral bands. This is often hard to achieve, because DSLR cameras or multiple devices with various optical systems are used for data collection, and the mutual spatial relation of the images is often unknown. Thus, in the original form, the algorithm was applicable only for data acquired using special scanners producing spatially registered images (as in [4]). In this work, we present an extension of the previous algorithm inspired by deep learning. The new concept allows processing of images only partially registered with pixel precision; subpixel accuracy is no longer needed. We suggest an extension of neural network input with neighboring pixels and allocation of extra ANN layers for translation compensation. The results are demonstrated on misregistered images captured by DSLR camera in VIS and NIR.

SUB-PIXEL ACCURACY CRACK WIDTH DETERMINATION ON CONCRETE BEAMS IN LOAD TESTS BY TRIANGLE MESH GEOMETRY ANALYSIS

Abstract. This paper deals with the determination of crack widths of concrete beams during load tests from monocular image sequences. The procedure starts in a reference image of the probe with suitable surface texture under zero load, where a large number of points is defined by an interest operator. Then a triangulated irregular network is established to connect the points. Image sequences are recorded during load tests with the load increasing continuously or stepwise, or at intermittently changing load. The vertices of the triangles are tracked through the consecutive images of the sequence with sub-pixel accuracy by least squares matching. All triangles are then analyzed for changes by principal strain calculation. For each triangle showing significant strain, a crack width is computed by a thorough geometric analysis of the relative movement of the vertices.

Fast Tracking of Fluid Invasion Using Time-Resolved Neutron Tomography

Water flow in a sandstone sample is studied during an experiment in situ in a neutron tomography setup. In this paper, a projection-based methodology for fast tracking of the imbibition front in 3D is presented. The procedure exploits each individual neutron 2D radiograph, instead of the tomographic-reconstructed images, to identify the 4D (space and time) saturation field, offering a much higher time resolution than more standard reconstruction-based methods. Based on strong space and time regularizations of the fluid flow, with an a priori defined space and time shape functions, the front shape is identified at each projection time step. This procedure aiming at a fast tracking the fluid advance is explored through two examples. The first one shows that the fluid motion that occurs during one single 180 $$^{^{\circ }}$$ scan can be resolved at 5 Hz with a sub-pixel accuracy whereas it cannot be unraveled with plain tomographic reconstruction. The second example is composed of 42 radiographs acquired all along a complete fluid invasion in the sample. This experiment uses the very same approach with the additional difficulty of large fluid displacement in between two projections. As compared to the classical approach based on full reconstructions at each invasion stage, the proposed methodology in the studied examples is roughly 300 times faster offering an enhanced time resolution.

Comparison of Stochastic Gradient-Based Optimization Techniques for Nonlinear Satellite Image Coregistration Problem

Information-oriented intensity-based cost functions are generally used for optimization frameworks in automatic satellite image registration. Optimization mechanics which updates the transform parameters in the iterative loop requires estimation of derivatives of the cost function to set-up update rules that retrieve the deformation model between the image pairs. Application of stochastic approximation of cost function and its derivatives for solving optimization problems while the objective function is non-differentiable or non-smooth or computed with noise is encountered in real-world problems. The known methods of approximation for solving these problems use the idea of stochastic gradient and certain rules of changing the step length for ensuring convergence. In this article, satellite image coregistration problem is chosen for comparing the performance of two important stochastic optimizers like adaptive stochastic gradient descent and simultaneous perturbation stochastic approximation. Coregistration datasets from Resourcesat-2 LISS-4 MX sensor are chosen for different terrains and features to study subpixel accuracies of order better than 1/20th of a pixel achieved in the comparison of two different optimization techniques employed in intensity-based automatic image registration framework.

