Geometric Correction Research Articles

Partial volume correction for Lu-177-PSMA SPECT.

The limited spatial resolution in SPECT images leads to partial volume effect (PVE), degrading the subsequent dosimetric accuracy. We aim to quantitatively evaluate PVE and partial volume corrections (PVC), i.e., recovery coefficient (RC)-PVC (RC-PVC), reblurred Van-Cittert (RVC) and iterative Yang (IY), in 177Lu-PSMA-617 SPECT images. We employed a geometrical cylindrical phantom containing five spheres (diameters ranging from 20 to 40mm) and 40 XCAT phantoms with various anatomical variations and activity distributions. SIMIND Monte Carlo code was used to generate realistic noisy projections. In the clinical study, sequential quantitative SPECT/CT imaging at 4 time-points post 177Lu-PSMA-617 injections were analyzed for 10 patients. Iterative statistical reconstruction methods were used for reconstruction with attenuation, scatter and geometrical collimator detector response corrections, followed by post-filters. The RC-curves were fit based on the geometrical phantom study and applied for XCAT phantom and clinical study in RC-PVC. Matched and 0.5-2.0 voxels (2.54-10.16mm) mismatched sphere masks were deployed in IY. The coefficient of variation (CoV) was measured on a uniform background on the geometrical phantom. RCs of spheres and mean absolute activity error (MAE) of kidneys and tumors were evaluated in simulation data, while the activity difference was evaluated in clinical data before and after PVC. In the simulation study, the spheres experienced significant PVE, i.e., 0.26 RC and 0.70 RC for the 20mm and 40mm spheres, respectively. RVC and IY improved the RC of the 20mm sphere to 0.37 and 0.75 and RC of the 40mm sphere to 0.96 and 1.04. Mismatch in mask increased the activity error for all spheres in IY. RVC increased noise and caused Gibbs ringing artifacts. For XCAT phantoms, both RVC and IY performed comparably and were superior to RC-PVC in reducing the MAE of the kidneys. However, IY and RC-PVC outperformed RVC for tumors. The XCAT phantom study and clinical study showed a similar trend in the kidney and tumor activity differences between non-PVC and PVC. PVE greatly impacts activity quantification, especially for small objects. All PVC methods improve the quantification accuracy in 177Lu-PSMA SPECT.

Prediction of the sound transmission loss of shape-varied sonic crystals: A transfer matrix approach.

This paper proposes a transfer matrix method (TMM) for modeling sonic crystals to predict the transmission loss of noise exiting an air extraction system. Because the crystals may be of different shapes (e.g., square, circular, or standardized airfoil profile to minimize airflow resistance) and must account for thermo-viscous losses, a discrete version of the TMM is used. Similar to the finite element method, a discretization of the geometry is first performed. Each element is modeled with a transfer matrix (TM) that includes the local thermo-viscous losses which attenuate the sound wave. For each element in parallel, the parallel TMM is employed. For the subsequently created elements in series, the classic TMM is used. This generates a global TM from which the sound transmission loss of the crystal network is deduced. The predictions obtained by the proposed method are compared to measurements in an acoustic tube for three different shapes of sonic crystals. The results show that a geometric tortuosity correction is necessary for the predicted bandgap center frequency to match the measurement. A correction is proposed, but this requires a possible refinement for more complicated profiles.

Sub-modelling based fatigue evaluation of welded details in composite trapezoidal corrugated web girders under coupled thermal-structural loading

Exploring the long-term performance of welded details in composite trapezoidal corrugated web (TCW) girders is a significant focus for the service life of these structures exposed to atmospheric environment and traffic flow. The majority of the present studies have been conducted without accounting for thermal stresses induced by temperature differences and accurately reflecting internal force transfers for the composite girders in flexural bending. The fatigue behaviour of the welded details in these girders under coupled thermal-structural loading is investigated herein through experimental and numerical methods. The results indicated three stages for the structural degradation from the test performance and justified a proper allowance of the cross-sectional stress in coordination with the flexural curvature in the derivation of S-N relations comparable to similar details in related design codes. A sub-modelling procedure is implemented to capture the thermal gradient, the local stress concentration, and the crack distribution in global modelling while replicate the semi-elliptical surface crack at the external side of the fillet weld toe in local modelling. The fatigue lives predicted from the proposed analytical model match reasonably well with experimental and numerical results, indicating its good applicability incorporating characteristic geometric correction factors into classical theoretical calculation for fatigue evaluation.

