Inverse Error Research Articles

Multitask Deep Learning for Least-Squares Imaging: Seismic Reflectivity Inversion and Quantitative Error Analysis

Multitask Deep Learning for Least-Squares Imaging: Seismic Reflectivity Inversion and Quantitative Error Analysis

Human optional stopping in a heteroscedastic world.

When making decisions, animals must trade off the benefits of information harvesting against the opportunity cost of prolonged deliberation. Deciding when to stop accumulating information and commit to a choice is challenging in natural environments, where the reliability of decision-relevant information may itself vary unpredictably over time (variable variance or "heteroscedasticity"). We asked humans to perform a categorization task in which discrete, continuously valued samples (oriented gratings) arrived in series until the observer made a choice. Human behavior was best described by a model that adaptively weighted sensory signals by their inverse prediction error and integrated the resulting quantities with a linear urgency signal to a decision threshold. This model approximated the output of a Bayesian model that computed the full posterior probability of a correct response, and successfully predicted adaptive weighting of decision information in neural signals. Adaptive weighting of decision information may have evolved to promote optional stopping in heteroscedastic natural environments. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Simultaneous inversion method of thermal barrier coating parameters based on electromagnetic/capacitive dual-module sensor.

Thermal barrier coating (TBC) of turbine blades can prevent aeroengine damage resulting from high temperature. TBC exhibits a multilayer complex structure of ceramic and bonding layers. The ceramic layer is dielectric, whereas the bonding layer is conductive. Disabling either layer can endanger aircraft safety. Changes in TBC parameters are indicative of failure. This study proposed a neural-network-based method to inverse the three key parameters of TBC simultaneously based on electromagnetic/capacitive dual-module sensor. Thus, this method can be used for monitoring the status of aeroengines. The experimental results revealed that the inversion error of thickness and permittivity of the ceramic layer and the conductivity of the bonding layer is less than 2%. Therefore, the proposed method can satisfy application requirements.

Analysis of the Bidirectional Characteristic of Radiation of Flat and Rough Water–Air Interfaces Based on the Theory of Radiative Transfer

The Lambertian property of objects is one of the basic hypotheses in remote sensing research. However, the spectral radiance of natural objects is always anisotropic. On the sea surface, a large amount of sea foam is generated at the water–air interface, induced by wind speed and breaking gravity waves. Additionally, the scattering characteristic at the water–air interface significantly influences the accuracy of ocean color remote sensing and its output. The bidirectionality of the water light field is one of the sources of errors in ocean color inversion. Therefore, the knowledge of the bidirectional reflectance distribution of water surfaces is of great significance in quantitative remote sensing or for the evaluation of measurement errors in surface optical parameters. To clarify the bidirectional reflectance distribution, we used the coupled ocean–atmosphere radiative transfer (COART) model to simulate the bidirectional radiance of water bodies and explored the anisotropy of radiance at the water–air interface. The results indicate that the downward and upward irradiance just below the water surface and the water-leaving radiance changed with the sun-viewing geometry. The downward and upward radiance just below the water surface decreased as the zenith angle of the incident light increased. This effect can be mitigated using a function of the viewing angle. Additionally, the viewing azimuth angle and rough sea surface had no significant effect on the downward and upward radiance. The water-leaving radiance had an obvious bidirectional reflectance characteristic. Additionally, a backward hotspot was found in the simulated results. Then, the transmission coefficient was calculated, and the bidirectional distribution characteristic was found for flat and rough sea surfaces. This study can be used as a reference to correct bidirectional errors and to guide the spectral measurements of water and its error control for rough sea surfaces.

Particle size distribution inversion using theWeibull-distribution adaptive-parameters cuckoosearch algorithm.

