Point-based Method Research Articles

A Risk Prediction Model to Identify People Living with HIV Who are High-risk for Disengagement from Care after HIV Diagnosis in South Africa.

The provision of ART in South Africa has transformed the HIV epidemic, resulting in an increase in life expectancy by over 10 years. Despite this, nearly 2million people living with HIV are not on treatment. The objective of this study was to develop and externally validate a practical risk assessment tool to identify people with HIV (PWH) at highest risk for attrition from care after testing. A machine learning model incorporating clinical and psychosocial factors was developed in a primary cohort of 498 PWH. LASSO regression analysis was used to optimize variable selection. Multivariable logistic regression analysis was applied to build a model using 80% of the primary cohort as a training dataset and validated using the remaining 20% of the primary cohort and data from an independent cohort of 96 participants. The risk score was developed using the Sullivan and D'Agostino point based method. Of 498 participants with mean age 35.7 years, 192 (38%) did not initiate ART after diagnosis. Controlling for site, factors associated with non-engagement in care included being < 35 years, feeling abandoned by God, maladaptive coping strategies using alcohol or other drugs, no difficulty concentrating, and having high levels of confidence in one's ability to handle personal challenges. An effective risk score can enable clinicians and implementers to focus on tailoring care for those most in need of ongoing support. Further research should focus on potential strategies to enhance the generalizability and evaluate the implementation of the proposed risk prediction model in HIV treatment programs.

Inverse Geometric Reconstruction Based on MW-NURBS Curves

Currently, rational curves such as the Non-Uniform Rational B-Spline (NURBS) play a significant role in both shape representation and shape reconstruction. NURBS weights are often real in nature and are referred to as challenging to assign, with the exception of conics. ‘Matrix Weighted Rational Curves’ are the expanded form of rational curves that result from replacing these real weights with matrices, or matrix weights. The only difference between these curves and conventional curves is the geometric definition of the matrix weights. In this paper, MW-NURBS curves are used to reconstruct space curves from their stereo perspectives. In particular, MW-NURBS fitting is carried out in stereo views, and the weight matrices for the MW-NURBS curves are produced using the normal vectors provided at the control points. Instead of needing to solve a complicated system, the MW-NURBS model can reconstruct curves by choosing control points and control normals from the input data. The efficacy of the proposed strategy is verified by using many examples based on both synthetic and real images. The various error types are compared to those of conventional methods like point-based and NURBS-based approaches. The results demonstrate that the errors acquired from the proposed approach are much fewer than those obtained from the point-based method and the NURBS-based method.

Comparison of the Accuracy and Efficiency of Two Dynamic Navigation System Workflow for Fiber-post Removal: Small versus Large Field-of-view Registration Workflows

IntroductionThis study investigates the feasibility of a dynamic navigation system (DNS) small field of view workflow (DNS-SFOVw) for fiber-post removal and compares its accuracy and efficiency to the conventional large field of view workflow (DNS-LFOVw). MethodsFifty-six extracted human maxillary molars were divided into DNS-SFOVw (n = 28) and DNS-LFOVw (n = 28). The palatal canal was restored with an intraradicular RelyX fiber post and luted with RelyX Unicem; a core buildup was used. Teeth were mounted in a 3D-printed surgical jaw. A preoperative cone-beam computed tomography (CBCT) scan was taken with a 40 × 40 mm FOV for the DNS-SFOVw and a single arch CBCT scan for the DNS-LFOVw. The drilling entry point, trajectory, angle, and depth were planned in the X-guide software. The DNS registration method for the DNS-SFOVw was virtual-based registration on teeth, and the marker point-based method was used for the DNS-LFOVw. The fiber posts were drilled out under DNS guidance. A postoperative CBCT scan was taken. Three-dimensional deviations, angular deflection, number of mishaps, registration, and total operation time were calculated. ResultsThe DNS-SFOVw was as accurate as DNS-LFOVw (P > .05). The DNS-LFOVw registration time was less than DNS-SFOVw (P < .05). There was no difference in the number of mishaps (P > .05). Both DNS-SFOVw and DNS-LFOVw were time-efficient, with DNS-LFOVw taking less total operational time (P < .05). ConclusionWithin the limitations of this in-vitro study, the DNS-SFOVw was as accurate as the DNS-LFOVw for fiberpost removal. Both DNS-LFOVw and DNS-SFOVw were time-efficient in removing fiber-posts.