Effective stress intensity factor range for fatigue cracks propagating in mixed mode I-II loading

The actual service axles are often subjected to mixed-mode loading, and predicting the mixed-mode I-II crack propagation behaviour using the mode I effective stress intensity factor (ΔKI) differs from the real service conditions. To effectively predict the fatigue crack propagation behaviour of actual service structures, the I-II stress intensity factor range (ΔKP-R) considering two closure effects was adopted to describe the fatigue crack propagation under mixed mode loading. A test database was established based on monitoring data of mode I and mixed-mode I-II (30/45/60°) crack propagation tests under different stress ratios. Combining domain knowledge and symbolic regression (SR) methods, an angle factor was proposed for constructing correlation functions between ΔKI and ΔKP-R. The results showed that the loading angle (α) only affects the initial projection of the load parallel and perpendicular to the fatigue crack growth (FCG) direction. Compared with the geometric correction factor, the correlation function acquired by the angle factor constructed by the SR method has higher accuracy, and the balance parameters (SCORE) obtained by the former are significantly higher than those obtained by the latter under the same function complexity. The SR verification results demonstrated that constructing mode I and I-II correlation functions with angle factors has a good predictive effect.

Fractional Einstein–Gauss–Bonnet Scalar Field Cosmology

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss–Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and α0=t0H0 and the fractional derivative order μ. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss–Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss–Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and α0, indicating that the solution is consistent with an accelerated expansion at late times with the values α0=1.38±0.05, m=1.44±0.05, and μ=1.48±0.17 (consistent with Ωm,0=0.311±0.016 and h=0.712±0.007), resulting in an age of the Universe t0=19.0±0.7 [Gyr] at 1σ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than ΛCDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.

Visualizing Plant Responses: Novel Insights Possible Through Affordable Imaging Techniques in the Greenhouse.

Efficient and affordable plant phenotyping methods are an essential response to global climatic pressures. This study demonstrates the continued potential of consumer-grade photography to capture plant phenotypic traits in turfgrass and derive new calculations. Yet the effects of image corrections on individual calculations are often unreported. Turfgrass lysimeters were photographed over 8 weeks using a custom lightbox and consumer-grade camera. Subsequent imagery was analyzed for area of cover, color metrics, and sensitivity to image corrections. Findings were compared to active spectral reflectance data and previously reported measurements of visual quality, productivity, and water use. Results confirm that Red-Green-Blue imagery effectively measures plant treatment effects. Notable correlations were observed for corrected imagery, including between yellow fractional area with human visual quality ratings (r = -0.89), dark green color index with clipping productivity (r = 0.61), and an index combination term with water use (r = -0.60). The calculation of green fractional area correlated with Normalized Difference Vegetation Index (r = 0.91), and its RED reflectance spectra (r = -0.87). A new chromatic ratio correlated with Normalized Difference Red-Edge index (r = 0.90) and its Red-Edge reflectance spectra (r = -0.74), while a new calculation correlated strongest to Near-Infrared (r = 0.90). Additionally, the combined index term significantly differentiated between the treatment effects of date, mowing height, deficit irrigation, and their interactions (p < 0.001). Sensitivity and statistical analyses of typical image file formats and corrections that included JPEG, TIFF, geometric lens distortion correction, and color correction were conducted. Findings highlight the need for more standardization in image corrections and to determine the biological relevance of the new image data calculations.