A Weibull-distribution adaptive-parameters cuckoo search (WACS) algorithm is proposed, which can converge quickly and prevent falling into local optimal values, and thus improve the global search performance of a cuckoo search (CS) algorithm. In simulations, particle size inversions were performed using the proposed algorithm for unimodal and bimodal particle systems obeying Johnson's SB, Rosin-Rammler, and normal distribution, and the results were compared to the original CS algorithm, Weibull-distribution CS algorithm, and adaptive-parameters CS algorithm. Among them, the WACS algorithm has the best accuracy. The relative root mean squared error (RRMSE) was three to four orders of magnitude lower than the CS algorithm. The noise immunity of the algorithm was verified by comparing the particle size inversion error. Random noise [1%, 10%] was added to the scattered light energy of the target function, in 1% noise increments. The WACS algorithm prevailed, and the advantage became more obvious as the noise increased. A small-angle forward scattering experimental platform was built, and ferric tetroxide particles were selected as the measured particles. Experimental measurements were carried out on a unimodal particle system (50µm) and bimodal particle system (50 and 100µm), while the WACS algorithm was used on particle size distribution inversion. Compared to the CS algorithm, the RRMSE of the WACS algorithm was approximately 51% lower on unimodal and 66% lower on bimodal particle population inversions.

Carbon Monoxide Detection Based on the Carbon Nanotube-Coated Fiber Gas Sensor

Accurate detection of the internal decomposition components of SF6 electrical equipment plays an important role in the evaluation of equipment status. However, gas samples are usually taken out for detection at present, which makes it difficult to understand the real situation inside the equipment. In this paper, a carbon nanotube-coated fiber gas sensor is proposed, which has the potential to be applied as a built-in gas sensor. The fiber loop ring-down (FLRD) gas detection system based on the carbon nanotube-coated fiber gas sensor was built, and the detectable decomposition components among the four typical SF6 decomposition components of SO2, SO2F2 and SOF2 and CO were analyzed. The results showed that the fiber gas sensor was most sensitive to CO. Based on density functional theory, it was found that single-walled carbon nanotubes had the best adsorption effect on CO molecules under the same conditions, with the adsorption energy reaching −0.150 Ha. The detection performance of the system for CO was studied, and the results showed that there was a good linear relationship between CO concentration and ring-down time: R2 was 0.984, the maximum inversion error of 0~200 ppm CO was 1.916 ppm, and the relative error was 4.10%. The sensitivity of the system was 0.183 ns/ppm, and the detection limit of the system was 19.951 ppm. The system had good stability, with the standard deviation of single-point repeatability being 0.00356, and the standard deviation of the long period of the experiment being 0.00606. The research results provide a new idea for the detection of SF6 decomposition components, and lay the foundation for the component detection method of built-in fiber sensor of SF6 electrical equipment.

Time-Lapse Cross-Well Monitoring of CO2 Sequestration Using Coda Wave Interferometry

In this study, we explored the capability of coda wave interferometry (CWI) for monitoring CO2 storage by estimating the seismic velocity changes caused by CO2 injection. Given that the CWI method is highly efficient, the primary aim of this study was to provide a quick detection tool for the long-term monitoring of CO2 storage safety. In particular, we looked at monitoring with a cross-well geometry. We also expected that CWI could help to reduce the inversion errors of existing methods. Time-lapse upgoing waves and downgoing waves from two-component datasets were utilized to efficiently monitor the area between the wells and provide a quick indication of possible CO2 leakage. The resulting mean velocity changes versus the depth indicated the depth where velocity changes occurred. Combining the upgoing and downgoing wavefields provided a more specific indication of the depth range for changes. The calculated velocity changes were determined using the time shift between the time-lapse wavefields caused by CO2 injection/leakage. Hence, the resulting velocity changes were closely related to the ratio of propagation path length through the CO2 injection/leakage layer over the length of the entire travel path. The results indicated that the noise level and repeatability of the time-lapse datasets significantly influenced the results generated using CWI. Therefore, denoising and time-lapse processing were very important for improving the detectability of any change. Applying CWI to time-lapse cross-well surveys can be an effective tool for monitoring CO2 in the subsurface at a relatively low computational cost. As a highly efficient monitoring method, it is sensitive to changes in the seismic response caused by velocity changes in the subsurface and provides additional constraints on the inversion results from conventional travel time tomography and full waveform inversion.

