Pixel-level Uncertainty Research Articles

Ultrasonic characterization of defects in polycrystalline materials based on TFM image reconstruction using denoising diffusion probabilistic models

This paper presents a refined ultrasonic total focusing method (TFM) for accurately characterizing key defect parameters including size, orientation, and location in complex materials. The proposed approach aims to accurately reconstruct the defect shape in images compromised by grain interference. First, a TFM image database was generated with varying defect parameters and grain noise levels by adopting a custom forward modeling process based on superposition of defect and grain scattering data. Second, a new architecture called TFM-DDPM was then proposed which incorporates TFM and the conditional denoising diffusion probabilistic model (DDPM). Third, pixel-level uncertainty can be quantified through repeated sampling of noise which follows a standard normal distribution. An acceptance criterion for the reconstruction was further established by analyzing the quantified uncertainty. In simulation, the median Dice coefficient between the de-noised TFMs of 30° cracks and their corresponding ground truth images increased from 0.5585 to 0.9137 using the proposed approach, and the median IoU metric rose from 0.3875 to 0.8408. By applying the 6-dB drop approach to the reconstructed images, the root mean squared errors (RMSEs) of size, angle and location were decreased by 93.59%, 86.90% and 86.25%, respectively. It is also demonstrated that our method can reject 69.19% of incorrect characterization results caused by high levels of noise and/or images with steeply inclined (e.g., 45°) cracks, while accepting 97.29% accurate results. Experimental results obtained on nickel-based alloy K403 specimens also exhibited significant improvements. For 2–3 mm cracks, the average sizing error reduced from 0.46 mm to 0.13 mm, and the error in crack angle decreased from 28.63° to 1.50°. Comparable performance enhancements were observed for 4–5 mm cracks using the proposed approach.

DaGAN++: Depth-Aware Generative Adversarial Network for Talking Head Video Generation.

Predominant techniques on talking head generation largely depend on 2D information, including facial appearances and motions from input face images. Nevertheless, dense 3D facial geometry, such as pixel-wise depth, plays a critical role in constructing accurate 3D facial structures and suppressing complex background noises for generation. However, dense 3D annotations for facial videos is prohibitively costly to obtain. In this paper, first, we present a novel self-supervised method for learning dense 3D facial geometry (i.e., depth) from face videos, without requiring camera parameters and 3D geometry annotations in training. We further propose a strategy to learn pixel-level uncertainties to perceive more reliable rigid-motion pixels for geometry learning. Second, we design an effective geometry-guided facial keypoint estimation module, providing accurate keypoints for generating motion fields. Lastly, we develop a 3D-aware cross-modal (i.e., appearance and depth) attention mechanism, which can be applied to each generation layer, to capture facial geometries in a coarse-to-fine manner. Extensive experiments are conducted on three challenging benchmarks (i.e., VoxCeleb1, VoxCeleb2, and HDTF). The results demonstrate that our proposed framework can generate highly realistic-looking reenacted talking videos, with new state-of-the-art performances established on these benchmarks.

Self-training with dual uncertainty for semi-supervised MRI image segmentation

The goal of semi-supervised MRI image segmentation is to train high-accuracy segmentation models using a small amount of labeled data and a large amount of unlabeled data, thereby alleviating the burden of manual annotation by physicians. Self-training is a traditional semi-supervised learning method aimed at acquiring additional image features by generating pseudo-labels for unlabeled data. However, this method may lead to an unstable training process due to differences between samples. Additionally, the predictions of model may contain erroneous noise, leading to low-confidence pseudo-labels. To address these issues, we proposed a dual uncertainty-guided self-training framework (DUST) for semi-supervised MRI image segmentation. Specifically, the two uncertainties consist of sample-level uncertainty and pixel-level uncertainty. The sample-level uncertainty is intended to achieve a stable and smooth training process. The pixel-level uncertainty is intended to rectify pseudo-labels. We conducted a series of experiments on two public MRI image datasets, ACDC2017 and Prostate2018. Compared to the baseline, we improved the Dice scores by 5.0% and 4.0% over the two datasets, respectively. Furthermore, the experimental results indicate that the proposed method has certain advantages compared to the comparative methods. This validates the feasibility and applicability of our method.

Dual uncertainty-guided multi-model pseudo-label learning for semi-supervised medical image segmentation.