Geometric and topological corrections to Schwarzschild black hole

In this paper, we compute departures in the black hole thermodynamics induced by either geometric or topological corrections to general relativity. Specifically, we analyze the spherically symmetric spacetime solutions of two modified gravity scenarios with Lagrangians L∼R1+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {L}\\sim R^{1+\\epsilon }$$\\end{document} and L∼R+ϵG2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {L}\\sim R+\\epsilon \\, \\mathcal {G}^2$$\\end{document}, where G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document} is the Euler density in four dimensions, while 0<ϵ≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 0<\\epsilon \\ll 1$$\\end{document} measures the perturbation around the Hilbert–Einstein action. Accordingly, we find the expressions of the Bekenstein–Hawking entropy by the Penrose formula, and the black hole temperature and horizon of the obtained solutions. We then investigate the heat capacities in terms of the free parameters of the theories under study. In doing so, we show that healing the problem of negative heat capacities can be possible under particular choices of the free constants, albeit with limitations on the masses allowed for the black hole solutions.

Exploring the Use of Fengyun-3 Meteorological Satellite for Monitoring Sea Ice to Provide Services for Polar Navigation

This paper explores the feasibility and effectiveness of using the Fengyun-3 meteorological satellite to monitor sea ice, providing services for ships navigating in polar regions. Firstly, it analyzes the impact of Arctic sea ice changes on ship navigation and the importance of sea ice monitoring in route planning. Next, it provides a detailed introduction to the data sources and processing methods of the Fengyun-3 satellite, including radiometric calibration, geometric correction, image registration, and cropping. Subsequently, it discusses the characteristics of sea ice in the visible spectrum and successfully extracts sea ice information using MERSI-II data with land, cloud, and seawater masking techniques. The study indicates that the comprehensive use of multi-spectral data and other observation methods can significantly enhance sea ice monitoring capabilities. In the future, integrating more advanced technologies is expected to achieve refined identification and short-term prediction of sea ice movement, thereby providing more scientific and efficient support for ships navigating in polar regions, enhancing navigation safety and efficiency, and offering a scientific basis for the development of Arctic shipping routes.

Thermal Infrared Orthophoto Geometry Correction Using RGB Orthophoto for Unmanned Aerial Vehicle

The geometric correction of thermal infrared (TIR) orthophotos generated by unmanned aerial vehicles (UAVs) presents significant challenges due to low resolution and the difficulty of identifying ground control points (GCPs). This study addresses the limitations of real-time kinematic (RTK) UAV data acquisition, such as network instability and the inability to detect GCPs in TIR images, by proposing a method that utilizes RGB orthophotos as a reference for geometric correction. The accelerated-KAZE (AKAZE) method was applied to extract feature points between RGB and TIR orthophotos, integrating binary descriptors and absolute coordinate-based matching techniques. Geometric correction results demonstrated a significant improvement in regions with stable and changing environmental conditions. Invariant regions exhibited an accuracy of 0.7~2 px (0.01~0.04), while areas with temporal and spatial changes saw corrections within 5~7 px (0.10~0.14 m). This method reduces reliance on GCP measurements and provides an effective supplementary technique for cases where GCP detection is limited or unavailable. Additionally, this approach enhances time and economic efficiency, offering a reliable alternative for precise orthophoto generation across various sensor data.

Image Matching for Multi spectral Image Satellite SIFT and Features

Abstract The Matching and registration of the satellite imagery play an essential role in many remote sensing and image processing applications. Certain steps, such as analysis of broad regions of interest and for the remotely detection. Pixel values in two or more images were play an important role in matching and detection algorithms between two or more images. In this work an image registration process (detection, extract and matching features) were utilized through using the sift algorithm to registration two image that have different resolutions (Landsat (30m) and Sentinel (10m)) utilize MATLAB program. A geometric correction was applied in this work for detect a correct points between these images. The results shows a corresponding between these two images. A preprocessing were utilized in good identifying features and accuracy of extracting information from satellite images.