Correcting Underestimation and Overestimation in PolInSAR Forest Canopy Height Estimation Using Microwave Penetration Depth

PolInSAR is an active remote sensing technique that is widely used for forest canopy height estimation, with the random volume over ground (RVoG) model being the most classic and effective forest canopy height inversion approach. However, penetration of microwave energy into the forest often leads to a downward shift of the canopy phase center, which leads to model underestimation of the forest canopy height. In addition, in the case of sparse and low forests, the canopy height is overestimated, owing to the large ground-to-volume amplitude ratio in the RVoG model and severe temporal decorrelation effects. To solve this problem, in this study, we conducted an experiment on forest canopy height estimation with the RVoG model using L-band multi-baseline fully polarized PolInSAR data obtained from the Lope and Pongara test areas of the AfriSAR project. We also propose various RVoG model error correction methods based on penetration depth by analyzing the model’s causes of underestimation and overestimation. The results show that: (1) In tall forest areas, there is a general underestimation of canopy height, and the value of this underestimation correlates strongly with the penetration depth, whereas in low forest areas, there is an overestimation of canopy height owing to severe temporal decorrelation; in this instance, overestimation can also be corrected by the penetration depth. (2) Based on the reference height RH100, we used training sample iterations to determine the correction thresholds to correct low canopy overestimation and tall canopy underestimation; by applying these thresholds, the inversion error of the RVoG model can be improved to some extent. The corrected R2 increased from 0.775 to 0.856, and the RMSE decreased from 7.748 m to 6.240 m in the Lope test area. (3) The results obtained using the infinite-depth volume condition p-value as the correction threshold were significantly better than the correction results for the reference height, with the corrected R2 value increasing from 0.775 to 0.914 and the RMSE decreasing from 7.748 m to 4.796 m. (4) Because p-values require a true height input, we extended the application scale of the method by predicting p-values as correction thresholds via machine learning methods and polarized interference features; accordingly, the corrected R2 increased from 0.775 to 0.845, and the RMSE decreased from 7.748 m to 6.422 m. The same pattern was obtained for the Pongara test area. Overall, the findings of this study strongly suggest that it is effective and feasible to use penetration depth to correct for RVoG model errors.

A digital twin of electrical tomography for quantitative multiphase flow imaging

Multiphase flow is ubiquitous in nature, industry and research, and accurate flow imaging is critical to understanding this complex phenomenon. Electrical tomography (ET) is a promising technique for multiphase flow visualization and characterization which provides a non-invasive and non-radiative way to unravel the internal physical properties at high temporal resolution. However, existing ET-based multiphase flow imaging methods are inadequate for quantitative imaging of multiphase flows due to inversion errors and limited ground truth data of fluid phases distribution. Here we report a digital twin (DT) framework of ET to address the challenges of real-time quantitative multiphase flow imaging. The proposed DT framework, building upon a synergistic integration of 3D field coupling simulation, model-based deep learning, and edge computing, allows ET to dynamically learn the flow features in the virtual space and implement the model in the physical system, thus providing excellent resolution and accuracy. The proposed DT framework is demonstrated using electrical capacitance tomography (ECT) of a gas-liquid two-phase flow. It can be readily extended to a broader range of tomography modalities, scenarios, and scales in biomedical, energy, and aerospace applications.

Fuzzy Neural Network Dynamic Inverse Control Strategy for Quadrotor UAV Based on Atmospheric Turbulence

Quadrotor UAV is vulnerable to external interference, which affects search and rescue. In this paper, a fuzzy neural network dynamic inverse controller (FNN-DIC) is designed to eliminate the instability of the attitude angle caused by atmospheric turbulence. Considering the complexity of atmospheric turbulence, the component model of atmospheric turbulence is obtained firstly based on the Dryden model, using Gaussian white noise as a random input signal and a designed shaping filter. Combined with the Newton-Euler equation, a nonlinear dynamic model for the quadrotor UAV with atmospheric disturbance is established. While the traditional nonlinear dynamic inverse cancels the nonlinearity of the controlled object, it relies on precise mathematical models. The fuzzy neural network can adaptively compensate for the inaccurate part of the model and the inverse error of the model caused by the external disturbance, and the stability of the control system is strictly proved by using the Lyapunov function. The experiments are carried out on the simulation platform, and the results show that the FNN method can ensure that the quadrotor UAV can still fly smoothly against strong disturbances, and that robustness of the system is significantly improved.