Semi-supervised medical image segmentation is currently a highly researched area. Pseudo-label learning is a traditional semi-supervised learning method aimed at acquiring additional knowledge by generating pseudo-labels for unlabeled data. However, this method relies on the quality of pseudo-labels and can lead to an unstable training process due to differences between samples. Additionally, directly generating pseudo-labels from the model itself accelerates noise accumulation, resulting in low-confidence pseudo-labels. To address these issues, we proposed a dual uncertainty-guided multi-model pseudo-label learning framework (DUMM) for semi-supervised medical image segmentation. The framework consisted of two main parts: The first part is a sample selection module based on sample-level uncertainty (SUS), intended to achieve a more stable and smooth training process. The second part is a multi-model pseudo-label generation module based on pixel-level uncertainty (PUM), intended to obtain high-quality pseudo-labels. We conducted a series of experiments on two public medical datasets, ACDC2017 and ISIC2018. Compared to the baseline, we improved the Dice scores by 6.5% and 4.0% over the two datasets, respectively. Furthermore, our results showed a clear advantage over the comparative methods. This validates the feasibility and applicability of our approach.

Digging Into Uncertainty-Based Pseudo-Label for Robust Stereo Matching.

Due to the domain differences and unbalanced disparity distribution across multiple datasets, current stereo matching approaches are commonly limited to a specific dataset and generalize poorly to others. Such domain shift issue is usually addressed by substantial adaptation on costly target-domain ground-truth data, which cannot be easily obtained in practical settings. In this paper, we propose to dig into uncertainty estimation for robust stereo matching. Specifically, to balance the disparity distribution, we employ a pixel-level uncertainty estimation to adaptively adjust the next stage disparity searching space, in this way driving the network progressively prune out the space of unlikely correspondences. Then, to solve the limited ground truth data, an uncertainty-based pseudo-label is proposed to adapt the pre-trained model to the new domain, where pixel-level and area-level uncertainty estimation are proposed to filter out the high-uncertainty pixels of predicted disparity maps and generate sparse while reliable pseudo-labels to align the domain gap. Experimentally, our method shows strong cross-domain, adapt, and joint generalization and obtains 1st place on the stereo task of Robust Vision Challenge 2020. Additionally, our uncertainty-based pseudo-labels can be extended to train monocular depth estimation networks in an unsupervised way and even achieves comparable performance with the supervised methods.

Anatomically-aware uncertainty for semi-supervised image segmentation

Semi-supervised learning relaxes the need of large pixel-wise labeled datasets for image segmentation by leveraging unlabeled data. A prominent way to exploit unlabeled data is to regularize model predictions. Since the predictions of unlabeled data can be unreliable, uncertainty-aware schemes are typically employed to gradually learn from meaningful and reliable predictions. Uncertainty estimation methods, however, rely on multiple inferences from the model predictions that must be computed for each training step, which is computationally expensive. Moreover, these uncertainty maps capture pixel-wise disparities and do not consider global information. This work proposes a novel method to estimate segmentation uncertainty by leveraging global information from the segmentation masks. More precisely, an anatomically-aware representation is first learnt to model the available segmentation masks. The learnt representation thereupon maps the prediction of a new segmentation into an anatomically-plausible segmentation. The deviation from the plausible segmentation aids in estimating the underlying pixel-level uncertainty in order to further guide the segmentation network. The proposed method consequently estimates the uncertainty using a single inference from our representation, thereby reducing the total computation. We evaluate our method on two publicly available segmentation datasets of left atria in cardiac MRIs and of multiple organs in abdominal CTs. Our anatomically-aware method improves the segmentation accuracy over the state-of-the-art semi-supervised methods in terms of two commonly used evaluation metrics.

Quantifying uncertainty in land-use land-cover classification using conformal statistics

Land-use land-cover (LULC) change is one of the most important anthropogenic threats to biodiversity and ecosystems integrity. As a result, the systematic generation of annual regional, national, and global LULC map products derived from the classification of satellite imagery data have become critical inputs for multiple scientific disciplines. The importance of quantifying pixel-level uncertainty to improve the robustness of downstream analyses has long been acknowledged but this practice is still not widely adopted in the generation of these LULC products. The lack of uncertainty quantification is likely due to the fact that most approaches that have been put forward for this task are too computationally intensive for large-scale analysis (e.g., bootstrapping). In this article, we describe how conformal statistics can be used to quantify pixel-level uncertainty in a way that is not computationally intensive, is statistically rigorous despite relying on few assumptions, and can be used together with any classification algorithm that produces class probabilities. Our simulation results show how the size of the predictive sets created by conformal statistics can be used as an indicator of classification uncertainty at the pixel level. Our analysis based on data from the Brazilian Amazon reveals that both forest and water have high certainty whereas pasture and the “natural (other)” category have substantial uncertainty. This information can guide additional ground-truth data collection and the resulting raster combining the LULC classification with the uncertainty results can be used to communicate in a transparent way to downstream users which classified pixels have high or low uncertainty. Given the importance of systematic LULC maps and uncertainty quantification, we believe that this approach will find wide use in the remote sensing community.