Determination of dynamic collapse limit states using the energy-based method for multi-story RC frames subjected to column removal scenarios

The Alternative Load Path method is widely adopted to perform progressive collapse analyses for reinforced concrete (RC) frame structures subjected to column removal scenarios. Considering that the progressive collapses are usually dynamic phenomena, nonlinear dynamic analyses can yield the most accurate results. However, the associated computational cost is high. Alternatively, the energy-based method (EBM) can be employed to efficiently calculate the maximum dynamic responses. Unfortunately, collapse or dynamic limit states (DLS) cannot be directly determined when the EBM is adopted for the progressive collapse analyses, because it is essentially a quasi-static approach. To tackle this issue, in this paper an EBM-Intersection Point-based (EBM-IP-based) method is proposed to effectively determine the DLS. The method is considering that the dynamic instability will occur once the dynamic capacity curve exceeds the corresponding static capacity curve. Hence, it is possible to determine the DLS by making a correction on the intersection point of the aforementioned two curves without performing nonlinear dynamic time-history analyses. Compared with the other energy components, the kinetic energy at the moment of the peak displacement response is relatively small and the effectiveness of the EBM is verified. Through both static pushdown analyses and incremental dynamic analyses for 48 column removal scenarios of six different multi-story RC frames, the effectiveness of the proposed EBM-IP-based method is verified and the associated coefficients are calibrated. Statistical information and (joint) probabilistic density functions (PDF) of the coefficients are identified. Further, stochastic analyses are carried out in order to quantify the model uncertainties when adopting the EBM-IP-based method. On the basis of all the calculation results, a Gumbel distribution is adopted to capture the PDF of the model uncertainty in relation to displacements, while a lognormal distribution is adopted to fit the PDF of the model uncertainty in terms of resistances. Moreover, a multi-variate Gaussian distribution model with two components is employed to fit the joint PDF.

An inflection point-based method for estimating metrics of mangrove phenology combining climatic factors and Landsat NDVI time series

ABSTRACT The present research evaluated the prospects of utilizing rainfall and temperature combined with Landsat-8 derived HANTS (Harmonic Analysis of Time Series) reconstructed NDVI for estimating the metrics of the mangrove phenology. The selected period of the study was from 2013 to 2020 for the Pichavaram mangroves of Tamil Nadu. The NDVI and ERA5 (ECMWF Re-Analysis) datasets of rainfall and temperature were the input datasets for developing the new algorithm. The ‘z-score sum’ provided a measure of the cumulative impact of rainfall and temperature, displaying its most negative value coinciding with the peak positive value of the NDVI time series datasets. The algorithm developed for phenological metrics estimation identified the common inflection points of the z-score sum and NDVI curves. The temporal analysis of metrics revealed the average Length of Season (LoS) as 230 days. The metrics also identified the drought year 2016 with the shortest LoS and the least Gross Primary Productivity (GPP) values. The analysis showed the influences of the preceding year’s monsoon rainfall on the GPP values of the later part of the phenological cycle. The temperatures during the days of PoS were found to be the optimum temperature for the growth of mangroves.

Dense-sparse representation matters: A point-based method for volumetric medical image segmentation

Deep learning methods utilizing Convolutional Neural Networks (CNNs) and Transformers have achieved remarkable success in volumetric medical image analysis. While successful, the symmetrical structure of numerous networks pays insufficient attention to the encoding phase, and the large amount of memory occupied by voxels leads to unnecessary redundancy in the network. In this paper, we present a novel approach to handle volumetric medical images by converting them into point cloud and introduce a new asymmetrical segmentation architecture. We propose a dual-path encoder that fully captures both dense and sparse representations of the input point cloud sampled from volumes. Moreover, the two obtained representations are subtracted at the skip connection as a complementary feature during the decoding stage. Experimental results on the Brain Tumor Segmentation (BraTS) and the Multi-sequence Cardiac MR Segmentation tasks demonstrate the great potential of our point-based method for volumetric medical image segmentation.

Realistic rendering method for specular reflections with continuous motion parallax in a computer-generated hologram.