Inversion of the Full-Depth Temperature Profile Based on Few Depth-Fixed Temperatures

Seawater temperature plays a key role in underwater acoustics and marine fishery, etc. In oceanographic surveys, it is often desirable to detect the temperature profile and obtain its spatio-temporal variation. The present study shows that the temperatures at the depths which are the three extreme points of the first two empirical orthogonal function (EOF) modes, contain the largest amount of information. Based on the back propagation (BP) neural network, a model for reconstructing the full-depth temperature profile using a few temperatures at fixed depth is established. The experimental result shows that the root mean square error (RMSE) of the temperature profile inversion in the test set is mostly less than 0.2 °C, and the three-dimensional temperature field obtained in this study is relatively reliable.

A precise inversion method of cable joint core temperature with non-embedded detection based on UMAP and ISSA-BPNN

Obtaining the core temperature of the cable joint is vital to ensure the safe operation of the modern power system with integration. To improve the speed and accuracy of core temperature inversion, this study proposed a non-embedded cable joint temperature inversion method named uniform manifold approximation and projection (UMAP) and the improved sparrow search algorithm (ISSA) optimized the back propagation neural network (BPNN). Firstly, UMAP is used to reduce the feature dimension of sample data input and enhance the data visualization effect. After dimension reduction, the model input features are consistent with the international ampacity calculation standard, and the calculation speed and accuracy of the model are improved. To improve the optimization ability of SSA, the Tent chaotic operator is introduced, and then the ISSA is used to optimize BPNN to address the issue of unstable output and easy falling into a local minimum. At last, the optimization ability and temperature inversion effect of the improved model were compared with other competing algorithms based on the 10 kV cable joint temperature-rise test and CEC2017 benchmark function. The experimental results show that the proposed method shortens the calculation time of the model, and the mean absolute error of temperature inversion is about 0.1°C. The overall performance is the most outstanding, the training data set is unbiased, and the interpretability of the model improves, which can provide a reliable reference for line operation and maintenance personnel.

Quantitative acquisition of differential absorption cross sections of chlorobenzenes at different temperatures

Chlorobenzene is considered an essential organic synthesis intermediate and a precursor for the generation of persistent organic compounds in the waste disposal process, for which accurate detection of gaseous chlorobenzene can further help understand and control various chemical processes and effectively reduce pollution. Differential optical absorption spectroscopy is a reliable online method for detecting gaseous chlorobenzenes. It is crucial to investigate the effect of temperature on the optical absorption of the chlorobenzenes to quantify chlorobenzenes more precisely at various temperatures. A method to fix the effect of temperature variation on absorption spectra of chlorobenzene is initially proposed in this study, and it gave accurate concentrations. The proposed method can effectively improve the accuracy of chlorobenzene concentration measurements with an inverse concentration deviation of 3.2 % or less. The differential absorption cross sections at various temperatures are studied to understand how chlorobenzene absorption cross sections vary with temperature. Such a study is also helpful in reducing the concentration inversion errors induced by the variation of absorption cross sections of chlorobenzene with temperature. A novel method of introducing the binary function of the differential absorption cross sections with respect to wavelength and temperature is also proposed. The fitting of the binary function is done by downscaling functions at fixed wavelength and fixed temperature,respectively. Both fitting approaches obtained continuous differential absorption cross sections in the 201–220 nm wavelength band and 288–473 K temperature range, along with less than 2.74 % deviation in the concentration inversion measurements. Finally,based on the temperature specificity of the shape of the differential absorption cross sections,we developed another method using differential absorption spectroscopy for the simultaneous measurement of temperature and concentration, with a temperature prediction error of less than 1.89 %. This method is favorable to the applications of differential absorption spectroscopy in simultaneous measurement of temperature and concentration.

