Error Map Research Articles

Learning Semantic Context from Normal Samples for Unsupervised Anomaly Detection

Unsupervised anomaly detection aims to identify data samples that have low probability density from a set of input samples, and only the normal samples are provided for model training. The inference of abnormal regions on the input image requires an understanding of the surrounding semantic context. This work presents a Semantic Context based Anomaly Detection Network, SCADN, for unsupervised anomaly detection by learning the semantic context from the normal samples. To achieve this, we first generate multi-scale striped masks to remove a part of regions from the normal samples, and then train a generative adversarial network to reconstruct the unseen regions. Note that the masks are designed in multiple scales and stripe directions, and various training examples are generated to obtain the rich semantic context . In testing, we obtain an error map by computing the difference between the reconstructed image and the input image for all samples, and infer the abnormal samples based on the error maps. Finally, we perform various experiments on three public benchmark datasets and a new dataset LaceAD collected by us, and show that our method clearly outperforms the current state-of-the-art methods.

Developing an Error Map for Cognitive Navigation System

Global Navigation Satellite System (GNSS) positioning is a widely used and a key intelligent transportation system (ITS) technology. An automotive navigation system is necessary when driving to an unfamiliar location. One difficulty regarding GNSS positioning occurs when an error is caused by various factors, which reduces the positioning accuracy and impacts the performance of applications such as navigation systems. However, there is no way for users to be aware of the magnitude of the error. In this paper, we propose a cognitive navigation system that uses an error map to provide users with information about the magnitude of errors to better understand the positioning accuracy. This technology can allow us to develop a new navigation system that offers a more user-friendly interface. We propose that the method will develop an error map by using two low-cost GNSS receivers to provide information about the magnitude of errors. We also recommend some applications that will work with the error map.

Modified Diffusion Tensor Image Processing Pipeline for Archived Studies of Patients With Leukoencephalopathy.

In archived diffusion tensor imaging (DTI) studies, a reversed-phase encoding (PE) scan required to correct the distortion in single-shot echo-planar imaging (EPI) may not have been acquired. Furthermore, DTI tractography is adversely affected by incorrect white matter segmentation due to leukoencephalopathy (LE). All these issues need to be addressed. To propose and evaluate a modified DTI processing pipeline with DIstortion COrrection using pseudo T2 -weighted images (DICOT) to overcome limitations in existing acquisition protocols. Retrospective feasibility. DICOT was assessed in simulated data and 84 acute lymphoblastic leukemia (ALL) patients with reversed PE acquired. The pipeline was then tested in 522 scans from 261 ALL patients without a reversed PE acquired. A 3 T; diffusion-weighted EPI; 3D magnetization prepared rapid acquisition gradient echo (MPRAGE). Repeated measures analysis of variance and Tukey post hoc tests were performed to compare fractional anisotropy (FA) values obtained by different methods. FA and corresponding absolute error maps were obtained using TOPUP, DICOT, INVERSION (Inverse contrast Normalization for VERy Simple registratION) and NO CORR (no correction). Each method was assessed by comparing to TOPUP. The pipeline in the ALL patients was evaluated based on the failure rate of the distortion correction using the global correlation values. Using DICOT reduced the mean absolute errors by an average of 32% in FA in simulation datasets. In 84 patients, the error reductions were approximately 15% in FA with DICOT, while it was 5% with INVERSION. No significant differences between the TOPUP and DICOT were observed in FA with P=0.090/0.894(AP/PA). Only 15 of 516 examinations requiring any additional manual intervention. This modified pipeline produced better results than the INVERSION. Furthermore, robust performance was demonstrated in archived patient scans acquired without an inverse PE necessary for TOPUP correction. 3 TECHNICAL EFFICACY: Stage 2.

MonodepthPlus: self-supervised monocular depth estimation using soft-attention and learnable outlier-masking

Self-supervised learning of depth from monocular videos has recently drawn attention as it has notable advantages over supervised ones in a training framework. We propose a self-supervised monocular depth estimation method with a set of improvements, which together result in both quantitatively and qualitatively improved depth maps compared to competing self-supervised methods. Our architecture amends current deep convolutional neural network backbone combined with attention mechanism to boost depth estimation performance. Additionally, for addressing moving objects and occlusion, we propose a learnable outlier-masking technique to exclude invalid pixels in photometric error map. Extensive experiments show the effectiveness of the proposed improvements. Our proposed model achieves state-of-the-art performance on KITTI dataset compared with other competing methods.