The CHROMA cloud-top pressure retrieval algorithm for the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) satellite mission

Abstract. This paper provides the theoretical basis and simulated retrievals for the Cloud Height Retrieval from O2 Molecular Absorption (CHROMA) algorithm. Simulations are performed for the Ocean Color Instrument (OCI), which is the primary payload on the forthcoming NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, and the Ocean Land Colour Instrument (OLCI) currently flying on the Sentinel 3 satellites. CHROMA is a Bayesian approach which simultaneously retrieves cloud optical thickness (COT), cloud-top pressure and height (CTP and CTH respectively), and (with a significant prior constraint) surface albedo. Simulated retrievals suggest that the sensor and algorithm should be able to meet the PACE mission goal for CTP error, which is ±60 mb for 65 % of opaque (COT ≥3) single-layer clouds on global average. CHROMA will provide pixel-level uncertainty estimates, which are demonstrated to have skill at telling low-error situations from high-error ones. CTP uncertainty estimates are well-calibrated in magnitude, although COT uncertainty is overestimated relative to observed errors. OLCI performance is found to be slightly better than OCI overall, demonstrating that it is a suitable proxy for the latter in advance of PACE's launch. CTP error is only weakly sensitive to correct cloud phase identification or assumed ice crystal habit/roughness. As with other similar algorithms, for simulated retrievals of multi-layer systems consisting of optically thin cirrus clouds above liquid clouds, retrieved height tends to be underestimated because the satellite signal is dominated by the optically thicker lower layer. Total (liquid plus ice) COT also becomes underestimated in these situations. However, retrieved CTP becomes closer to that of the upper ice layer for ice COT ≈3 or higher.

Exploring uncertainty measures in convolutional neural network for semantic segmentation of oral cancer images.

Oral cancer is one of the most prevalent cancers, especially in middle- and low-income countries such as India. Automatic segmentation of oral cancer images can improve the diagnostic workflow, which is a significant task in oral cancer image analysis. Despite the remarkable success of deep-learning networks in medical segmentation, they rarely provide uncertainty quantification for their output. We aim to estimate uncertainty in a deep-learning approach to semantic segmentation of oral cancer images and to improve the accuracy and reliability of predictions. This work introduced a UNet-based Bayesian deep-learning (BDL) model to segment potentially malignant and malignant lesion areas in the oral cavity. The model can quantify uncertainty in predictions. We also developed an efficient model that increased the inference speed, which is almost six times smaller and two times faster (inference speed) than the original UNet. The dataset in this study was collected using our customized screening platform and was annotated by oral oncology specialists. The proposed approach achieved good segmentation performance as well as good uncertainty estimation performance. In the experiments, we observed an improvement in pixel accuracy and mean intersection over union by removing uncertain pixels. This result reflects that the model provided less accurate predictions in uncertain areas that may need more attention and further inspection. The experiments also showed that with some performance compromises, the efficient model reduced computation time and model size, which expands the potential for implementation on portable devices used in resource-limited settings. Our study demonstrates the UNet-based BDL model not only can perform potentially malignant and malignant oral lesion segmentation, but also can provide informative pixel-level uncertainty estimation. With this extra uncertainty information, the accuracy and reliability of the model’s prediction can be improved.