A computer-generated hologram (CGH) enables the display of virtual images and videos as well as the communication and storage of holographic data. The point-based method, which is a CGH-calculation method for representing the surface of an object as a set of point-light sources, has not been sufficiently studied in terms of realistic representation. This paper proposes a CGH-calculation method for realistic rendering using ray tracing to be used with a point-based method. Experiments were conducted with an optical system to confirm the effectiveness of the proposed method in terms of hidden-surface removal in mirror images and its implementation on multiple mirror surfaces. The results indicate that the proposed method enabled hidden-surface removal with continuous parallax and reflection on mirror surfaces.

Accuracy of instrument tip position using fiber optic shape sensing for navigated bronchoscopy

The purpose of this study was to evaluate the accuracy of a method for estimating the tip position of a fiber optic shape-sensing (FOSS) integrated instrument being inserted through a bronchoscope. A modified guidewire with a multicore optical fiber was inserted into the working channel of a custom-made catheter with three electromagnetic (EM) sensors. The displacement between the instruments was manually set, and a point-based method was applied to match the position of the EM sensors to corresponding points on the shape. The accuracy was evaluated in a realistic bronchial model. An additional EM sensor was used to sample the tip of the guidewire, and the absolute deviation between this position and the estimated tip position was calculated. For small displacements between the tip of the FOSS integrated tool and the catheter, the median deviation in estimated tip position was ≤5 mm. For larger displacements, deviations exceeding 10 mm were observed. The deviations increased when the shape sensor had sharp curvatures relative to more straight shapes. The method works well for clinically relevant displacements of a biopsy tool from the bronchoscope tip, and when the path to the lesion has limited curvatures. However, improvements must be made to our configuration before pursuing further clinical testing.

IFM calculator: An algorithm for interfragmentary motion calculation in finite element analysis

BackgroundInterfragmentary motion (IFM) is a complex state that significantly impacts the healing process of fractures following implant placement. It is crucial to fully consider the IFM state after implantation in the design and biomechanical testing of implants. However, current finite element analysis software lacks direct tools for calculating IFM, and existing IFM tools do not offer a comprehensive solution in terms of accuracy, functionality, and visualization. MethodsIn our study, we developed a Python-based algorithm for calculating IFM that addresses limitations. Our algorithm automatically calculated IFM distances, sliding distances, gaps, as well as the angles and rotation of the two fracture surfaces using all nodes on both sides of the fracture ends. Researchers could input data and selected desired parameters in the interface. The algorithm then performed the necessary calculations and presented the results in a clear and concise manner. The algorithm also provided comprehensive data export capabilities, allowing researchers to customize analyses based on specific needs.To provide a more intuitive demonstration of the calculation process and usage of IFM-Cal, we conducted simulations in Ansys using two rectangular blocks to compare the accuracy and function of three different methods (Point based method, contact tool and IFM-Cal). ResultsThe point-based method and the contact tool could not accurately calculate IFA, while IFM-Cal could provide a comprehensive evaluation of IFA. In simulation 1, the IFM distances calculated using the point sampling method, contact tool, and IFM-Cal were 2.00 mm, 3.15 mm, and 2.00 mm, respectively. In simulation 2, both the point sampling method and contact tool failed to calculate the interfragmentary angle (IFA), while the IFM-Cal algorithm estimated an angle of -7.87°, which had a small error compared to the ground-truth value of 7.9°. ConclusionWe have developed an algorithm for computing IFM which can be utilized in finite element analysis and biomechanical experiments. By conducting comparative simulations with other existing algorithms, we have demonstrated the superior accuracy and expanded evaluation capabilities of our algorithm.

Optimal selection of dictionary atoms for sparse dictionary learning of time-varying monitoring data in two-dimensional geotechnical problems

Geotechnical monitoring data (e.g., settlement monitoring data) are often sparsely measured at limited locations, but the corresponding geotechnical quantities of interest (e.g., ground settlement) usually vary in both temporal and spatial dimensions. The sparsely measured monitoring data can be efficiently leveraged under a sparse dictionary learning (SDL) framework, which represents a spatio-temporally varying quantity (e.g., settlement) by a weighted summation of dictionary atoms. However, selection of dictionary atoms in SDL greatly affects the SDL performance, and under-fitting or over-fitting problems are frequently encountered, particularly when dealing with limited monitoring data. To tackle these problems, a knee point-based method is proposed in this study to properly select dictionary atoms for optimizing the SDL performance. The proposed method not only automatically determines dictionary atom IDs and weights, but also strikes a balance between the under-fitting and over-fitting. The proposed approach is illustrated using a real case history of embankments constructed on soft clay in Australia. The proposed approach significantly improves the prediction of time-varying settlements that also spatially vary over a two-dimensional (2D) space (e.g., a vertical cross-section), particularly at subsequent time steps and spatial locations without monitoring data. Effects of the dictionary atom quantity on settlement predictions are also investigated.