Stochastic dynamics of a piezoelectric energy harvester with fractional damping under Gaussian colored noise excitation

This paper introduces the fractional damping for a piezoelectric energy harvester subjected to Gaussian colored noise and investigates the dynamic response by the stochastic averaging method. To successfully achieve this goal, the original system is decoupled into the equivalent stochastic system through variable transformation at first. Then the stochastic averaging approach is employed to construct the theoretical results. Furthermore, the feasibility and performance of the stochastic averaging method are evaluated with the assistance of the numerical results from Monte Carlo simulation. Finally, we concentrate on discussing the effect of fractional orders and system parameters on the mean square voltage and analyzing the effectiveness of the stochastic averaging method for the piezoelectric energy harvesting system by heat maps of the relative error in a quantitative perspective.

NM-GAN: Noise-modulated generative adversarial network for video anomaly detection

As an important and challenging task for intelligent video surveillance systems, video anomaly detection is generally referred to as automatic recognition of video frames that contain abnormal targets, behavior or events. Although it has been widely applied in real scenes, anomaly detection remains a challenging task because of the vague definition of anomaly and the lack of the anomaly samples. Inspired by the widespread application of Generative Adversarial Network (GAN), we propose an end-to-end pipeline called NM-GAN which assembles an encode-decoder reconstruction network and a CNN-based discrimination network in a GAN-like architecture. The generalization ability of the reconstruction network is properly modulated via the adversarial learning around reconstruction error maps and noise maps. Meanwhile, the discrimination network is trained to distinguish anomaly samples from normal samples based on the reconstruction error maps. Finally, the output of the discrimination network is transferred to evaluate anomaly score of the input frame. The thorough proof-of-principle experiments and ablation tests on several popular datasets reveal that the proposed model enhance the generalization ability of the reconstruction network and the distinguishability of the discrimination network significantly. The comparison with the state-of-the-art shows that the proposed NM-GAN model outperforms most competing models in precision and stability.

Auto-AD: Autonomous Hyperspectral Anomaly Detection Network Based on Fully Convolutional Autoencoder

Hyperspectral anomaly detection is aimed at detecting observations that differ from their surroundings, and is an active area of research in hyperspectral image processing. Recently, autoencoders (AEs) have been applied in hyperspectral anomaly detection; however, the existing AE-based methods are complicated and involve manual parameter setting and preprocessing and/or postprocessing procedures. In this article, an autonomous hyperspectral anomaly detection network (Auto-AD) is proposed, in which the background is reconstructed by the network and the anomalies appear as reconstruction errors. Specifically, through a fully convolutional AE with skip connections, the background can be reconstructed while the anomalies are difficult to reconstruct, since the anomalies are relatively small compared to the background and have a low probability of occurring in the image. To further suppress the anomaly reconstruction, an adaptive-weighted loss function is designed, where the weights of potential anomalous pixels with large reconstruction errors are reduced during training. As a result, the anomalies have a higher contrast with the background in the map of reconstruction errors. The experimental results obtained on a public airborne data set and two unmanned aerial vehicle-borne hyperspectral data sets confirm the effectiveness of the proposed Auto-AD method.

Quantum unary approach to option pricing

We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude distribution corresponding to the asset value at maturity is generated using a low depth circuit; second, the computation of the expected return is computed with simple controlled gates; and third, standard Amplitude Estimation is used to gain quantum advantage. On the positive side, unary representation remarkably simplifies the structure and depth of the quantum circuit. Amplitude distributions uses quantum superposition to bypass the role of classical Monte Carlo simulation. The unary representation also provides a post-selection consistency check that allows for a substantial mitigation in the error of the computation. On the negative side, unary representation requires linearly many qubits to represent a target probability distribution, as compared to the logarithmic scaling of binary algorithms. We compare the performance of both unary vs. binary option pricing algorithms using error maps, and find that unary representation may bring a relevant advantage in practice for near-term devices.

