Pixel Pairs Research Articles

Data Hiding Technique for Color Images using Pixel Value Differencing and Chaotic Map

The huge advance in information technology and communication resulted in extreme usage of digital networks that makes information security playing an important role as never before. Steganography is the art of hiding secret message bits into different multimedia data using either spatial domain or frequency domain to provide security for the transferred information against unauthorized access. Most of the techniques that apply Pixel Value Differencing approach (PVD) depend on sequential embedding manner, which lacks security. In the proposed method, a complex chaotic map is used to randomly choose the coefficients pairs for embedding the secret message. First, the cover image is transformed using IWT. Then, the embedding process starts in the highest frequency band of IWT and continues to the next sub-bands. Adaptive embedding is performed according to intensity variation between pixel pairs using PVD and Least Significant Bit substitution (LSB). Non-sequential embedding performed by using chaotic map lets the method more secure. The experimental results show that the proposed technique achieves high PSNR with improved capacity compared to other techniques.

Ensemble Entropy Metric for Hyperspectral Anomaly Detection

In hyperspectral anomaly detection, anomalies are rare targets that exhibit distinct spectral signatures from the background. Thus, anomalies are with low probabilities of occurrence in hyperspectral images. In this article, we develop a new technique for hyperspectral anomaly detection that adopts a new information theory perspective, to fully utilize the aforementioned concepts. Our goal is to transform system entropy into quantitative metrics of anomaly conspicuousness of pixels. To do so, two tasks are first completed: first, the construction of occurrence probability of pixels based on the density peak clustering algorithm, and second, the valid system definitions for pixels in specific anomaly detection problems with multiviews. Specifically, three types of systems are separately established by pixel pairs to conform to the definitions of three entropy definitions in information theory, i.e., Shannon entropy, joint entropy, and relative entropy. Then, three individual entropy-based metrics that assess the anomaly conspicuousness are defined. In addition, we design a standard deviation-based ensemble strategy for the integrated representation of the three individual metrics, which considers both logic “OR” and “AND” operations to simultaneously improve the detection rate and reduce the false alarm rate. Our experimental results obtained on two publicly available datasets with anomalies of different sizes and shapes demonstrate the superiority of our newly proposed anomaly detection method.

Local Transformer With Spatial Partition Restore for Hyperspectral Image Classification

Convolutional neural network (CNN) has exhibited enormous potentials in hyperspectral image (HSI) classification owing to excellent locally modeling ability. Although excellent performance of CNN-based methods has been witnessed, there still have some limitations of their internal network backbone. On the one hand, modeling long-distance context dependencies is an inborn defect, which leads to receptive field limitation and insufficient feature capture in HSI. On the other hand, CNN-based methods usually need various sample distribution to train and cannot infer dynamically, which may not capture the inherent changes of HSI data well. To overcome the above issues, we propose a novel local transformer with spatial partition restore network (SPRLT-Net) for HSI classification. Firstly, local transformer is introduced to obtain the spatial attention weights dynamically by measuring the similarity between related pixel pairs. Secondly, a spatial partition restore (SPR) module is designed to split the input patch into several overlapping continuous sub-patches as sequential. With the obtained attention weights at hand, the SPR module restores the sequential to the original patch. Finally, a fully connected layer is used for classification. SPRLT-Net can capture global context dependencies, and the dynamical attention weights can adapt the inherent changes of HSI spatial pixels. Experimental results based on spatially disjoint samples and randomly selected samples of five benchmark data sets demonstrate that SPRLT-Net outperforms the other state-of-the-art methods in terms of classification accuracy, generalization performance, and computational complexity.

An Investigation on Inter-Calibrating EMI/GF-5 With TROPOMI/S5p in Ultraviolet–Visible Spectra