Measurement uncertainty of IR thermographic flow visualization measurements for transition detection on wind turbines in operation

The application of thermographic flow visualization on wind turbines in operation differs from the well-established application in wind tunnel experiments. The necessary temperature difference between the rotor blade and the flow only relies on the absorbed solar radiation, which often leads to a low signal-to-noise ratio. Furthermore, a large distance of up to 400 m exists between the rotor blade and the thermographic camera for ground based measurements, mainly due to the height of the wind turbine. This results in a poor spatial resolution as well as a small numerical aperture, which means a small detectable radiant power further degrades the signal-to-noise ratio. In order to determine the limits of measurability for the localization of the laminar-turbulent transition, the fundamental effects on the measurement uncertainty are investigated. For this purpose, the measurement uncertainty budgets for three signal processing algorithms are derived and validated with wind tunnel experiments and field measurements on a 1.5 MW wind turbine under sunny and cloudy weather conditions. As a result, the achievable standard uncertainty of the laminar-turbulent transition position for a temperature difference of 2 K amounts to 0.16 pixels in this case, which corresponds to 0.17% chord length. In addition, the measurement uncertainty is currently not limited by the measurement system (detector noise and fixed pattern noise of the camera), but by flow induced temperature fluctuations and fluctuations of the laminar-turbulent transition position itself. Hence, the field measurements on wind turbines in operation are still limited by the flow characteristics, i.e., the measurement object itself. Finally, one of the presented signal processing methods allows a robust, automated flow characterization for wind turbines in operation with subpixel accuracy in all of the presented measurements.

ILLUMINATION INVARIANT CHANGE DETECTION (IICD): FROM EARTH TO MARS

Abstract. Multi-temporal Earth Observation and Mars orbital imagery data with frequent repeat coverage provide great capability for planetary surface change detection. When comparing two images taken at different times of day or in different seasons for change detection, the variation of topographic shades and shadows caused by the change of sunlight angle can be so significant that it overwhelms the real object and environmental changes, making automatic detection unreliable. An effective change detection algorithm therefore has to be robust to the illumination variation. This paper presents our research on developing and testing an Illumination Invariant Change Detection (IICD) method based on the robustness of phase correlation (PC) to the variation of solar illumination for image matching. The IICD is based on two key functions: i) initial change detection based on a saliency map derived from pixel-wise dense PC matching and ii) change quantization which combines change type identification, motion estimation and precise appearance change identification. Experiment using multi-temporal Landsat 7 ETM+ satellite images, Rapid eye satellite images and Mars HiRiSE images demonstrate that our frequency based image matching method can reach sub-pixel accuracy and thus the proposed IICD method can effectively detect and precisely segment large scale change such as landslide as well as small object change such as Mars rover, under daily and seasonal sunlight changes.

Global DEMs to tackle RPC biases and the overfitting phenomenon in high-resolution satellite imagery

ABSTRACTThe overfitting phenomenon and rational polynomial coefficients (RPCs) biases are two crucial issues that degrade the accuracy of geospatial products derived from high-resolution satellite images. The overfitting phenomenon is caused by both a large number of RPCs and strong correlations among them. The RPC biases arise from uncertainties in the global positioning system receivers and inertial measurement units. In this article, an innovative framework based on the genetic algorithm (GA) and the least squares (LS) algorithm, called GALS, is proposed to overcome these problems simultaneously. In this method, the GA is applied to select the optimum RPCs, while the LS algorithm is used to estimate the values of the optimally selected RPCs. The GALS method requires various sets of well-distributed ground control points (GCPs). To tackle the problem of GCP collection, we generated a large number of digital elevation model (DEM)-derived GCPs (DEMGCPs), using a global DEM (GDEM) and vendor-provided RPCs, refined by only one GCP. To evaluate the performance of this framework, four IRS-P5 data sets were used. The GALS is compared to two competing methods, L1-norm-regularized LS and ridge estimation by considering two scenarios using 50 GCPs and the DEMGCPs. The results demonstrate the superiority of GALS in both scenarios. Furthermore, GALS using DEMGCPs led to far more accurate and stable results when compared to GALS using GCPs. Compared to the vendor-provided RPCs, the results of the GALS using DEMGCPs also indicate a major improvement, single-pixel or subpixel accuracy with around 15 RPCs, and only 1 GCP, in both accuracy and reliability of georeferencing for all IRS-P5 data sets.