Nine years of SMOS sea surface salinity global maps at the Barcelona Expert Center

Abstract. After more than 10 years in orbit, the Soil Moisture and Ocean Salinity (SMOS) European mission is still a unique, high-quality instrument for providing soil moisture over land and sea surface salinity (SSS) over the oceans. At the Barcelona Expert Center (BEC), a new reprocessing of 9 years (2011–2019) of global SMOS SSS maps has been generated. This work presents the algorithms used in the generation of BEC global SMOS SSS product v2.0, as well as an extensive quality assessment. Three SMOS SSS fields are distributed: a high-resolution level-3 product (with DOI https://doi.org/10.20350/digitalCSIC/12601, Olmedo et al., 2020a) consisting of binned SSS in 9 d maps at 0.25∘×0.25∘; low-resolution level-3 SSS computed from the binned salinity by applying a smoothing spatial window of 50 km radius; and level-4 SSS (with DOI https://doi.org/10.20350/digitalCSIC/12600, Olmedo et al., 2020b) consisting of daily 0.05∘×0.05∘ maps that are computed by multifractal fusion with sea surface temperature maps. For the validation of BEC SSS products, we have applied a battery of tests aimed at the assessment of quality of the products both in value and in structure. First, we have compared BEC SSS products with near-to-surface salinity measurements provided by Argo floats. Secondly, we have assessed the geophysical consistency of the products characterized by singularity analysis, and the effective spatial resolutions are also estimated by means of power density spectra and singularity density spectra. Finally, we have calculated full maps of SSS errors by using correlated triple collocation. We have compared the performance of the BEC SMOS product with other satellite SSS and reanalysis products. The main outcomes of this quality assessment are as follows. (i) The bias between BEC SMOS and Argo salinity is lower than 0.02 psu at a global scale, while the standard deviation of their difference is lower than 0.34 and 0.27 psu for the high- and low-resolution level-3 fields (respectively) and 0.24 psu for the level-4 salinity. (ii) The effective spatial resolution is around 40 km for all SSS products and regions. (iii) The results from triple collocation show the BEC SMOS level-4 product as the product with the lowest estimated salinity error in most of the global ocean and the BEC SMOS high-resolution level-3 as the one with the lowest estimated salinity error in regions strongly affected by rainfall and continental freshwater discharge.

Development of thermal error mapping model for the dry gear hobbing machine based on CNN-DAE integrated structure and its application

The dry cutting gear hobbing machine is a specialized manufacturing equipment for small-module gears. During the continuous large-volume gear cutting process, the thermal error plays a major negative role in the quality of gear making. In this paper, based on the convolutional neural network and the denoising auto-encoder algorithm, we developed a new mapping model between features of characteristic signals and the thermal-induced deviation of the spacing between the hob and the workpiece. In the modeling, the temperature change of key thermal points, the hob spindle current signal, and the corresponding thermal-induced deviation trend of spacing between the hob and the worktable in a continuous gear cutting experiment were collected and sampled. Those samples were fed into the TensorFlow framework to train the integrated mathematical structure. Finally, the mapping model was obtained, which was capable to accurately and quickly quantify the thermal error of the YDE-type dry gear hobbing machine. Accordingly, a thermal error compensation system was developed as well. To prove the accountabilities of this newly proposed mapping model as well as the corresponding thermal error compensation system, another continuous gear cutting verification experiment was carried out on the dry gear hobbing machine equipped with this new thermal error compensation system. The experiment results showed that with the help of the newly proposed thermal error model and compensation system, the M values of machined gears, which directly reflected the effect of the thermal error on the gear hobbing accuracy, remained in a practically acceptable range (± 0.02 mm) in the continuous gear cutting, which proved the reliability of our proposed new mapping model.

Accelerated radial echo-planar spectroscopic imaging using golden angle view-ordering and compressed-sensing reconstruction with total variation regularization.