Seq2Morph: A deep learning deformable image registration algorithm for longitudinal imaging studies and adaptive radiotherapy.

To simultaneously register all the longitudinal images acquired in a radiotherapy course for analyzing patients' anatomy changes for adaptive radiotherapy (ART). To address the unique needs of ART, we designed Seq2Morph, a novel deep learning-based deformable image registration (DIR) network. Seq2Morph was built upon VoxelMorph which is a general-purpose framework for learning-based image registration. The major upgrades are (1) expansion of inputs to all weekly cone-beam computed tomography (CBCTs) acquired for monitoring treatment responses throughout a radiotherapy course, for registration to their planning CT; (2) incorporation of 3D convolutional long short-term memory between the encoder and decoder of VoxelMorph, to parse the temporal patterns of anatomical changes; and (3) addition of bidirectional pathways to calculate and minimize inverse consistency errors (ICEs). Longitudinal image sets from 50 patients, including a planning CT and 6 weekly CBCTs per patient, were utilized for network training and cross-validation. The outputs were deformation vector fields for all the registration pairs. The loss function was composed of a normalized cross-correlation for image intensity similarity, a DICE for contour similarity, an ICE, and a deformation regularization term. For performance evaluation, DICE and Hausdorff distance (HD) for the manual versus predicted contours of tumor and esophagus on weekly basis were quantified and further compared with other state-of-the-art algorithms, including conventional VoxelMorph and large deformation diffeomorphic metric mapping (LDDMM). Visualization of the hidden states of Seq2Morph revealed distinct spatiotemporal anatomy change patterns. Quantitatively, Seq2Morph performed similarly to LDDMM, but significantly outperformed VoxelMorph as measured by GTV DICE: (0.799±0.078, 0.798±0.081, and 0.773±0.078), and 50% HD (mm): (0.80±0.57, 0.88±0.66, and 0.95±0.60). The per-patient inference of Seq2Morph took 22 s, much less than LDDMM (∼30 min). Seq2Morph can provide accurate and fast DIR for longitudinal image studies by exploiting spatial-temporal patterns. It closely matches the clinical workflow and has the potential to serve both online and offline ART.

An image registration method for voxel-wise analysis of whole-body oncological PET-CT

Whole-body positron emission tomography-computed tomography (PET-CT) imaging in oncology provides comprehensive information of each patient’s disease status. However, image interpretation of volumetric data is a complex and time-consuming task. In this work, an image registration method targeted towards computer-aided voxel-wise analysis of whole-body PET-CT data was developed. The method used both CT images and tissue segmentation masks in parallel to spatially align images step-by-step. To evaluate its performance, a set of baseline PET-CT images of 131 classical Hodgkin lymphoma (cHL) patients and longitudinal image series of 135 head and neck cancer (HNC) patients were registered between and within subjects according to the proposed method. Results showed that major organs and anatomical structures generally were registered correctly. Whole-body inverse consistency vector and intensity magnitude errors were on average less than 5 mm and 45 Hounsfield units respectively in both registration tasks. Image registration was feasible in time and the nearly automatic pipeline enabled efficient image processing. Metabolic tumor volumes of the cHL patients and registration-derived therapy-related tissue volume change of the HNC patients mapped to template spaces confirmed proof-of-concept. In conclusion, the method established a robust point-correspondence and enabled quantitative visualization of group-wise image features on voxel level.

A 39-GHz Phase-Inverting Variable Gain Power Amplifier in 65-nm CMOS for 5G Communication

This letter presents a 39-GHz phase-inverting variable gain power amplifier (VGPA) for 5G communication. Adopting a Gilbert structure-based variable gain amplifier (VGA) stage, the VGPA realized the dB-linear gain control characteristic as well as 180° phase inversion. At 0°/180° phase states, the 39-GHz VGPA achieves the maximum gain of 38.7/38.9 dB with gain tuning range of 5.6/5.2 dB, respectively. Over 38–43 GHz, the phase inversion error is limited within 5.9°, and the rms phase error is less than 3.6°/2.2°. Meanwhile, with the metal interleaving coplanar transformer matching network, this VGPA achieves 17.7/17.6-dBm Psat and 13.2/13.36-dBm OP1 dB, with the power added efficiency (PAE) of 35%/34.5% and 13.6%/14.4% at the saturation and 1-dB compression points, respectively. Over the gain control states, the OP1 dB fluctuation is less than 0.3 dB. Implemented in a 65-nm CMOS process, the proposed VGPA consumes 150 mW with a chip area of 0.3 mm2.