Camera Calibration with Phase-Shifting Wedge Grating Array

Planar targets with known features have been widely used for camera calibration in various vision systems. This paper utilizes phase-shifting wedge grating (PWG) arrays as an active calibration target. Features points are encoded into the carrier phase, which can be accurately calculated using the phase-shifting algorithm. The 2π-phase points are roughly extracted with edge detection and then optimized by windowed bicubic fitting with sub-pixel accuracy. Two 2π-phase lines for each PWG are obtained using linear fitting method. The PWG centers that are used as feature points are detected through computing the intersections of 2π-phase lines. Experiment results indicate that the proposed method is accurate and reliable.

Lateral position correction in ptychography using the gradient of intensity patterns

Ptychography, a form of Coherent Diffractive Imaging, is used with short wavelengths (e.g. X-rays, electron beams) to achieve high-resolution image reconstructions. One of the limiting factors for the reconstruction quality is the accurate knowledge of the illumination probe positions. Recently, many advances have been made to relax the requirement for the probe positions accuracy. Here, we analyse and demonstrate a straightforward approach that can be used to correct the probe positions with sub-pixel accuracy. Simulations and experimental results with visible light are presented in this work.

An automatic optimum number of well-distributed ground control lines selection procedure based on genetic algorithm

The procedure of selecting an optimum number and best distribution of ground control information is important in order to reach accurate and robust registration results. This paper proposes a new general procedure based on Genetic Algorithm (GA) which is applicable for all kinds of features (point, line, and areal features). However, linear features due to their unique characteristics are of interest in this investigation. This method is called Optimum number of Well-Distributed ground control Information Selection (OWDIS) procedure. Using this method, a population of binary chromosomes is randomly initialized. The ones indicate the presence of a pair of conjugate lines as a GCL and zeros specify the absence. The chromosome length is considered equal to the number of all conjugate lines. For each chromosome, the unknown parameters of a proper mathematical model can be calculated using the selected GCLs (ones in each chromosome). Then, a limited number of Check Points (CPs) are used to evaluate the Root Mean Square Error (RMSE) of each chromosome as its fitness value. The procedure continues until reaching a stopping criterion. The number and position of ones in the best chromosome indicate the selected GCLs among all conjugate lines. To evaluate the proposed method, a GeoEye and an Ikonos Images are used over different areas of Iran. Comparing the obtained results by the proposed method in a traditional RFM with conventional methods that use all conjugate lines as GCLs shows five times the accuracy improvement (pixel level accuracy) as well as the strength of the proposed method. To prevent an over-parametrization error in a traditional RFM due to the selection of a high number of improper correlated terms, an optimized line-based RFM is also proposed. The results show the superiority of the combination of the proposed OWDIS method with an optimized line-based RFM in terms of increasing the accuracy to better than 0.7 pixel, reliability, and reducing systematic errors. These results also demonstrate the high potential of linear features as reliable control features to reach sub-pixel accuracy in registration applications.

Digital Speckle Photography of Subpixel Displacements of Speckle Structures Based on Analysis of Their Spatial Spectra

We have investigated the capabilities of the method of digital speckle interferometry for determining subpixel displacements of a speckle structure formed by a displaceable or deformable object with a scattering surface. An analysis of spatial spectra of speckle structures makes it possible to perform measurements with a subpixel accuracy and to extend the lower boundary of the range of measurements of displacements of speckle structures to the range of subpixel values. The method is realized on the basis of digital recording of the images of undisplaced and displaced speckle structures, their spatial frequency analysis using numerically specified constant phase shifts, and correlation analysis of spatial spectra of speckle structures. Transformation into the frequency range makes it possible to obtain quantities to be measured with a subpixel accuracy from the shift of the interference-pattern minimum in the diffraction halo by introducing an additional phase shift into the complex spatial spectrum of the speckle structure or from the slope of the linear plot of the function of accumulated phase difference in the field of the complex spatial spectrum of the displaced speckle structure. The capabilities of the method have been investigated in natural experiment.