To implement a novel, accelerated, 2D radial echo-planar spectroscopic imaging (REPSI) sequence using undersampled radial k-space trajectories and compressed-sensing reconstruction, and to compare results with those from an undersampled Cartesian spectroscopic sequence. The REPSI sequence was implemented using golden-angle view-ordering on a 3T MRI scanner. Radial and Cartesian echo-planar spectroscopic imaging (EPSI) data were acquired at six acceleration factors, each with time-equivalent scan durations, and reconstructed using compressed sensing with total variation regularization. Results from prospectively and retrospectively undersampled phantom and in vivo brain data were compared over estimated concentrations and Cramer-Rao lower-bound values, normalized RMS errors of reconstructed metabolite maps, and percent absolute differences between fully sampled and reconstructed spectroscopic images. The REPSI method with compressed sensing is able to tolerate greater reductions in scan time compared with EPSI. The reconstruction and quantitation metrics (i.e., spectral normalized RMS error maps, metabolite map normalized RMS error values [e.g., for total N-acetyl asparate, REPSI = 9.4% vs EPSI = 16.3%; acceleration factor = 2.5], percent absolute difference maps, and concentration and Cramer-Rao lower-bound estimates) showed that accelerated REPSI can reduce the scan time by a factor of 2.5 while retaining image and quantitation quality. Accelerated MRSI using undersampled radial echo-planar acquisitions provides greater reconstruction accuracy and more reliable quantitation for a range of acceleration factors compared with time-equivalent compressed-sensing reconstructions of undersampled Cartesian EPSI. Compared to the Cartesian approach, radial undersampling with compressed sensing could help reduce 2D spectroscopic imaging acquisition time, and offers a better trade-off between imaging speed and quality.

Direct Image-Based Attenuation Correction using Conditional Generative Adversarial Network for SPECT Myocardial Perfusion Imaging.

Attenuation correction (AC) is important for an accurate interpretation and quantitative analysis of SPECT myocardial perfusion imaging. Dedicated cardiac SPECT systems have invaluable efficacy in the evaluation and risk stratification of patients with known or suspected cardiovascular disease. However, most dedicated cardiac SPECT systems are standalone, not combined with a transmission imaging capability such as computed tomography (CT) for generating attenuation maps for AC. To address this problem, we propose to apply a conditional generative adversarial network (cGAN) for generating attenuation-corrected SPECT images (SPECTGAN ) directly from non-corrected SPECT images (SPECTNC ) in image domain as a one-step process without requiring additional intermediate step. The proposed network was trained and tested for 100 cardiac SPECT/CT data from a GE Discovery NM 570c SPECT/CT, collected retrospectively at Yale New Haven Hospital.The generated images were evaluated quantitatively through the normalized root mean square error (NRMSE), peak signal to noise ratio (PSNR), and structural similarity index (SSIM) and statistically through joint histogram and error maps. In comparison to the reference CT-based correction (SPECTCTAC ), NRMSEs were 0.2258±0.0777 and 0.1410±0.0768 (37.5% reduction of errors); PSNRs 31.7712±2.9965 and 36.3823±3.7424 (14.5% improvement in signal to noise ratio); SSIMs 0.9877±0.0075 and 0.9949±0.0043 (0.7% improvement in structural similarity) for SPECTNC and SPECTGAN , respectively. This work demonstrates that the conditional adversarial training can achieve accurate CT-less attenuation correction for SPECT MPI, that is quantitatively comparable to CTAC. Standalone dedicated cardiac SPECT scanners can benefit from the proposed GAN to reduce attenuation artifacts efficiently.

Estimating Compton scatter distributions with a regressional neural network for use in a real-time staff dose management system for fluoroscopic procedures.

Staff-dose management in fluoroscopic procedures is a continuing concern due to insufficient awareness of radiation dose levels. To maintain dose as low as reasonably achievable (ALARA), we have developed a software system capable of monitoring the procedure room scattered radiation and the dose to staff members in real-time during fluoroscopic procedures. The scattered-radiation display system (SDS) acquires imaging-system signal inputs to update technique and geometric parameters used to provide a color-coded mapping of room scatter. We have calculated a discrete look-up-table (LUT) of scatter distributions using Monte-Carlo (MC) software and developed an interpolation technique for the multiple parameters known to alter the spatial shape of the distribution. However, the file size for the LUT's can be large (~2GB), leading to long SDS installation times in the clinic. Instead, this work investigated the speed and accuracy of a regressional neural network (RNN) that we developed for predicting the scatter distribution from imaging-system inputs without the need for the LUT and interpolation. This method greatly reduces installation time while maintaining real-time performance. Results using error maps derived from the structural similarity index indicate high visual accuracy of predicted matrices when compared to the MC-calculated distributions. Dose error is also acceptable with a matrix element-averaged percent error of 31%. This dose-monitoring system for staff members can lead to improved radiation safety due to immediate visual feedback of high-dose regions in the room during the procedure as well as enhanced reporting of individual doses post-procedure.