Computable error bounds of multidimensional Euler inversion and their financial applications

Transform inversion is an efficient approximation procedure in operations research, yet the inversion results are sometimes unstable which calls for comprehensive error analysis. This article proposes a multidimensional Euler inversion (MEI) algorithm with computable error bounds. We design mild sufficient conditions that validate the inversion formula, and provide closed-form upper bounds of the inversion errors. Numerical experiments are conducted to compute the joint probability of default and barrier option prices under complicated stochastic models, and output the associated error bounds.

Development of a Pixel-Wise Forest Transmissivity Model at Frequencies of 19 GHz and 37 GHz for Snow Depth Inversion in Northeast China

Satellite passive microwave remote sensing has been extensively used to estimate snow depth (SD) and snow water equivalent (SWE) across both regional and continental scales. However, the presence of forests causes significant uncertainties in the estimations of snow parameters. Forest transmissivity is one of the most important parameters for describing the microwave radiation and scattering characteristics of forest canopies. Although many researchers have constructed models for the functional relationship between forest transmissivity and forest vegetation parameters (e.g., stand growth and accumulation), such relationships are strongly limited by the inversion accuracy of vegetation parameters, forest distribution types, and scale-transformation effects in terms of regional or global scale applications. In this research, we propose a pixel-wise forest transmissivity estimation model (Pixel-wise γ Model) based on long-term series satellite brightness temperature (TB) data for the satellite remote sensing inversion of snow parameters. The model performance is evaluated and applied in SD inversion. The results show that the SD inversion errors RMSE and Bias are 9.8 cm and −1.5 cm, respectively; the SD inversion results are improved by 41% and 84% after using the Pixel-wise γ Model, compared with the forest transmissivity model applied in the GlobSnow v3.0 product. The proposed forest transmissivity model does not depend on forest cover parameters and other ground measurement parameters, which greatly improves its application scope and simplicity.

Estimation of Cumulative Organ Maximum Dose and Confidence Intervals for MRI-Guided Adaptive Radiotherapy of Abdominal Cancer

<h3>Purpose/Objective(s)</h3> The maximum dose (Dmax), e.g., D0.03cc (dose to 0.03cc volume), of adjacent organs at risk (OARs) is a primary dose-limiting constraint in MRI-guided adaptive radiotherapy (MRgART) of abdominal cancer. We utilized inverse consistency error (ICE) maps to estimate voxel-wise uncertainties in deformable image registration (DIR) based dose accumulation (DDA) and confidence intervals in cumulative OARs Dmax during MRgART for pancreatic cancer. <h3>Materials/Methods</h3> Motion-average reference (first fraction) and subsequent daily MRIs, collected in MRgART for five pancreatic cancer patients treated with 33 Gy in 5 fractions on a 1.5T MR-Linac, were registered using a free-form DIR algorithm based on feature similarity scoring metrics and were used to accumulate daily doses. Forward and reverse DIRs were performed, and ICE maps were calculated in the reference image. The correlation between ICE and actual registration error (RE) was assessed by identifying anatomical landmarks (63) in a reference-daily image pair and measuring the landmark REs (after forward-DIR) and ICEs (after forward and reverse DIRs). To account for the deformation vector field spatial uncertainty affecting the DDA, for each voxel in the reference image we associated a cloud of dose grid points centered at the voxel landing coordinates in the daily image with a radius proportional to the ICE length. We considered that the cloud would encompass the "true" registration point with a high likelihood. The uncertainty in the dose mapped to each voxel from each fraction was determined as the standard deviation of the grid point doses within the cloud. The maxima and minima of the dose distributions were computed from the cumulative uncertainties, and confidence intervals for Dmax were determined. <h3>Results</h3> The measured REs and ICEs for landmarks indicated a positive correlation between these errors (Pearson's correlation coefficient r=0.795, p-value=7.04 × 10⁻¹⁵), RE being about twice ICE. The ICEs averaged 1.5 mm and 2.5 mm in the duodenum and stomach. For the duodenum, cumulative D0.03cc and D1cc at the end of treatment ranged from 85.7% to 100.4% of the plan constraint value (confidence intervals included). The uncertainty intervals were between 1.1% and 2.2% in four cases and approximately 7% for the fifth case. Cumulative D0.03cc in the stomach varied from 89.4% to 102.8%, with uncertainty intervals that extended from 2.5% to 6.4%. All Dmax lower limits were below 100%. <h3>Conclusion</h3> Voxel-wise uncertainties in DIR-based dose accumulation during MRgART of abdominal cancer can be estimated using an ICE-based technique. The derived confidence intervals for cumulative Dmax (D1cc or D0.03cc) of OARs (the duodenum and stomach) can be utilized to guide daily dose adaptation throughout MRgART.