Reliable wavefront reconstruction from a single lateral shearing interferogram using Bayesian convolutional neural network

The reconstruction of the original wavefront from its sheared information is an ill-posed inverse problem in the sense of Hadamard. In this paper, we present a new technique for reconstructing the wavefront from a single lateral shearing interferogram using a Bayesian convolutional neural network. With the synthesized data, the trained network can robustly invert the physical model, recover the spectral leakage problem caused by the shear operation, and reconstruct the desired phase distribution. In addition, a quantitative pixel-level uncertainty measure of the reconstruction results is provided simultaneously, which can be used as an indicator to judge the validity of reconstruction accuracy in the absence of ground truth. Numerical experiments are carried out to investigate the robustness and accuracy of the method, in which the effects of different noise levels and shear distances on reconstruction accuracy are evaluated. We further show that the uncertainty maps are highly indicative of the true error and properly calibrated. Finally, optical tests on reconstructing the topology of object deformation have confirmed that our method can considerably increase the accuracy of wavefront reconstruction as compared with the two baseline methods.

Extended validation and evaluation of the OLCI–SLSTR SYNERGY aerosol product (SY_2_AOD) on Sentinel-3

Abstract. We present the first extended validation of a new SYNERGY global aerosol product (SY_2_AOD), which is based on synergistic use of data from the Ocean and Land Color Instrument (OLCI) and the Sea and Land Surface Temperature Radiometer (SLSTR) sensors aboard the Copernicus Sentinel-3A (S3A) and Sentinel-3B (S3B) satellites. Validation covers period from 14 January 2020 to 30 September 2021. Several approaches, including statistical analysis, time series analysis, and comparison with similar aerosol products from the other spaceborne sensor, the Moderate Resolution Imaging Spectroradiometer (MODIS), were applied for validation and evaluation of S3A and S3B SY_2 aerosol products, including aerosol optical depth (AOD) provided at different wavelengths, AOD pixel-level uncertainties, fine-mode AOD, and Angström exponent. Over ocean, the performance of SY_2 AOD (syAOD) retrieved at 550 nm is good: for S3A and S3B, Pearson correlation coefficients with the Maritime Aerosol Network (MAN) component of the AErosol RObotic NETwork (AERONET) are 0.88 and 0.85, respectively; 88.6 % and 89.5 % of pixels fit into the MODIS error envelope (EE) of ±0.05 ± 0.2 × AOD. Over land, correlation coefficients with AERONET AOD (aAOD) are 0.60 and 0.63 for S3A and S3B, respectively; 51.4 % and 57.9 % of pixels fit into MODIS EE. Reduced performance over land is expected since the surface reflectance and angular distribution of scattering are higher and more difficult to predict over land than over ocean. The results are affected by a large number of outliers. Evaluation of the per-retrieval uncertainty with the χ2 test indicates that syAOD prognostic uncertainties (PU) are slightly underestimated (χ2 = 3.1); if outliers are removed, PU describes the syAOD error well (χ2 = 1.6). The regional analysis of the Angström exponent, which relates to the aerosol size distribution, shows spatial correlation with expected sources. For 40 % of the matchups with AERONET in the Northern Hemisphere (NH) and for 60 % of the matchups in the Southern Hemisphere (SH), which fit into the AE size range of [1, 1.8], an offset between SY_2 AE (syAE) and AERONET AE (aAE) is within ±0.25. General overestimation of low (< 0.5) syAE and underestimation of high (> 1.8) syAE results in high (0.94, globally) overall bias. Good agreement (bias < 0.03) was observed between Sy_2 fine-mode AOD (syFMAOD) and AERONET fine-mode AOD (aFMAOD) for aFMAOD < 1. At aFMAOD > 1, syFMAOD is considerably underestimated (by 0.3–0.5 in different aFMAOD ranges) in the NH. In the SH, only a few aFMAOD values above 1 are measured. The fine-mode fraction (FMF) in the SY_2 AOD product (syFMF) in the range of [0, 0.7] is overestimated; the positive offset of 0.3–0.5 for low (< 0.25) FMF gradually decreases. Differences between the annual and seasonal AOD values from SY_2 and MODIS (mod) Dark Target and Deep Blue products are within 0.02 for the study area (30∘ S–60∘ N, 80∘ W–45∘ E). The agreement is better over ocean; however, a difference up to 0.6 exists between syFMF and modFMF. Over bright land surface (Saharan desert) the difference in AOD between the two products is highest (up to 0.11); the sign of the difference varies over time and space. For both S3A and S3B AOD products, validation statistics are often slightly better in the Southern Hemisphere. In general, the performance of S3B is slightly better.

Estimating pixel-level uncertainty in ocean color retrievals from MODIS.