High Precision Edge Detection Algorithm for Mechanical Parts

Abstract High precision and high efficiency measurement is becoming an imperative requirement for a lot of mechanical parts. So in this study, a subpixel-level edge detection algorithm based on the Gaussian integral model is proposed. For this purpose, the step edge normal section line Gaussian integral model of the backlight image is constructed, combined with the point spread function and the single step model. Then gray value of discrete points on the normal section line of pixel edge is calculated by surface interpolation, and the coordinate as well as gray information affected by noise is fitted in accordance with the Gaussian integral model. Therefore, a precise location of a subpixel edge was determined by searching the mean point. Finally, a gear tooth was measured by M&amp;M3525 gear measurement center to verify the proposed algorithm. The theoretical analysis and experimental results show that the local edge fluctuation is reduced effectively by the proposed method in comparison with the existing subpixel edge detection algorithms. The subpixel edge location accuracy and computation speed are improved. And the maximum error of gear tooth profile total deviation is 1.9 μm compared with measurement result with gear measurement center. It indicates that the method has high reliability to meet the requirement of high precision measurement.

Influence of reconstruction scale, spatial resolution and pixel spatial relationships on the sub-pixel mapping accuracy of a double-calculated spatial attraction model

Mixed pixels universally exist in remote sensing images, and they are one of the main obstacles for further improving the accuracy of land cover recognition and classification. Since the concept of sub-pixel mapping (SPM) is proposed, SPM technology has rapidly become an important method to solve the problem of mixed pixels. To further improve SPM accuracy, this paper first proposes a double-calculated spatial attraction model (DSAM) combining the advantages of the spatial attraction model (SAM) and the pixel swap model (PSM). Then, based on the full validation of the proposed DSAM, how multiple factors affect the SPM accuracy is analyzed using the multispectral remote sensing (MRS) images. Finally, by analyzing the maximum variations in the ranges of the overall accuracy and the kappa coefficient under different multiple factors, the order of factors influencing SPM accuracy is determined as follows: reconstruction scale > image spatial resolution > pixel spatial relationships. The results can serve as a reference for other scholars in setting model parameters and selecting the appropriate remote sensing data, thereby helping them achieve more accurate SPM results.

Towards breaking the spatial resolution barriers: An optical flow and super-resolution approach for sea ice motion estimation

Estimation of sea ice motion at fine scales is important for a number of regional and local level applications, including modeling of sea ice distribution, ocean-atmosphere and climate dynamics, as well as safe navigation and sea operations. In this study, we propose an optical flow and super-resolution approach to accurately estimate motion from remote sensing images at a higher spatial resolution than the original data. First, an external example learning-based super-resolution method is applied on the original images to generate higher resolution versions. Then, an optical flow approach is applied on the higher resolution images, identifying sparse correspondences and interpolating them to extract a dense motion vector field with continuous values and subpixel accuracies. Our proposed approach is successfully evaluated on passive microwave, optical, and Synthetic Aperture Radar data, proving appropriate for multi-sensor applications and different spatial resolutions. The approach estimates motion with similar or higher accuracy than the original data, while increasing the spatial resolution of up to eight times. In addition, the adopted optical flow component outperforms a state-of-the-art pattern matching method. Overall, the proposed approach results in accurate motion vectors with unprecedented spatial resolutions of up to 1.5 km for passive microwave data covering the entire Arctic and 20 m for radar data, and proves promising for numerous scientific and operational applications.

Physical, spectral, and dynamical properties of asteroid (107) Camilla and its satellites