Inter-calibration is a general method to harmonize the in-orbit spectral radiance of the target instrument with the reference instrument in the visible and infrared spectra. This study proposes and applies an inter-calibration method to the space-based ultraviolet and visible (UVIS) grating radiometers. Based on pixel pairs derived from simultaneous nadir overpasses (SNO), the in-orbit spectral radiances from the Environmental trace gas Monitoring Instrument onboard the Chinese high-resolution remote sensing satellite GaoFen-5 (EMI/GF-5) and the TROPOspheric Monitoring Instrument onboard the Sentinel-5 Precursor satellite (TROPOMI/S5p) are compared through the double difference method, where the individual window channel method is also adopted for comparison. Uncertainties from SNO thresholds, instrument spectral specification and radiative transfer simulation are estimated. The SNO thresholds, including time, distance, viewing angle and scene uniformity of 300 s, 3 km, 0.01 and 0.01, are determined to get collocations for UVIS instruments. Several factors, including instrument line shape (ILS), instrument spectral accuracy, reference solar spectrum, surface albedo and atmospheric polarization, can influence the radiometric difference obtained by the double difference method. Accurate SAO2010 solar spectrum and wavelength accuracy can substantially reduce the dependence of radiometric difference on wavelength. Errors introduced by scalar approximation and parameterized ILS can be neglected. The surface albedo greatly affects the simulated radiance at wavelengths longward of 330 nm. The results show that radiometric differences obtained by using the double difference method are consistent with those derived from individual window channel method, with the discrepancy within 0.4%. An ocean-land calibration difference of 1.5% is found between EMI and TROPOMI at the UVIS band. Inter-calibration using the double difference method can minimize the spectral variations in full spectral radiance inter-comparison for grating hyperspectral instruments, and the radiometric difference can be estimated comprehensively. The wavelength dependence can also be easily derived from the results of double difference method. The double difference method is recommended for radiometric comparison for UVIS hyperspectral spectrometers.

Clustering Feature Constraint Multiscale Attention Network for Shadow Extraction From Remote Sensing Images

Shadow extraction is an important and challenging task in remote sensing image analysis because the presence of shadows not only reduces radiation information but also affects the interpretation of remote sensing images. In this article, a clustering feature constraint multiscale attention network for shadow extraction from remote sensing images is proposed. First, in addition to the pixel-level description of the traditional neural network, our method focuses on the clustering relationships between pixel pairs to obtain the pixel group features of shadows. The feature extraction capability of the network is improved with a reweighting mechanism at the pixel level and pixel group features. Second, we employ a feature fusion algorithm by considering contextual information to improve the network’s attention toward shadow areas and enhance the nonlinear expression ability during the encoding and decoding layers. Furthermore, considering the most prominent multiscale features of shadows in remote sensing images, a deep multiscale feature aggregation structure is established to better fit the multiscale feature expression of shadows. Finally, we construct a shadow extraction dataset to verify the proposed approach. We compare our method with the results of state-of-the-art deep learning models. The results show that the intersection over union (IOU) of our method is improved by 0.85%–9.51% and that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F1$ </tex-math></inline-formula> -score is improved by 0.73–6.48. In addition, the test results for images with different resolutions prove that the proposed approach is more robust than the other methods.

MCMC generation of cosmological fields far beyond Gaussianity

Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to analyze best such non-Gaussian fields, e.g. to infer the physical laws that created them. This problem could be solved if a parametric non-Gaussian sampling distribution for such fields were known, as this distribution could serve as likelihood during inference. We therefore create a sampling distribution for non-Gaussian random fields. Our approach is capable of handling strong non-Gaussianity, while perturbative approaches such as the Edgeworth expansion cannot. To imitate cosmological structure formation, we enforce our fields to be (i) statistically isotropic, (ii) statistically homogeneous, and (iii) statistically independent at large distances. We generate such fields via a Monte Carlo Markov Chain technique and find that even strong non-Gaussianity is not necessarily visible to the human eye. We also find that sampled marginals for pixel pairs have an almost generic Gauss-like appearance, even if the joint distribution of all pixels is markedly non-Gaussian. This apparent Gaussianity is a consequence of the high dimensionality of random fields. We conclude that vast amounts of non-Gaussian information can be hidden in random fields that appear nearly Gaussian in simple tests, and that it would be short-sighted not to try and extract it.