The spectral distribution of marine remote sensing reflectance, Rrs, is the fundamental measurement of ocean color science, from which a host of bio-optical and biogeochemical properties of the water column can be derived. Estimation of uncertainty in these derived properties is thus dependent on knowledge of the uncertainty in satellite-retrieved Rrs (uc(Rrs)) at each pixel. Uncertainty in Rrs, in turn, is dependent on the propagation of various uncertainty sources through the Rrs retrieval process, namely the atmospheric correction (AC). A derivative-based method for uncertainty propagation is established here to calculate the pixel-level uncertainty in Rrs, as retrieved using NASA's multiple-scattering epsilon (MSEPS) AC algorithm and verified using Monte Carlo (MC) analysis. The approach is then applied to measurements from the Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite, with uncertainty sources including instrument random noise, instrument systematic uncertainty, and forward model uncertainty. The uc(Rrs) is verified by comparison with statistical analysis of coincident retrievals from MODIS and in situ Rrs measurements, and our approach performs well in most cases. Based on analysis of an example 8-day global products, we also show that relative uncertainty in Rrs at blue bands has a similar spatial pattern to the derived concentration of the phytoplankton pigment chlorophyll-a (chl-a), and around 7.3%, 17.0%, and 35.2% of all clear water pixels (chl-a ≤ 0.1 mg/m3) with valid uc(Rrs) have a relative uncertainty ≤ 5% at bands 412 nm, 443 nm, and 488 nm respectively, which is a common goal of ocean color retrievals for clear waters. While the analysis shows that uc(Rrs) calculated from our derivative-based method is reasonable, some issues need further investigation, including improved knowledge of forward model uncertainty and systematic uncertainty in instrument calibration.

A unified uncertainty network for tumor segmentation using uncertainty cross entropy loss and prototype similarity

Uncertainty estimation and out-of-distribution (OOD) detection are topics of practical significance in deep convolutional neural network-based tumor segmentation tasks. We propose a unified uncertainty segmentation network to handle these two tasks with a single network. The uncertainty cross entropy loss is proposed to guide the network to directly output the prediction uncertainty of each pixel instead of executing several times in the prediction phase. We extend the uncertainty to the case level to address OOD sample detection problems. Case-level uncertainty is estimated based on prototype similarity. We perform pixel-level uncertainty experiments and OOD detection experiments on four datasets. The experimental results show that our proposed method is more suitable for uncertainty estimation in tumor segmentation than existing methods. Our proposed method only needs to modify the network output and loss function and does not need to execute the network multiple times when estimating uncertainty. Moreover, our method shows improved performance in tumor segmentation.

Systematic Propagation of AVHRR AOD Uncertainties—A Case Study to Demonstrate the FIDUCEO Approach

The AVHRR aerosol optical depth (AOD) is inverted from measured reflectances in the red band using a statistical correlation of surface reflectance with mid-infrared channel reflectances and a modelling climatology of the aerosol type. For such a sensor not specifically designed for AOD retrieval, propagating uncertainties is crucial because the sensitivity of the retrieved AOD to the measured signal varies largely with retrieval conditions (AOD itself, surface brightness, aerosol optical properties/aerosol type, observing geometry). In order to quantify the different contributions to the AOD uncertainties, we have undertaken a thorough analysis of the retrieval operator and its sensitivities to the used input and auxiliary variables. Uncertainties are then propagated from measured reflectances to geophysical retrieved AOD datasets at the super-pixel level and further to gridded daily and monthly products. The propagation uses uncertainty correlations of separate uncertainty contributions from the FIDUCEO easyFCDR level1b products (common fully correlated, independent random, and structured parts) and estimated uncertainty correlation structures of other major effects in the retrieval (surface brightness, aerosol type ensemble, cloud mask). The pixel-level uncertainties are statistically validated against true error estimates versus AERONET ground-based AOD measurements. It is shown that a 10-year time record over Europe compares well to a merged multi-satellite record and that pixel-level uncertainties provide a meaningful representation of error distributions. The study demonstrates the benefits of new recipes for uncertainty characterization from the Horizon-2020 project FIDUCEO (“Fidelity and uncertainty in climate data records from Earth Observations”) and extends them further with recent additions developed within the ESA Climate Change Initiative.