The population of large 100+ km asteroids is thought to be primordial. As such, they are the most direct witnesses of the early history of our Solar System available. Those among them with satellites allow study of the mass, and hence density and internal structure. We study here the dynamical, physical, and spectral properties of the triple asteroid (107) Camilla from lightcurves, stellar occultations, optical spectroscopy, and high-contrast and high-angular-resolution images and spectro-images.Using 80 positions measured over 15 years, we determine the orbit of its larger satellite, S/2001 (107) 1, to be circular, equatorial, and prograde, with root-mean-square residuals of 7.8 mas, corresponding to a sub-pixel accuracy. From 11 positions spread over three epochs only, in 2015 and 2016, we determine a preliminary orbit for the second satellite S/2016 (107) 1. We find the orbit to be somewhat eccentric and slightly inclined to the primary’s equatorial plane, reminiscent of the properties of inner satellites of other asteroid triple systems. Comparison of the near-infrared spectrum of the larger satellite reveals no significant difference with Camilla. Hence, both dynamical and surface properties argue for a formation of the satellites by excavation from impact and re-accumulation of ejecta in orbit.We determine the spin and 3-D shape of Camilla. The model fits well each data set: lightcurves, adaptive-optics images, and stellar occultations. We determine Camilla to be larger than reported from modeling of mid-infrared photometry, with a spherical-volume-equivalent diameter of 254 ± 36 km (3σuncertainty), in agreement with recent results from shape modeling (Hanus et al., 2017, A&A 601). Combining the mass of (1.12 ± 0.01) × 1019 kg (3σuncertainty) determined from the dynamics of the satellites and the volume from the 3-D shape model, we determine a density of 1,280 ± 130 kg · m−3 (3 σ uncertainty). From this density, and considering Camilla’s spectral similarities with (24) Themis and (65) Cybele (for which water ice coating on surface grains was reported), we infer a silicate-to-ice mass ratio of 1–6, with a 10–30% macroporosity.

Registration for images in the presence of additive and multiplicative fixed-pattern noise.

Image registration under conditions of fixed-pattern noise is a difficult problem that has not been solved in the literature. While traditional registration methods are adequate for additive random noise, these are not suited to spatially invariant noise that is additive or multiplicative. We present a method for image registration using a difference operation in the frequency domain. Shift values are then computed by dividing by the object Fourier transform and inverse transforming. The method described is valid for both additive and multiplicative noise and determines shifts with sub-pixel accuracy. Additionally, minimal prior knowledge of the corrupting pattern is required. We compare our method with previous registration methods for varying amounts of noise. Results are presented for both simulated images and images recorded from a thermal camera with significant fixed-pattern noise.

PMSC: PatchMatch-Based Superpixel Cut for Accurate Stereo Matching

Estimating the disparity and normal direction of one pixel simultaneously, instead of only disparity, also known as 3D label methods, can achieve much higher subpixel accuracy in the stereo matching problem. However, it is extremely difficult to assign an appropriate 3D label to each pixel from the continuous label space R3 while maintaining global consistency because of the infinite parameter space. In this paper, we propose a novel algorithm called PatchMatch-based superpixel cut to assign 3D labels of an image more accurately. In order to achieve robust and precise stereo matching between local windows, we develop a bilayer matching cost, where a bottom-up scheme is exploited to design the two layers. The bottom layer is employed to measure the similarity between small square patches locally by exploiting a pretrained convolutional neural network, and then, the top layer is developed to assemble the local matching costs in large irregular windows induced by the tangent planes of object surfaces. To optimize the spatial smoothness of local assignments, we propose a novel strategy to update 3D labels. In the procedure of optimization, both segmentation information and random refinement of PatchMatch are exploited to update candidate 3D label set for each pixel with high probability of achieving lower loss. Since pairwise energy of general candidate label sets violates the submodular property of graph cut, we propose a novel multilayer superpixel structure to group candidate label sets into candidate assignments, which thereby can be efficiently fused by α-expansion graph cut. Extensive experiments demonstrate that our method can achieve higher subpixel accuracy in different data sets, and currently ranks first on the new challenging Middlebury 3.0 benchmark among all the existing methods.

Parametric Evaluation of Errors Using Isolated Dots for Movement Measurement by Image Cross-Correlation.

Digital Image Correlation (DIC) is a common tool for assessing the movement of objects in a scene. Among others, one of the most popular techniques consists of tracking a dotted texture imitating speckle patterns. In this work, we analyzed the individual dots that form this pattern in order to propose an optimum size, shape, and dynamic range that allows minimizing the tracking error. Tracking was accomplished by using normalized cross-correlation with peak interpolation in order to obtain subpixel accuracy. For the models here used, we show that dot radii of 30–40 px with 150 gray levels are enough to obtain an accurate subpixel tracking resolution. Also, we show that 0.002 px is the performance limit of this technique, being this limit in accordance with the experimentally achievable subpixel limit.