Comparing Multiple Extended Object Tracking with Point Based Multi Object Tracking for LiDAR in a Maritime Context

In this paper, we compare a recently developed multiple extended object tracking method with a point-based tracker for maritime applications by evaluating the methods on both real and simulated LiDAR data. Being able to track other vessels is a key part of maritime situational awareness, and multi-object tracking is well suited to this task. Traditionally, multi-object tracking uses the point approximation to simplify the target tracking problem, meaning that an object is assumed to only generate a single measurement. With recent advances in sensor technology, this approximation is no longer valid. Multiple extended object tracking instead makes use of methods that estimates the extent of a target using all available measurements. However, the target models used in extended object tracking are by necessity more complex. We compare these two approaches on real and simulated LiDAR data, which was gathered by tracking smaller vessels. We find that the extended object method has greater performance on simulated data and experimental data with comparatively little wake clutter. However, on experimental data with more wake clutter, the point-based method outperforms the extended object method since it is less sensitive to the disturbance caused by wake clutter. We can conclude that multiple extended object tracking methods have the potential to be more accurate for LiDAR data, but since the models are more complex, measurement sources need to be modeled correctly.

Improving Estimation of Tree Parameters by Fusing ALS and TLS Point Cloud Data Based on Canopy Gap Shape Feature Points

Airborne laser scanning (ALS) and terrestrial laser scanning (TLS) are two ways to obtain forest three-dimensional (3D) spatial information. Due to canopy occlusion and the features of different scanning methods, some of the forest point clouds acquired by a single scanning platform may be missing, resulting in an inaccurate estimation of forest structure parameters. Hence, the registration of ALS and TLS point clouds is an alternative for improving the estimation accuracy of forest structure parameters. Currently, forest point cloud registration is mainly conducted based on individual tree attributes (e.g., location, diameter at breast height, and tree height), but the registration is affected by individual tree segmentation and is inefficient. In this study, we proposed a method to automatically fuse ALS and TLS point clouds by using feature points of canopy gap shapes. First, the ALS and TLS canopy gap boundary vectors were extracted by the canopy point cloud density model, and the turning or feature points were obtained from the canopy gap vectors using the weighted effective area (WEA) algorithm. The feature points were then aligned, the transformation parameters were solved using the coherent point drift (CPD) algorithm, and the TLS point clouds were further aligned using the recovery transformation matrix and refined by utilizing the iterative closest point (ICP) algorithm. Finally, individual tree segmentations were performed to estimate tree parameters using the TLS and fusion point clouds, respectively. The results show that the proposed method achieved more accurate registration of ALS and TLS point clouds in four plots, with the average distance residuals of coarse and fine registration of 194.83 cm and 2.14 cm being much smaller compared with those from the widely used crown feature point-based method. Using the fused point cloud data led to more accurate estimates of tree height than using the TLS point cloud data alone. Thus, the proposed method has the potential to improve the registration of ALS and TLS point cloud data and the accuracy of tree height estimation.

HV-Net: Hypervolume Approximation Based on DeepSets

In this letter, we propose HV-Net, a new method for hypervolume approximation in evolutionary multi-objective optimization. The basic idea of HV-Net is to use DeepSets, a deep neural network with permutation invariant property, to approximate the hypervolume of a non-dominated solution set. The input of HV-Net is a non-dominated solution set in the objective space, and the output is an approximated hypervolume value of this solution set. The performance of HV-Net is evaluated through computational experiments by comparing it with two commonly-used hypervolume approximation methods (i.e., point-based method and line-based method). Our experimental results show that HV-Net outperforms the other two methods in terms of both the approximation error and the runtime, which shows the potential of using deep learning techniques for hypervolume approximation.