DeepHCS++: Bright-field to fluorescence microscopy image conversion using multi-task learning with adversarial losses for label-free high-content screening

In this paper, we propose a novel microscopy image translation method for transforming a bright-field microscopy image into three different fluorescence images to observe the apoptosis, nuclei, and cytoplasm of cells, which visualize dead cells, nuclei of cells, and cytoplasm of cells, respectively. These biomarkers are commonly used in high-content drug screening to analyze drug response. The main contribution of the proposed work is the automatic generation of three fluorescence images from a conventional bright-field image; this can greatly reduce the time-consuming and laborious tissue preparation process and improve throughput of the screening process. Our proposed method uses only a single bright-field image and the corresponding fluorescence images as a set of image pairs for training an end-to-end deep convolutional neural network. By leveraging deep convolutional neural networks with a set of image pairs of bright-field and corresponding fluorescence images, our proposed method can produce synthetic fluorescence images comparable to real fluorescence microscopy images with high accuracy. Our proposed model uses multi-task learning with adversarial losses to generate more accurate and realistic microscopy images. We assess the efficacy of the proposed method using real bright-field and fluorescence microscopy image datasets from patient-driven samples of a glioblastoma, and validate the method's accuracy with various quality metrics including cell number correlation (CNC), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), cell viability correlation (CVC), error maps, and R2 correlation.

Optical performance of progressive addition lenses (PALs) with astigmatic prescription

The progressive addition lens (PAL) is a spectacle lens design with progressive refractive power changes across the lens surface to provide sharp vision at different viewing distances for patients with reduced accommodative strength. It has gained in popularity not just for presbyopic patients, but also patients with occupational (office, driving, or digital device) and therapeutic (e.g., myopia control) needs. However, despite the increasing prevalence of astigmatism in adults > 40 years old who rely on PAL correction, no metric is available to reflect the optical variation in PALs with astigmatic prescriptions. Based on recent studies, four novel optical metrics sensitive to variation of refractive power across the lens surface of PALs have been developed. These metrics were used to compare the optical performance of PALs of various prescriptions, designs, and manufacturers. For each lens, the refractive power profile was first measured with a Moire-deflectometry-based instrument.The data was then exported and analyzed using a two-dimensional error map for each of the four metrics. The results revealed significant impacts of astigmatic prescription, providing evidence for the usefulness of these metrics in quantifying the optical performance of PALs for patients with astigmatic prescriptions.

Kinematic calibration of a 5-axis parallel machining robot based on dimensionless error mapping matrix

Accuracy problem is one of the most challenging issues for the application of parallel robots in manufacturing industry, and kinematic calibration is a feasible approach to solve it. Although lots of researches have brought up a diversity of calibration methods, there are still rooms for the improvement of the accuracy, efficiency and robustness of these calibration effects. In this paper, an improved method for kinematic calibration of a 5-axis parallel machining robot is proposed, which includes a new forward kinematic solution (FKS) based on dual quaternion and a modified error modeling process leading to dimensionless error mapping matrixes (EMMs). On this basis, an iterative identification procedure is schemed, and the kinematics and identification simulations are carried out. The kinematics simulation results show that the proposed FKS has wider convergence range and faster computation speed than Levenberg-Marquardt algorithm, while the identification simulation results show that the residual pose errors with the proposed dimensionless EMMs are lower than that with the conventional EMM in various units. Additionally, the procedure of the full pose measurement with a laser tracker and an auxiliary tool is introduced, and thereby the contrast experiments of kinematic calibration on the prototype are conducted. The experiment results indicate that the residual position and orientation errors based on the dimensionless EMM decrease by 97.67% and 86.85% of the original values, respectively, at least, and by 76.77% and 38.65% of that based on the conventional EMM, respectively, at most. Consequently, it is further confirmed that the proposed calibration method is effective in enhancing the identification accuracy of the geometric errors and improving the positioning accuracy of the studied parallel robot.

