Global Root Mean Square Error Research Articles

Validating a Novel 2D to 3D Knee Reconstruction Method on Preoperative Total Knee Arthroplasty Patient Anatomies.

As advanced technology continues to evolve, incorporating robotics into surgical procedures has become imperative for precision and accuracy in preoperative planning. Nevertheless, the integration of three-dimensional (3D) imaging into these processes presents both financial considerations and potential patient safety concerns. This study aims to assess the accuracy of a novel 2D-to-3D knee reconstruction solution, RSIP XPlan.ai™ (RSIP Vision, Jerusalem, Israel), on preoperative total knee arthroplasty (TKA) patient anatomies. Accuracy was calculated by measuring the Root Mean Square Error (RMSE) between X-ray-based 3D bone models generated by the algorithm and corresponding CT bone segmentations (distances of each mesh vertex to the closest vertex in the second mesh). The RMSE was computed globally for each bone, locally for eight clinically relevant bony landmark regions, and along simulated bone cut contours. In addition, the accuracies of three anatomical axes were assessed by comparing angular deviations to inter- and intra-observer baseline values. The global RMSE was 0.93 ± 0.25 mm for the femur and 0.88 ± 0.14 mm for the tibia. Local RMSE values for bony landmark regions were 0.51 ± 0.33 mm for the five femoral landmarks and 0.47 ± 0.17 mm for the three tibial landmarks. The RMSE along simulated cut contours was 0.75 ± 0.35 mm for the distal femur cut and 0.63 ± 0.27 mm for the proximal tibial cut. Anatomical axial average angular deviations were 1.89° for the trans epicondylar axis (with an inter- and intra-observer baseline of 1.43°), 1.78° for the posterior condylar axis (with a baseline of 1.71°), and 2.82° (with a baseline of 2.56°) for the medial-lateral transverse axis. The study findings demonstrate promising results regarding the accuracy of XPlan.ai™ in reconstructing 3D bone models from plain-film X-rays. The observed accuracy on real-world TKA patient anatomies in anatomically relevant regions, including bony landmarks, cut contours, and axes, suggests the potential utility of this method in various clinical scenarios. Further validation studies on larger cohorts are warranted to fully assess the reliability and generalizability of our results. Nonetheless, our findings lay the groundwork for potential advancements in future robotic arthroplasty technologies, with XPlan.ai™ offering a promising alternative to conventional CT scans in certain clinical contexts.

Performance Comparison of Deterministic and Stochastic Modifications in Stokes’s and Hotine’s Formulas: The Case of Jilin Province, China

The high-precision regional geoid model provides important fundamental geospatial information for developing and applying many disciplines. Deterministic and stochastic modifications are applied to Stokes’s and Hotine’s formulas of geoid modeling to reduce errors. Based on the Experimental Geopotential Model 2019 (XGM2019), this paper used Stokes’s and Hotine’s formulas to analyze the variation of global root mean square error (RMSE) with modification parameters for two deterministic (Wong and Gore; and Vaníček and Kleusberg) and three stochastic modifications (biased, unbiased, and optimum). Taking the quasigeoid refinement of Jilin Province as an example, the global RMSE, approximate geoid undulation, and additive corrections were calculated. The parameter analysis and the global RMSE calculation showed that the variation of the modification limits and the terrestrial gravity data error variance had a centimeter-level effect on the global RMSE. In contrast, the impact of the integration radius was relatively small. The stochastic modifications were better than the deterministic ones in calculating the global RMSE. The global RMSE of Hotine’s formula was smaller than that of Stokes’s, and its unbiased and optimum modifications reached the minimum value of 12.9 mm. The validation of XGM2019 and the refined quasigeoid based on the high accuracy GPS/leveling points showed that the standard deviation (STD) of XGM2019 was 5.8 cm in Jilin Province, and the refined optimal quasigeoid model was 2.9 cm. Stokes’s and Hotine’s formulas provided the same accuracy in the study area. In the western plain area, the accuracy of the deterministic modifications was 2.0 cm, which was about 0.4 cm higher than that of the stochastic modifications. In the eastern mountainous area, the stochastic modifications were better than the deterministic ones, and the accuracy was about 3.2 cm. Stokes’s and Hotine’s formulas based on deterministic and stochastic modifications significantly improve the accuracy of the XGM2019. The deterministic and stochastic modifications show millimeter-level differences in plain and mountainous areas.