Workspace optimization of 1T2R parallel manipulators with a dimensionally homogeneous constraint-embedded Jacobian

This paper presents the workspace optimization of one-translational two-rotational (1T2R) parallel manipulators using a dimensionally homogeneous constraint-embedded Jacobian. The mixed degrees of freedom of 1T2R parallel manipulators, which cause dimensional inconsistency, make it difficult to optimize their architectural parameters. To solve this problem, a point-based approach with a shifting property, selection matrix, and constraint-embedded inverse Jacobian is proposed. A simplified formulation is provided, eliminating the complex partial differentiation required in previous approaches. The dimensional homogeneity of the proposed method was analytically proven, and its validity was confirmed by comparing it with the conventional point-based method using a 3-PRS manipulator. Furthermore, the approach was applied to an asymmetric 2-RRS/RRRU manipulator with no parasitic motion. This mechanism has a T-shape combination of limbs with different kinematic parameters, making it challenging to derive a dimensionally homogeneous Jacobian using the conventional method. Finally, optimization was performed, and the results show that the proposed method is more efficient than the conventional approach. The efficiency and simplicity of the proposed method were verified using two distinct parallel manipulators.

Deep learning for large-scale point cloud segmentation in tunnels considering causal inference

This work designs an integrated deep learning approach to accomplish a multi-label segmentation of various objects including seepage from 3D point clouds of tunnels. 3D laser scanning is first utilized to collect raw point clouds from the operating tunnels. An integration approach based on projection strategy and point-based method is developed. A causal inference-based data augmentation approach is proposed to enhance the segmentation performance between the seepage and the segment class. A Dempster–Shafer (D-S) evidence-based feature fusion model is established to combine the local feature with global features from different CNN models. A real cross-river tunnel section in China is applied as a case study for illustration. Results verify that (1) the integration framework shows an outperforming performance of seepage segmentation, and the Intersection over Union (IOU), Precision, Recall, and F1 score for seepage segmentation achieve 0.70, 0.896, 0.762, and 0.824, respectively; (2) the segmentation model achieves competitive results in multiple classes, and the segmentation F1 score of the cable, segment, pipe, powertrack and the track classes obtain 0.913, 0.911, 0.993, 0.898, and 0.963, respectively; (3) the segmentation model is superior to other SOTA point cloud segmentation algorithms in terms of evaluation metrics.

Image-guided navigation system for minimally invasive total hip arthroplasty (MITHA) using an improved position-sensing marker.

Minimally invasive total hip arthroplasty (MITHA) is a treatment for hip arthritis, and it causes less tissue trauma, blood loss, and recovery time. However, the limited incision makes it difficult for surgeons to perceive the instruments' location and orientation. Computer-assisted navigation systems can help improve the medical outcome of MITHA. Directly applying existing navigation systems for MITHA, however, suffers from problems of bulky fiducial marker, severe feature-loss, multiple instruments tracking confusion, and radiation exposure. To tackle these problems, we propose an image-guided navigation system for MITHA using a novel position-sensing marker. A position-sensing marker is proposed to serve as the fiducial marker with high-density and multi-fold ID tags. It results in less feature span and enables the use of ID for each feature, overcoming the problem of bulky fiducial markers and multiple instruments tracking confusion. And the marker can be recognized even when a large part of locating features is obscured. As for the elimination of intraoperative radiation exposure, we propose a point-based method to achieve patient-image registration based on anatomical landmarks. Quantitative experiments are conducted to evaluate the feasibility of our system. The accuracy of instrument positioning is achieved at 0.33 ± 0.18mm, and that of patient-image registration is achieved at 0.79 ± 0.15mm. And qualitative experiments are also performed, verifying that our system can be used in compact surgical spatial volume and can address severe feature-loss and tracking confusion problems. In addition, our system does not require any intraoperative medical scans. Experimental results indicate that our proposed system can assist surgeons without larger space occupations, radiation exposure, and extra incision, showing its potential application value in MITHA.

An End-to-End Point-Based Method and a New Dataset for Street-Level Point Cloud Change Detection

An End-to-End Point-Based Method and a New Dataset for Street-Level Point Cloud Change Detection

A high-resolution map of coastal vegetation for two Arctic Alaskan parklands: An object-oriented approach with point training data.