Weakly Supervised Segmentation of COVID19 Infection with Scribble Annotation on CT Images

Segmentation of infections from CT scans is important for accurate diagnosis and follow-up in tackling the COVID-19. Although the convolutional neural network has great potential to automate the segmentation task, most existing deep learning-based infection segmentation methods require fully annotated ground-truth labels for training, which is time-consuming and labor-intensive. This paper proposed a novel weakly supervised segmentation method for COVID-19 infections in CT slices, which only requires scribble supervision and is enhanced with the uncertainty-aware self-ensembling and transformation-consistent techniques. Specifically, to deal with the difficulty caused by the shortage of supervision, an uncertainty-aware mean teacher is incorporated into the scribble-based segmentation method, encouraging the segmentation predictions to be consistent under different perturbations for an input image. This mean teacher model can guide the student model to be trained using information in images without requiring manual annotations. On the other hand, considering the output of the mean teacher contains both correct and unreliable predictions, equally treating each prediction in the teacher model may degrade the performance of the student network. To alleviate this problem, the pixel level uncertainty measure on the predictions of the teacher model is calculated, and then the student model is only guided by reliable predictions from the teacher model. To further regularize the network, a transformation-consistent strategy is also incorporated, which requires the prediction to follow the same transformation if a transform is performed on an input image of the network. The proposed method has been evaluated on two public datasets and one local dataset. The experimental results demonstrate that the proposed method is more effective than other weakly supervised methods and achieves similar performance as those fully supervised.

Identifying and Quantifying Pixel-Level Uncertainty among Major Satellite Derived Global Land Cover Products

Accurate global land cover (GLC), as a key input for scientific communities, is important for a wide variety of applications. In order to understand the current suitability and limitation of GLC products, the discrepancy and pixel-level uncertainty in major GLC products in three epochs are assessed in this study by using an integrated uncertainty index (IUI) that combines the thematic uncertainty and local classification accuracy uncertainty. The results show that the overall spatial agreements (Ao values) between GLC products are lower than 58%, and the total areas of forests are very consistent in major GLC products, but significant differences are found in different forest classes. The misclassification among different forest classes and mosaic types can account for about 20% of the total disagreements. The mean IUI almost reaches 0.5, and high uncertainty mostly occurs in transition zones and heterogeneous areas across the world. Further efforts are needed to make in the land cover classifications in areas with high uncertainty. Designing a classification scheme for climate models, with explicit definitions of land cover classes in the threshold of common attributes, is urgently needed. Information of the pixel-level uncertainty in major GLC products not only give important implications for the specific application, but also provide a quite important basis for land cover fusion.

A review and framework for the evaluation of pixel-level uncertainty estimates in satellite aerosol remote sensing

Abstract. Recent years have seen the increasing inclusion of per-retrieval prognostic (predictive) uncertainty estimates within satellite aerosol optical depth (AOD) data sets, providing users with quantitative tools to assist in the optimal use of these data. Prognostic estimates contrast with diagnostic (i.e. relative to some external truth) ones, which are typically obtained using sensitivity and/or validation analyses. Up to now, however, the quality of these uncertainty estimates has not been routinely assessed. This study presents a review of existing prognostic and diagnostic approaches for quantifying uncertainty in satellite AOD retrievals, and it presents a general framework to evaluate them based on the expected statistical properties of ensembles of estimated uncertainties and actual retrieval errors. It is hoped that this framework will be adopted as a complement to existing AOD validation exercises; it is not restricted to AOD and can in principle be applied to other quantities for which a reference validation data set is available. This framework is then applied to assess the uncertainties provided by several satellite data sets (seven over land, five over water), which draw on methods from the empirical to sensitivity analyses to formal error propagation, at 12 Aerosol Robotic Network (AERONET) sites. The AERONET sites are divided into those for which it is expected that the techniques will perform well and those for which some complexity about the site may provide a more severe test. Overall, all techniques show some skill in that larger estimated uncertainties are generally associated with larger observed errors, although they are sometimes poorly calibrated (i.e. too small or too large in magnitude). No technique uniformly performs best. For powerful formal uncertainty propagation approaches such as optimal estimation, the results illustrate some of the difficulties in appropriate population of the covariance matrices required by the technique. When the data sets are confronted by a situation strongly counter to the retrieval forward model (e.g. potentially mixed land–water surfaces or aerosol optical properties outside the family of assumptions), some algorithms fail to provide a retrieval, while others do but with a quantitatively unreliable uncertainty estimate. The discussion suggests paths forward for the refinement of these techniques.

Variance-Preserving Estimation of Intensity Values Obtained From Omics Experiments.