Instance-level Context Attention Network for instance segmentation

Instance segmentation has made great progress in recent years. However, current mainstream detection-based methods ignore the process of distinguishing different instances in the same detected region, making it hard to segment the correct instance when a detected region contains multiple instances. To address this problem, we propose an Instance-level Context Attention Network (ICANet) to generate more discriminative features for different instances based on the context from their respective instance scopes, called instance-level context. Specifically, given a detected region, we first propose an instance attention module to obtain the specific attention maps that focus on the relationships between pixel pairs from the same instance by learning an embedding space. With this type of attention map, the features from the same instance achieve mutual gains, while the features from different instances become more discriminative. Then, we propose a spatial attention module to incorporate spatial information and enhance feature representations based on both feature and spatial relations. Moreover, to obtain clearer attention maps, we further propose a weight clipping strategy to filter out the noise by cutting off the lower weight. We perform extensive experiments to verify the effectiveness of the proposed method. As reported in the results, our method steadily outperforms the baseline by over 1.5% on the COCO dataset using different backbones and 3.7% on the Cityscapes dataset, which demonstrates the effectiveness of our method.

TransCD: scene change detection via transformer-based architecture

Scene change detection (SCD) is a task to identify changes of interest between bi-temporal images acquired at different times. A critical idea of SCD is how to identify interesting changes while overcoming noisy changes induced by camera motion or environment variation, such as viewpoint, dynamic changes and outdoor conditions. The noisy changes cause corresponding pixel pairs to have spatial difference (position relation) and temporal difference (intensity relation). Due to the limitation of local receptive field, it is difficult for traditional models based on convolutional neural network (CNN) to establish long-range relations for the semantic changes. In order to address the above challenges, we explore the potential of a transformer in SCD and propose a transformer-based SCD architecture (TransCD). From the intuition that a SCD model should be able to model both interesting and noisy changes, we incorporate a siamese vision transformer (SViT) in a feature difference SCD framework. Our motivation is that SViT is able to establish global semantic relations and model long-range context, which is more robust to noisy changes. In addition, different from the pure CNN-based models with high computational complexity, the proposed model is more efficient and has fewer parameters. Extensive experiments on the CDNet-2014 dataset demonstrate that the proposed TransCD (SViT-E1-D1-32) outperforms the state-of-the-art SCD models and achieves 0.9361 in terms of the F1 score with an improvement of 7.31%.

Spatial-driven features based on image dependencies for person re-identification

Person re-identification (Re-ID) aims to search for the same pedestrian in different cameras, which is a crucial research direction in pattern recognition. Recent deep learning methods have advanced the development of Re-ID. However, the existing approaches easily result in performance degradation in the case of larger scene data because they do not adequately consider the spatial dependencies of both the inter-image and the intra-image. The paper proposes a novel Spatial-Driven Network (SDN) to learn particularly discriminative features with abundant semantic information from both the inter-image and the intra-image dependencies for person Re-ID. Firstly, we design a global-correlation attention module to capture the inter-image dependencies among a series of different pedestrian images. Secondly, we present a local-correlation attention module to compute the intra-image dependencies from any pair of pixels within each pedestrian image. Furthermore, we propose a specific network integration mechanism, which carefully combines the above two complementary modules to match well the solution of the spatial dependency problem. We implement numerous experiments to assess the proposed SDN on mainstream person Re-ID databases. The results demonstrate that the proposed SDN outperforms most of the state-of-the-art methods in typical key criteria.

A CONUS-scale study of wildfire and evapotranspiration: Spatial and temporal response and controlling factors

Evapotranspiration (ET) accounts for a substantial portion of regional water budgets in much of the southeast and fire-prone western United States (US). Even small changes in ET rates can translate to meaningful shifts in runoff patterns and makes forecasting the direction and magnitude of wildfire-induced ET alteration of critical importance. We use 1 km ET estimates from the operational Simplified Surface Energy Balance (SSEBop) product for the conterminous US (CONUS) to evaluate post-fire ET and evaporation ratio (ET/P) shifts in the first five post-fire years in approximately 5500 unique fires. Pixels with similar ET/P responses to fire are grouped through k-means clustering and the resultant cluster distribution is explored over space and time. The largest changes in post-fire ET/P are observed in the southwestern CONUS where first-year ratios are reduced by 50 to 90% and pre-fire ratios are rarely recovered by post-fire year five. Regional and intra-fire ET/P response variability is also highest in the western CONUS where climatic, topographic, and ecologic gradients are steep. Post-fire ET/P modifications are small to negligible in the east-southeast CONUS, and 18% of all pixels analyzed exhibit small to moderate increases in post-fire year one ET/P. A comparison of burned and unburned pixel pairs confirms the role of fire in the shifts but also indicates a high degree of background variability in the ET and precipitation data. Although the biggest percent ET/P reductions occur in shrub/scrub landscapes in much of the west, the biggest magnitude ET changes often occur in evergreen forests. Higher burn severities are consistently correlated with greater post-fire ET/P reductions, while relationships between post-fire ET/P shifts and numerous other landscape attributes (e.g., pre-fire vegetation type) vary in both direction and magnitude in different parts of the CONUS. Further work can be conducted to refine controlling relationships within more homogeneous sub-regions.