Nonlinear local wave-direction estimation for in-sight and out-of-sight damage localization in composite plates

In this study, a novel wave processing algorithm: “local wave-direction estimation (LWDE)”, is proposed to localize sources of guided waves using full-field scanning laser Doppler (SLDV) measurements. The LWDE algorithm uses angular bandpass filters in the wavenumber domain to determine the local propagation direction of the guided wave. The obtained local wave-direction map is converted into an error map by the use of a virtual local wave-direction map. The resulting error map reveals the sources of guided waves as local minima. The exploitation of local directional wave information provides the opportunity to scan only a small part of the component for localization of out-of-sight sources of guided waves. The source localization performance of LWDE is illustrated for localization of multiple piezoelectric sources in a quasi-isotropic CFRP plate.LWDE is further coupled to nonlinear vibrations in view of damage localization (NL-LWDE). The second higher harmonic component is extracted from the SLDV measurement and the sources of this higher harmonic component are localized. Damages behave as sources of higher harmonics and are thus localized by this NL-LWDE approach. This is demonstrated for a cross-ply CFRP plate with low velocity impact damage. The proposed combination of (i) nonlinear vibration filtering, (ii) direction estimation using angular bandpass filtering in the wavenumber domain and (iii) error map construction using the virtual wave-direction map results in a robust and baseline-free NDT technique. It can be used for accurate localization of multiple in-sight or out-of-sight damages in composite plates with unknown material properties and layup.

Unsupervised Pixel-Wise Hyperspectral Anomaly Detection via Autoencoding Adversarial Networks

We propose a completely unsupervised pixel-wise anomaly detection method for hyperspectral images. The proposed method consists of three steps called data preparation, reconstruction, and detection. In the data preparation step, we apply a background purification to train the deep network in an unsupervised manner. In the reconstruction step, we propose to use three different deep autoencoding adversarial network (AEAN) models including 1D-AEAN, 2D-AEAN, and 3D-AEAN which are developed for working on spectral, spatial, and joint spectral-spatial domains, respectively. The goal of the AEAN models is to generate synthesized hyperspectral images (HSIs) which are close to real ones. A reconstruction error map (REM) is calculated between the original and the synthesized image pixels. In the detection step, we propose to use a WRX-based detector in which the pixel weights are obtained according to REM. We compare our proposed method with the classical RX, WRX, support vector data description-based (SVDD), collaborative representation-based detector (CRD), adaptive weight deep belief network (AW-DBN) detector and deep autoencoder anomaly detection (DAEAD) method on real hyperspectral datasets. The experimental results show that the proposed approach outperforms other detectors in the benchmark.

Constraints for Time-Multiplexed Structured Light with a Hand-held Camera


 
 Multi-frame structured light in projector-camera systems affords high-density and non-contact methods of 3D surface reconstruction. However, they have strict setup constraints which can become expensive and time-consuming. Here, we investigate the conditions under which a projective homography can be used to compensate for small perturbations in pose caused by a hand-held camera. We synthesize data using a pinhole camera model and use it to determine the average 2D reprojection error per point correspondence. This error map is grouped into regions with specified upper-bounds to classify which regions produce sufficiently minimal error to be considered feasible for a structured-light projector-camera system with a hand-held camera. Empirical results demonstrate that a sub-pixel reprojection accuracy is achievable with a feasible geometric constraints
 

Mapping Gaia Parallax Systematic Errors over the Sky with Faint Milky Way Stars

Abstract Parallaxes measured by the Gaia mission have huge significance for astronomy, but parallaxes in Gaia DR2 are known to have systematic errors that depend on the source position and other quantities. We use the abundant information in faint Milky Way stars, along with the Gaia Object Generator simulation of the Gaia catalog, to probe the spatial dependence of Gaia DR2 parallax systematic errors in an empirical way. The parallax signal, concentrated in thick disk turnoff stars with magnitude G ∼ 17, is sufficient to construct maps of the parallax systematic error over the majority of the sky. These maps show a locally regular “waffle pattern” on ∼1° scales following Gaia scan directions, stronger linear “scar” features, and coherent variations on larger scales. The parallax bias maps also retain traces of astrophysical effects such as dust clouds. The waffle pattern, known from earlier maps of the Magellanic Clouds, extends over the entire sky; its local rms amplitude averages 15 μas and varies by about a factor of two. The strength of this pattern increases by a factor ∼6 from magnitude G = 13 to G = 20. Correlations with parallaxes of quasars and of stars with independent distance estimates support our bias estimates. Using similar methods, we map systematic errors in the proper motion and examine the relationship with the parallax systematics. We provide a code package to access and query our bias maps. Similar tests on the general stellar population should be useful in quantifying systematic errors in future Gaia releases.