Bering Land Bridge National Preserve and Cape Krusenstern National Monument in northwest Alaska have approximately 1600 km of predominantly soft-sediment coastlines along the Chukchi Sea, a shallow bay of the Arctic Ocean. Over the past decade, marine vessel traffic through the Bering Strait has grown exponentially to take advantage of new ice-free summer shipping routes, increasing the risk of oil spills in these fragile ecosystems. We present a high-resolution coastal vegetation map to serve as a baseline for potential spill response, restoration, and change detection. We segmented 663 km2 of high-resolution multispectral satellite images by the mean-shift method and collected 40 spectral, topographic and spatial variables per segment. The segments were classified using photo-interpreted points as training data, and verified with field based plots. Digitizing points, rather than polygons, and intersecting them with the segmentation allows for rapid collection of training data. We classified the map segments using Random Forest because of its high accuracy, computational speed, and ability to incorporate non-normal, high-dimensional data. We found creating separate classification models by each satellite scene gave highly similar results to models combining the entire study area, and that reducing the number of variables had little impact on accuracy. A unified, study area-wide Random Forest model for both parklands produced the highest accuracy of various models attempted. We mapped 18 distinct classes, with an out-of-bag error of 11.6%, resulting in an improvement to the past per-pixel classification of this coast, and in higher spatial and vegetation classification resolution. The resulting map demonstrates the utility of our point-based method and provides baseline data for incident preparedness and change detection. Elevation is highly correlated with the ordination of the vegetation types, and was the most important variable in all tested classification models. The vegetation classification brings together the largest amount of vegetation data for the Chukchi Sea coast yet documented.

Set-valued estimators for Uncertain Linear Parameter-Varying systems

In this paper, we tackle the problem of state estimation for uncertain linear systems when bounds are known for the disturbances, noise and initial state. Practical systems often have parameters that cannot be measured precisely at every iteration. The framework of Uncertain Linear Parameter-Varying systems (Uncertain LPVs) have attracted attention from the community and have seen applications from the aerospace industry to mechatronic systems, among many other examples. By formulating the problem as the solution of a feasibility program, we show that the optimal convex solution can be computed through an enumeration of the vertices of the estimates. Resorting to this result, three algorithms are proposed: an approximation algorithm using only set operations; an exact convex hull method returning the optimal convex set suitable for cases where estimates do not have a large number of vertices; and an event-triggering algorithm suitable for fault/attack detection that combines both the convex and nonconvex methods. Simulations are conducted using a motor speed model where some of the parameters cannot be measured exactly pointing out that the uncertainty matrices are responsible for the accuracy of the approximation algorithm, and also that the point-based method is suitable for online estimation.

A leading-edge-based method for correction of slope-induced errors in ice-sheet heights derived from radar altimetry

Abstract. Satellite radar altimetry has been an important tool for cryospheric applications such as measuring ice-sheet height or assessing anomalies in snow and ice properties (e.g. the extensive melt in Greenland in 2012). Although accurate height measurements are key for such applications, slope-induced errors due to undulating topography within the kilometre-wide beam-limited footprint can cause multi-metre errors. Two main correction methods that have been developed (referred to as the slope- and point-based methods) neglect either the actual topography or the actual footprint that can be estimated by a combination of the leading edge and topography. Therefore, a leading edge point-based (LEPTA) method is presented that corrects for the slope-induced error by including the leading edge information of the radar waveform to determine the impact point. The principle of the method is that only the points on the ground that are within the range determined by the beginning and end of the leading edge are used to determine the impact point. Benchmarking of the LEPTA method against the slope- and point-based methods based on CryoSat-2 Low Resolution Mode (LRM) acquisitions over Greenland in 2019 shows that, when compared to ICESat-2 observations, the LEPTA method has a stable performance both in the flat, interior regions of Greenland and in regions with more complex topography. The median difference between the slope-corrected CryoSat-2 heights using LEPTA and the ICESat-2 heights is at the millimetre level, whereas the slope and point-based methods can have a 0.21 and 0.48 m difference, respectively, and the Level-2I (L2I) data provided by ESA have a 0.01 m difference. The median absolute deviation of height differences between CryoSat-2 and ICESat-2, which we use as an indicator of the variation in errors, is also the lowest for LEPTA (0.09 m) in comparison to the aforementioned methods (0.19 m for slope method and 0.10 m for point-based method) and ESA Level-2 data (0.14 m). Although ESA Level-2 products and the point-based method have good performance in either the median or the median absolute deviation, LEPTA shows a good performance in both metrics. Based on that, we recommend considering LEPTA for obtaining accurate height measurements with radar altimetry data, especially towards the margins of the LRM coverage where the surface slopes increase.