Dual Crisscross Attention Module for Road Extraction from Remote Sensing Images.

Traditional pixel-based semantic segmentation methods for road extraction take each pixel as the recognition unit. Therefore, they are constrained by the restricted receptive field, in which pixels do not receive global road information. These phenomena greatly affect the accuracy of road extraction. To improve the limited receptive field, a non-local neural network is generated to let each pixel receive global information. However, its spatial complexity is enormous, and this method will lead to considerable information redundancy in road extraction. To optimize the spatial complexity, the Crisscross Network (CCNet), with a crisscross shaped attention area, is applied. The key aspect of CCNet is the Crisscross Attention (CCA) module. Compared with non-local neural networks, CCNet can let each pixel only perceive the correlation information from horizontal and vertical directions. However, when using CCNet in road extraction of remote sensing (RS) images, the directionality of its attention area is insufficient, which is restricted to the horizontal and vertical direction. Due to the recurrent mechanism, the similarity of some pixel pairs in oblique directions cannot be calculated correctly and will be intensely dilated. To address the above problems, we propose a special attention module called the Dual Crisscross Attention (DCCA) module for road extraction, which consists of the CCA module, Rotated Crisscross Attention (RCCA) module and Self-adaptive Attention Fusion (SAF) module. The DCCA module is embedded into the Dual Crisscross Network (DCNet). In the CCA module and RCCA module, the similarities of pixel pairs are represented by an energy map. In order to remove the influence from the heterogeneous part, a heterogeneous filter function (HFF) is used to filter the energy map. Then the SAF module can distribute the weights of the CCA module and RCCA module according to the actual road shape. The DCCA module output is the fusion of the CCA module and RCCA module with the help of the SAF module, which can let pixels perceive local information and eight-direction non-local information. The geometric information of roads improves the accuracy of road extraction. The experimental results show that DCNet with the DCCA module improves the road IOU by 4.66% compared to CCNet with a single CCA module and 3.47% compared to CCNet with a single RCCA module.

A High Fidelity Authentication Scheme for AMBTC Compressed Image Using Reference Table Encoding

In this paper, we propose a high-quality image authentication method based on absolute moment block truncation coding (AMBTC) compressed images. The existing AMBTC authentication methods may not be able to detect certain malicious tampering due to the way that the authentication codes are generated. In addition, these methods also suffer from their embedding technique, which limits the improvement of marked image quality. In our method, each block is classified as either a smooth block or a complex one based on its smoothness. To enhance the image quality, we toggle bits in bitmap of smooth block to generate a set of authentication codes. The pixel pair matching (PPM) technique is used to embed the code that causes the least error into the quantization values. To reduce the computation cost, we only use the original and flipped bitmaps to generate authentication codes for complex blocks, and select the one that causes the least error for embedment. The experimental results show that the proposed method not only obtains higher marked image quality but also achieves better detection performance compared with prior works.

Pencil shell matrix based image steganography with elevated embedding capacity

Image steganography is a mechanism that imperceptibly conceals information in a cover image while also enabling the concealed details to be reliably retrieved from that image. The three important criteria for calculating the effect and impact of any steganographic method are high embedding ability, better visual quality and privacy and security. In this paper, a double layered pencil shaped shell matrix based image steganography methodology with high security is proposed and with this extra layer an extra 2 bits can be hidden within every single pixel pair of the pencil shaped shell matrix. Dependent on the shell matrix made of pencil-shaped shells, every private digit is fitted in each cover pixel pair. Various experimental outcomes imply that the proposed methodology has achieved a higher capacity of 3.0 bpp with average 43.25 dB of PSNR and it outperforms other existing shell matrix based image steganographic schemes. Furthermore, the results of RS analysis, JPEG compression analysis, Q-index analysis, normalized absolute error (NAE) analysis etc. are clearly proves the robustness and security of the proposed methodology. Numerous sectors of various private and government organizations, including intellectual property rights, education, intelligent bureau, defence, etc. can be benefited immensely from this scheme.