Evaluation of F10.7, Sunspot Number and Photon Flux Data for Ionosphere TEC Modeling and Prediction Using Machine Learning Techniques

Considering the growing volumes and varieties of ionosphere data, it is expected that automation of analytical model building using modern technologies could lead to more accurate results. In this work, machine learning techniques are applied to ionospheric modeling and prediction using sun activity data. We propose Total Electron Content (TEC) spectral analysis, using discrete cosine transform (DCT) to evaluate the relation to the solar features F10.7, sunspot number and photon flux data. The ionosphere modeling procedure presented is based on the assessment of a six-year period (2014–2019) of data. Different multi-dimension regression models were considered in experiments, where each geographic location was independently evaluated using its DCT frequency components. The features correlation analysis has shown that 5-year data seem more adequate for training, while learning curves revealed overfitting for polynomial regression from the 4th to 7th degrees. A qualitative evaluation using reconstructed TEC maps indicated that the 3rd degree polynomial regression also seems inadequate. For the remaining models, it can be noted that there is seasonal variation in root-mean-square error (RMSE) clearly related to the equinox (lower error) and solstice (higher error) periods, which points to possible seasonal adjustment in modeling. Elastic Net regularization was also used to reduce global RMSE values down to 2.80 TECU for linear regression.

Sparse regularization for reconstructing transient sources with time domain nearfield acoustical holography.

In this paper, the ℓ1-norm sparse regularization method is applied to the time domain reconstruction of transient acoustic fields such as impulse noise. This method properly reconstructs the back-propagated sound field where its amplitude should be null: for transient sources, this occurs mostly for positions and times that precede the arrival of the first wave front. Therefore, it significantly reduces causal errors typically found in time domain reconstruction when standard Tikhonov regularizations is applied. The reconstructions obtained from both Tikhonov and sparse regularization methods are compared using a transient baffled piston model, and show that the global root-mean-square (RMS) error is significantly reduced when using sparse regularization. The improvement provided depends on the level of sparsity of the reconstructed signal. For the studied cases, it can represent a reduction of the global RMS error by up to a factor of 3. The performance of Pareto frontier curve for predicting the optimal sparse regularization parameter is examined; it leads to accurate predictions especially for lower noise levels. Finally, sparse regularization is applied to experimental data over time and spatial domains in order to obtain an accurate reconstruction of the transient sound field produced by an impacted plate.

Satellite-derived CO2 flux in the surface seawater of the Austral Ocean south of Australia

ABSTRACTA step by step algorithm for air–sea CO2 flux (F(CO2)) calculation from satellite parameters is presented in this study. Parameters used for F(CO2) calculation are: (1) sea surface temperature (SST) and chlorophyll-a (chl-a) from Moderate Resolution Imaging Spectroradiometer Aqua (MODIS Aqua), (2) sea surface salinity (SSS) estimated from MODIS Aqua SST using multiple linear regression, (3) seawater CO2 fugacity (f(CO)) estimated by MODIS Aqua SST and chl-a using feedforward neural networks, (4) atmospheric CO2 fugacity (f(CO)) from the Cape Grim station, and (5) wind speed from the Quick and Advanced Scatterometer (QSCAT and ASCAT). In situ data provided by (1) the Surveillance de l’Océan Austral – Monitoring the Southern Ocean (SURVOSTRAL) project, (2) the Integrated Marine Observed System (IMOS) project, and (3) Mesures à l’INterface Eau-aiR de la Variabilité des échanges de CO2 (MINERVE) project collected on the research vessel L’Astrolabe, are used to establish and validate the models. These models are then tested using remote sensing data. This work focus on the southern ocean from the south of Australia to the Antarctica coasts (between 43.5° S and 67° S), on the period of spring and Austral summer (from October to March, between 2002/2003 and 2014/2015). In each step, the result’s precision of experiments was determined by the root mean square error (RMSE). Results show (1) an improvement of satellite SSS estimation with a precision of ±0.16 using SST and latitude, (2) an estimation of f(CO) by satellite data with a good accuracy of ±9.45 µatm (0.96 Pa), and (3) a calculation of F(CO2) using satellite data with a global RMSE of about ±3 mmol CO2 m–2 day–1 . The interpolated F(CO2) shows that, in the period of austral spring and summer, this region absorbs the atmospheric CO2, and becomes a stronger sink of CO2 throughout the years (from an overall average absorption of about 2 mmol CO2 m–2 day–1 in 2002/2003 to about 7 mmol CO2 m–2 day–1 in 2014/2015).