A study in enhancement of satellite images

Satellite image enhancement is the method, which is commonly used in the field of satellite image processing for the betterment of the feature visualization and for clear visibility to properly identify those features. These satellite images have many atmospheric barriers like distortion and noise because they are captured from a very high and far distance. After the image capturing, some geometric corrections and radiometric corrections are carried out on those images, but these corrections are not enough for all the applications. So, it is needed to enhance the image restored before using it for feature identification. Nowadays, there are so many approaches for assuring effective image enhancement. However, there are so many drawbacks that need to be addressed in future. Hence, this article illustrates a clear and elaborate survey of various research articles presenting satellite image enhancement methods, such as machine learning-based techniques, optimization-based techniques, wavelet-based techniques, filter-based techniques and Histogram equalization-based techniques. Finally, the analysis is given in the survey based on the classification of research methods, publication year, utilized datasets and performance measures towards enhancement of satellite images. At last, issues and research gaps in methods are given in such a way that the motivation for developing an effective method for enabling effective enhancement is revealed.

Enhancing wind turbine load response tool through geometric non-linearities correction: Case study on DEFlex and design load comparison

This paper introduces a rapid correction technique applied in DEFlex, Ørsted’s in-house aero-servo-hydro-elastic solver for offshore wind turbines. The technique addresses geometric non-linearities from large wind turbine blade deflections, focusing specifically on correcting the angle of attack for torsional deflections. To assess the implementation, comparisons were made with the literature and HAWC2, using the IEA 15-MW wind turbine blade subjected to static and simplified dynamic loading. Additionally, simulations of normal operation scenarios, both with and without turbulence, were performed on a real wind turbine exceeding 10 MW rated power. The results were compared with Siemens Gamesa Renewable Energys tool BHawC, which utilizes a co-rotational formulation for capturing large blade deflections. The findings reveal that coupling DEFlex with the correction method accurately captures the angle of attack dynamics and significantly improves the agreement of fatigue loads.

Geometric correction of cone beam computed laminography based on projected address translation

Precise alignment of the system scan geometry is crucial to the reconstruction quality of computed laminography (CL). Different from computed tomography (CT), a challenging task for CL image reconstruction is to deal with rotational axes that are no longer symmetrical. In this paper, we take advantage of the fact that the difference between the inverse of the projected transverse coordinates of two points rotated about the axis of rotation under the CL scan geometry sums to zero when the projection angle differs by 180 deg. Based on this fact, the projection data under the scanned geometry with errors are aligned to the theoretical projection geometry. To validate this calibration method, a numerical printed circuit board (PCB) phantom was simulated. The results demonstrate that this method is capable of achieving high accuracy compared to the previous methods. The experimental results on printed circuit boards (PCB) demonstrate that the method can effectively improve geometric alignment accuracy of CL and obtain high-resolution reconstructed images.

Automated confidence estimation in deep learning auto-segmentation for brain organs at risk on MRI for radiotherapy.