MetaFlow: a meta-learning-based network for optical flow estimation

Convolutional neural networks (CNNs) have achieved success in optical flow estimation using labeled datasets, but they fail to build an internal representation to fast adapt to the specific task. On the other hand, limited by the lack of ground truth, existing CNNs-based methods suffer from high noise sensitivity and inferior generalization performance. We integrate the meta-learning technique with optical flow estimation, which can learn internal features to search optimal initial state parameters of the network. Meanwhile, we devise an enhanced network termed MetaFlow to further improve performance. MetaFlow extracts per-pixel features, builds correlation volumes for all pairs of pixels, and iteratively updates optical flow through optical flow predictor using meta-learning. In addition, we propose a meta-transfer pretraining approach to obtain initial network weights, which can efficiently avoid network overfitting. Empirical experiments on MPI Sintel and KITTI benchmarks have shown that the proposed MetaFlow achieves the state-of-the-art results and performs outstanding in challenging scenarios such as textureless regions and abrupt motions.

Detection of the multivariate geochemical anomalies associated with mineralization using a deep convolutional neural network and a pixel-pair feature method

Machine learning (ML) algorithms are widely applied in various fields owing to their strong ability to abstract high-level features from a large number of training samples. However, few supervised ML algorithms have been applied in geochemical prospecting and mineral exploration because mineralization is a rare geological event that leads to an insufficient number of training samples. Generating a large number of training samples is crucial for the application of supervised ML in geochemical prospecting and mineral exploration. In this study, a novel anomaly detection framework combined with a pixel-pair feature (PPF) method and a deep convolutional neural network (CNN) was employed to identify the multivariate geochemical anomalies associated with mineralization. First, the PPF method was employed to generate sufficient training samples by recombining the pixel pairs of the labeled samples. Then, a multilayer supervised CNN framework, which consists of 13 convolutional layers, an average pooling layer, and a fully connected layer, was trained with these pixel pairs for geochemical anomaly recognition. The testing procedure was based on the fact that neighboring pixels belong to the same class with a high probability. The dual-window detector was applied to detect multivariate geochemical anomalies related to Fe polymetallic mineralization in the southwest Fujian Province of China. The identified geochemical anomalies exhibited a close spatial correlation with the known mineral deposits, which validates the potential of the proposed method. Therefore, the method developed in this study can enhance the application of supervised ML in geochemical prospecting and mineral exploration.

Water-Body Segmentation for Multi-Spectral Remote Sensing Images by Feature Pyramid Enhancement and Pixel Pair Matching

ABSTRACT Water-body image segmentation is a fundamental operation of many important applications, such as water resources allocation, ecological assessment, flood control, etc. Mainstream neural network based segmentation algorithms are still far from satisfactory for segmenting water-body; complex natural land and water boundaries can easily lead to inaccurate classification with little boundary detail preserved. To improve the performance of water-body segmentation, we propose a novel technique based on feature pyramid enhancement and pixel pair matching. By constructing feature enhancement sub-nets for different scales and superimposing the feature maps together, our technique preserves and transmits more spatial information to the backbone network, hence alleviating the common problem of detail loss in deepened network. Moreover, for each pixel, our technique employs a novel loss term to make the network learn from the classification results of similar neighbouring pixels in order to smooth out small local errors. Experiments on a new water-body dataset, namely DT-1, demonstrate that the proposed methods have improved by at least 1.24% in segmentation precision in comparison with state-of-the-art methods, including the fully connected network (FCN8S), U-Net, SegNet, RefineNet, and DeepLabv3+, which effectively captures the details of water and reduces pixel classification error of the water boundary.

High-Capacity Embedding Method Based on Double-Layer Octagon-Shaped Shell Matrix

Data hiding is a technique that embeds a secret message into a cover medium and transfers the hidden information in the secret message to the recipient. In the past, several data hiding methods based on magic matrix have used various geometrical shapes to transmit secret data. The embedding capacity achieved in these methods was often limited due to simple geometrical layouts. This paper proposes a data hiding scheme based on a double-layer octagon-shaped shell matrix. Compared to previous octagon-shaped data hiding methods, the proposed method embeds a total of 7 bits in each pixel pair, reaching an embedding capacity of 3.5 bits per pixel (bpp). Experimental results show that the proposed scheme has a higher embedding capacity compared to other irreversible data hiding schemes. Using the proposed method, it is possible to maintain the Peak Signal to Noise Ratio (PSNR) within an acceptable range with the embedding time less than 2 s.