An Estimate of Uncertainty in Deformable Image Registration-Based Accumulated Biological Equivalent Dose for Re-Irradiation

<h3>Purpose/Objective(s)</h3> We describe a dose volume histogram (DVH) overlay technique to estimate uncertainty in deformable image registration (DIR) based accumulated biologically equivalent dose (BED) for re-irradiation planning. We compare applicability of two DIR methods, contour-based (C-DIR) and image intensity and contour hybrid (H-DIR) DIR for BED accumulation. <h3>Materials/Methods</h3> Patient CT-based re-irradiation plans to the same anatomic regions as in their initial irradiations over a four-year period were analyzed. Among the organs-at-risk (OARs) for which BED was accumulated were stomach, heart, and esophagus. Physical dose distributions were converted to BED using OAR-specific parameters based on a linear-quadratic-linear model. For C-DIR, the registration was based only upon the contours drawn on both images. H-DIR is an image intensity-based DIR technique which includes contour-based registration to augment the DIR results. All prior BEDs were warped to the most recent CT image for accumulation. Data input to the DVH overlay workflow were the two CT images to be registered, the deformation vector field, the BED on the earlier CT, and the contours on the later CT. The later-CT contours were warped to the earlier CT, and the earlier-CT BED was warped to the later CT; BED DVHs from both images were then calculated and overlaid. For a fully invertible DIR, the two DVHs for the OAR should be identical; differences between the DVHs were interpreted as BED uncertainties due to inverse consistency error. For a given DVH point, the uncertainty was obtained from the differences between the overlaid DVHs. <h3>Results</h3> For an abdomen case, the stomach accumulated BED_max is 3% higher using C-DIR versus H-DIR; ΔBED_max is approximately 2% for both DIR methods. The higher isodoses were distal to the stomach for all plans; H-DIR, which accounts for regions distal to the OAR, is appropriate for re-irradiation BED calculations. For a thoracic case, both DIR methods yield similar results for the heart. The difference between H-DIR and C-DIR for accumulated heart BED_max is 2.4%; ΔBED_max is 0.9% and 0.6% for H-DIR and C-DIR, respectively. For the esophagus, accumulated BED_max is 54% higher using H-DIR instead of C-DIR, and ΔBED_max is much lower for C-DIR (0.2%) than for H-DIR (1.7%). Visual inspection showed that the BED distribution on the esophagus using H-DIR is unreasonable, attributed to H-DIR relying too heavily upon image intensity features. For accurate BED accumulation in the esophagus, C-DIR is essential during the re-irradiation planning for this case. <h3>Conclusion</h3> The DVH overlay technique can estimate the uncertainty in accumulated BED for re-irradiation scenarios. Caution should be exercised in using various DIR methods before applying DIR dose accumulation for re-irradiation planning. Contour-based DIR may be the preferred registration method for re-irradiation dose accumulation.