We have built a novel AI-driven QA method called AutoConfidence (ACo), to estimate segmentation confidence on a per-voxel basis without gold standard segmentations, enabling robust, efficient review of automated segmentation (AS). We have demonstrated this method in brain OAR AS on MRI, using internal and external (third-party) AS models. Thirty-two retrospectives, MRI planned, glioma cases were randomly selected from a local clinical cohort for ACo training. A generator was trained adversarialy to produce internal autosegmentations (IAS) with a discriminator to estimate voxel-wise IAS uncertainty, given the input MRI. Confidence maps for each proposed segmentation were produced for operator use in AS editing and were compared with "difference to gold-standard" error maps. Nine cases were used for testing ACo performance on IAS and validation with two external deep learning segmentation model predictions [external model with low-quality AS (EM-LQ) and external model with high-quality AS (EM-HQ)]. Matthew's correlation coefficient (MCC), false-positive rate (FPR), false-negative rate (FNR), and visual assessment were used for evaluation. Edge removal and geometric distance corrections were applied to achieve more useful and clinically relevant confidence maps and performance metrics. ACo showed generally excellent performance on both internal and external segmentations, across all OARs (except lenses). MCC was higher on IAS and low-quality external segmentations (EM-LQ) than high-quality ones (EM-HQ). On IAS and EM-LQ, average MCC (excluding lenses) varied from 0.6 to 0.9, while average FPR and FNR were ≤0.13 and ≤0.21, respectively. For EM-HQ, average MCC varied from 0.4 to 0.8, while average FPR and FNR were ≤0.37 and ≤0.22, respectively. ACo was a reliable predictor of uncertainty and errors on AS generated both internally and externally, demonstrating its potential as an independent, reference-free QA tool, which could help operators deliver robust, efficient autosegmentation in the radiotherapy clinic.

Impact of geometric correction on echo-planar imaging-based apparent diffusion coefficient maps for abdominal radiotherapy

Objective. The apparent diffusion coefficient (ADC) extracted from diffusion-weighted magnetic resonance imaging (DWI) is a potential biomarker in radiotherapy (RT). DWI is often implemented with an echo-planar imaging (EPI) read-out due to speed, but unfortunately low geometric accuracy follows. This study aimed to investigate the influence of geometric distortions on the ADCs extracted from the gross tumor volume (GTV) and on the shape of the GTV in abdominal EPI-DWI. Approach. Twenty-one patients had EPI-DWI scans on a 1.5 T MRI sim before treatment and on a 1.5 T MRI-Linac at one of the first treatment fractions. Off-resonance correction with and without eddy current correction were applied to ADC maps. The clinical GTVs were deformed based on the same (but inverted) corrections to assess the local-regional geometric influence of distortions. Mean surface distance (MSD), Hausdorff distance (HD), and Dice similarity coefficient (DSC) were calculated to compare the original and distorted GTVs, and ADC values were calculated based on a mono-exponential model. Phantom measurements were performed to validate the applied correction method. Main results. The median (range) ADC change within the GTV after full distortion correction was 1.3% (0.02%–6.9%) for MRI-Sim and 1.5% (0.1%–6.4%) for MRI-Linac. The additional effect of the eddy current correction was small in both systems. The median (range) MSD, HD, and DSC comparing the original and off-resonance distorted GTVs for all patients were 0.43 mm (0.11–0.94 mm), 4.00 mm (1.00–7.81 mm) and 0.93 (0.82–0.99), respectively. Significance. Overall effect of distortion correction was small in terms of derived ADC values, indicating that distortion correction is unimportant for prediction of outcomes based on ADC. However, large local geometric changes occurred after off-resonance distortion correction for some patients, suggesting that if the spatial information from ADC maps is to be used for dose painting strategies, corrections should be applied.

Multi-scale feature fusion segmentation and lightweight ensemble deep learning approach for urban slum classification using satellite images

ABSTRACT Although there are some drawbacks to satellite imaging, such as the difficulty in identifying slums in highly populated metropolitan areas, it is nonetheless a useful tool for preliminary screening and can support on-the-ground and other data sources. Hence, we proposed the MSFF-Seg (Multi-Scale Feature Fusion-based Segmentation) model for urban slum classification using satellite images. Hence we proposed the MSFF-Seg model for urban slum classification using satellite images. Initially, three types of corrections are performed in preprocessing such as geometric correction which is corrected by Enhanced Scale Invariant Feature Transform (ESIFT), radiometric correction which is corrected by Ground-based Relative Radiometric Calibration (GRRC), and atmospheric correction which is corrected by homomorphic filter. After completion of preprocessing phase, segmentation is initiated by Tweak Mask RCNN which extracts the features in multilevel for segmentation that increases the segmentation accuracy. The segmented images are fed into an ensemble classifier for urban slum identification. Here, three types of deep learning are used for ensemble learning namely Schematic Convolutional Neural Network (SCNN), Shallow MobileNet, and Lite ShuffleNet. They extract multiple features from the segmented region, based on the extracted features. LGBM performed urban slum classification which classifies the images into two classes such as slums and non-slums. Finally, the performance of this research is evaluated based on several performance metrics like accuracy (98%), precision (96%), recall (94%), and F1 score (97%), which proved that the proposed work achieved superior performance in urban slum classification.