Testing regression equations to derive long-term global soil moisture datasets from passive microwave observations

Within the framework of the efforts of the European Space Agency (ESA) to develop the most consistent and complete record of surface soil moisture (SSM), this study investigated a statistical approach to retrieve a global and long-term SSM dataset from space-borne observations. More specifically, this study investigated the ability of physically based statistical regressions to retrieve SSM from two passive microwave remote sensing observations: the Advanced Microwave Scanning Radiometer (AMSR-E; 2003–Sept. 2011) and the Soil Moisture and Ocean Salinity (SMOS) satellite. Regression coefficients were calibrated using AMSR-E horizontal and vertical brightness temperature (TB) observations and SMOS level 3 SSM (SMOSL3; as a training dataset). This calibration process was carried out over the June 2010–Sept. 2011 period, over which both SMOS and AMSR-E observations coincide. Based on these calibrated coefficients, a global SSM product (referred here to as AMSR-reg) was computed from the AMSR-E TB observations during the 2003–2011 period. The regression quality was assessed by evaluating the AMSR-reg SSM product against the SMOSL3 SSM product over the period of calibration, in terms of correlation (R) and Root Mean Square Error (RMSE). A good agreement (mean global R = 0.60 and mean global RMSE = 0.057 m3/m3), was obtained between the AMSR-reg and SMOSL3 SSM products particularly over Australia, central USA, central Asia, and the Sahel. In a second step, the AMSR-reg SSM retrievals and commonly used AMSR-E SSM retrievals derived from the Land Parameter Retrieval Model (AMSR-LPRM), were evaluated against two kinds of SSM references (i) the global MERRA-Land SSM simulations and (ii) in situ measurements over 2003–2009. The results demonstrated that both AMSR-reg and AMSR-LPRM (better when considering global simulations) successfully captured the temporal dynamics of the references used having comparable correlation values. AMSR-reg was more consistent with MERRA-land than AMSR-LPRM in terms of unbiased RMSE (ubRMSE) with a global average of ubRMSE of 0.055 m3/m3 for AMSR-reg and 0.084 m3/m3 for AMSR-LPRM. In conclusion, the statistical regression, which is tested here for the first time using long-term spaceborne TB datasets, appears to be a promising approach for retrieving SSM from passive microwave remote sensing TB observations.

An integral approach to regional gravity field refinement using earth gravity models

The idea of this paper is to refine the terrestrial gravimetric data with the Earth's gravity models (EGMs) and produce a high quality source of gravity data. For this purpose, biased and unbiased integral estimators are presented. These estimators are used to refine gravimetric data over Fennoscandia with the ITG-GRACE2010s and GO_CONS_GCF_2_DIR_R2 EGMs, which are the recent products of the gravity field and climate experiment (GRACE) and the gravity field and steady-state ocean circulation explorer (GOCE) satellite missions. Numerical results show that the biased integral estimator has smaller global root mean square error (RMSE) than the unbiased one. Also a simple strategy is presented to down-weight the low-frequencies the terrestrial data in spectral combination. The gravity anomalies, computed by EGM08, are compared to the refined anomalies for evaluation purpose. In the case of using a cap size of 1° for integration the EGM08 gravity anomalies are more correlated with the refined ones. Also the band-limited kernels can simply be generated to maximum degree of the used EGMs for both estimators. Comparisons of the combined anomalies and those of EGM08 show insignificant differences between the biased and unbiased estimators in practice. However, the biased estimator seems to be proper one for gravity data refinement due to its smaller global RMSE.