Faced with the lack of reliability and reproducibility in omics studies, more careful and robust methods are needed to overcome the existing challenges in the multi-omics analysis. In conventional omics data analysis, signal intensity values (denoted by M and values) are estimated neglecting pixel-level uncertainties, which may reflect noise and systematic artifacts. For example, intensity values from two-color microarray data are estimated by taking the mean or median of the pixel intensities within the spot and then subjected to a within-slide normalization by LOWESS. Thus, focusing on estimation and normalization of gene expression profiles, we propose a spot quantification method that takes into account pixel-level variability. Also, to preserve relevant variation that may be removed in LOWESS normalization with poorly chosen parameters, we propose a parameter selection method that is parsimonious and considers intrinsic characteristics of microarray data, such as heteroskedasticity. The usefulness of the proposed methods is illustrated by an application to real intestinal metaplasia data. Compared with the conventional approaches, the analysis is more robust and conservative, identifying fewer but more reliable differentially expressed genes. Also, the variability preservation allowed the identification of new differentially expressed genes. Using the proposed approach, we have identified differentially expressed genes involved in pathways in cancer and confirmed some molecular markers already reported in the literature.

Evaluation of SMAP, SMOS-IC, FY3B, JAXA, and LPRM Soil Moisture Products over the Qinghai-Tibet Plateau and Its Surrounding Areas

High-quality and long time-series soil moisture (SM) data are increasingly required for the Qinghai-Tibet Plateau (QTP) to more accurately and effectively assess climate change. In this study, to evaluate the accuracy and effectiveness of SM data, five passive microwave remotely sensed SM products are collected over the QTP, including those from the soil moisture active passive (SMAP), soil moisture and ocean salinity INRA-CESBIO (SMOS-IC), Fengyun-3B microwave radiation image (FY3B), and two SM products derived from the advanced microwave scanning radiometer 2 (AMSR2). The two AMSR2 products are generated by the land parameter retrieval model (LPRM) and the Japan Aerospace Exploration Agency (JAXA) algorithm, respectively. The SM products are evaluated through a two-stage data comparison method. The first stage is direct validation at the grid scale. Five SM products are compared with corresponding in situ measurements at five in situ networks, including Heihe, Naqu, Pali, Maqu, and Ngari. Another stage is indirect validation at the regional scale, where the uncertainties of the data are quantified by using a three-cornered hat (TCH) method. The results at the regional scale indicate that soil moisture is underestimated by JAXA and overestimated by LPRM, some noise is contained in temporal variations in SMOS-IC, and FY3B has relatively low absolute accuracy. The uncertainty of SMAP is the lowest among the five products over the entire QTP. In the SM map composed by five SM products with the lowest pixel-level uncertainty, 66.64% of the area is covered by SMAP (JAXA: 19.39%, FY3B: 10.83%, LPRM: 2.11%, and SMOS-IC: 1.03%). This study reveals some of the reasons for the different performances of these five SM products, mainly from the perspective of the parameterization schemes of their corresponding retrieval algorithms. Specifically, the parameterization configurations and corresponding input datasets, including the land-surface temperature, the vegetation optical depth, and the soil dielectric mixing model are analyzed and discussed. This study provides quantitative evidence to better understand the uncertainties of SM products and explain errors that originate from the retrieval algorithms.

Linear Support Tensor Machine With LSK Channels: Pedestrian Detection in Thermal Infrared Images.

Pedestrian detection in thermal infrared images poses unique challenges because of the low resolution and noisy nature of the image. Here, we propose a mid-level attribute in the form of the multidimensional template, or tensor, using local steering kernel (LSK) as low-level descriptors for detecting pedestrians in far infrared images. LSK is specifically designed to deal with intrinsic image noise and pixel level uncertainty by capturing local image geometry succinctly instead of collecting local orientation statistics (e.g., histograms in histogram of oriented gradients). In order to learn the LSK tensor, we introduce a new image similarity kernel following the popular maximum margin framework of support vector machines facilitating a relatively short and simple training phase for building a rigid pedestrian detector. Tensor representation has several advantages, and indeed, LSK templates allow exact acceleration of the sluggish but de facto sliding window-based detection methodology with multichannel discrete Fourier transform, facilitating very fast and efficient pedestrian localization. The experimental studies on publicly available thermal infrared images justify our proposals and model assumptions. In addition, the proposed work also involves the release of our in-house annotations of pedestrians in more than 17 000 frames of OSU color thermal database for the purpose of sharing with the research community.