Refined Prior Guided Category-Level 6D Pose Estimation and Its Application on Robotic Grasping

Estimating the 6D pose and size of objects is crucial in the task of visual grasping for robotic arms. Most current algorithms still require the 3D CAD model of the target object to match with the detected points, and they are unable to predict the object’s size, which significantly limits the generalizability of these methods. In this paper, we introduce category priors and extract high-dimensional abstract features from both the observed point cloud and the prior to predict the deformation matrix of the reconstructed point cloud and the dense correspondence between the reconstructed and observed point clouds. Furthermore, we propose a staged geometric correction and dense correspondence refinement mechanism to enhance the accuracy of regression. In addition, a novel lightweight attention module is introduced to further integrate the extracted features and identify potential correlations between the observed point cloud and the category prior. Ultimately, the object’s translation, rotation, and size are obtained by mapping the reconstructed point cloud to a normalized canonical coordinate system. Through extensive experiments, we demonstrate that our algorithm outperforms existing methods in terms of performance and accuracy on commonly used benchmarks for this type of problem. Additionally, we implement the algorithm in robotic arm-grasping simulations, further validating its effectiveness.

Influence of electrode contact arrangements on Polarisation-Electric field measurements of ferroelectric ceramics: A case study of BaTiO3

A range of partial top full bottom electrodes are used to explore the use of bi-polar Polarisation-Electric field (P–E) measurements to quantify recoverable energy (Wrec), energy loss (Wloss) and the efficiency (η) of ferroelectric BaTiO3 ceramics. The values obtained are dependent on the ratio of sample thickness (S) and top contact radius (r). With increasing S/r from 0.17 to 1.96 the P–E responses become increasingly distorted and broader. Measurements show Wrec increases by a factor of ∼ 1.4 but Wloss increases by a factor of ∼7 with η decreasing from ∼ 29% to 8%. Finite element modelling was used to simulate the experimental set-up of the sample/electrode arrangements using the Jiles-Atherton model to replicate the ferroelectric behaviour of BaTiO3. These models demonstrate the experimentally applied electric field using a simple geometric correction for sample thickness is an underestimation of the actual field experienced by the material under the top contact at high S/r values. We stress the importance of reporting the contact sizes and thicknesses of samples when using P–E measurements to assess Wrec, Wloss and η in non-linear dielectric materials. This will allow a fairer comparison of performances between various types of materials being considered for high-energy-density ceramic capacitors.

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. In this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

Background adaptive PosMarker based on online generation and detection for locating watermarked regions in photographs

Robust watermarking technology can embed invisible messages in screens to trace the source of unauthorized screen photographs. Locating the four vertices of the embedded region in the photograph is necessary, as existing watermarking methods require geometric correction of the embedded region before revealing the message. Existing localization methods suffer from a performance trade-off: either causing unaesthetic visual quality by embedding visible markers or achieving poor localization precision, leading to message extraction failure. To address this issue, we propose a background adaptive position marker, PosMarker, based on the gray level co-occurrence matrix and the noise visibility function. Besides, we propose an online generation scheme that employs a learnable generator to cooperate with the detector, allowing joint optimization between the two. This simultaneously improves both visual quality and detection precision. Extensive experiments demonstrate the superior localization precision of our PosMarker-based method compared to others.