Novel Secure Hybrid Image Steganography Technique Based on Pattern Matching

The secure communication of information is a major concern over the internet. The information must be protected before transmitting over a communication channel to avoid security violations. In this paper, a new hybrid method called compressed encrypted data embedding (CEDE) is proposed. In CEDE, the secret information is first compressed with Lempel Ziv Welch (LZW) compression algorithm. Then, the compressed secret information is encrypted using the Advanced Encryption Standard (AES) symmetric block cipher. In the last step, the encrypted information is embedded into an image of size 512 × 512 pixels by using image steganography. In the steganographic technique, the compressed and encrypted secret data bits are divided into pairs of two bits and pixels of the cover image are also arranged in four pairs. The four pairs of secret data are compared with the respective four pairs of each cover pixel which leads to sixteen possibilities of matching in between secret data pairs and pairs of cover pixels. The least significant bits (LSBs) of current and imminent pixels are modified according to the matching case number. The proposed technique provides double-folded security and the results show that stego image carries a high capacity of secret data with adequate peak signal to noise ratio (PSNR) and lower mean square error (MSE) when compared with existing methods in the literature.

An Autonomous, Optically-Powered, Direct-to-Digital Sun-Angle Recorder for Honey Bee Flight Tracking

An autonomous sensor for insect flight tracking that captures and stores solar angle-of-incidence without the use of a conventional ADC is presented. The chip uses pairs of Angle-Sensitive Pixels as differential 1-bit ADCs, and an array of these sensors provides a many-bit encoding of angle-of-incidence. Digitization occurs immediately within the pixel by use of a novel in-pixel comparator, thus enabling ultra-low-power, direct-to-digital capture of angle-of-incidence. These measurements are stored in an on-chip memory throughout the flight and can be uploaded to a base station via magnetic backscatter at the end of the flight. To permit full autonomy, the system is powered by on-chip photovoltaics, providing open-circuit voltages in the range of 0.40 − 0.50 V in natural sunlight, the intensity of which can vary throughout a flight. The system consumes a simulated 630nW at nominal supply voltage of 0.45 V, and circuit topologies amenable to photovoltaic power conditions are presented. The chip is envisioned as a flight recorder to be mounted on honey bees to track their trajectories, and bee flights were emulated by carrying the chip along a 226 m outdoor trajectory and downloading the recorded flight data from the chip at a base station in the field. Across 18 trials of the same trajectory, which emulates a small sample of tagged bees visiting known feeding sites and returning to their hive, the average reconstructed final position is 9.6 m away from the true final position, an error less than 5% of the total trajectory length.

Using Triple Collocation Observations to Estimate Satellite Measurement Noise

Knowing how much measurement noise is in a signal is critical for evaluating the overall performance of a satellite observation. We developed a triple collocation observation (TCO) algorithm for estimating measurement noise by collocation comparing the local deviations of three satellite data sets. When we evaluated our algorithm with a synthetic data set, the results showed that the algorithm effectively derived measurement noise from satellite signals despite the many intermission signal differences among the satellites. The TCO algorithm produced &#x003C;6.66&#x0025; uncertainty in the measurement noise estimates that we derived from the synthetic data set. In addition, to maximally isolate measurement noise from ocean color images, we developed a set of data quality control criteria to apply when identifying synchronous pixel pairs. Using images from the Medium Resolution Spectral Imager II (MERSI II), the Visible Infrared Imaging Radiometer Suite (VIIRS), and the Moderate Resolution Imaging Spectroradiometer (MODIS) instruments, we applied our data quality control criteria and found that the TCO algorithm produced measurement noise consistent with the measured prelaunch or specifications for VIIRS and MERSI II instrument noise. However, the TCO measurement noise was significantly lower than the spaced MODIS noise because MODIS&#x2019;s extended service time likely produced instrument degradation. Overall, MODIS performed better than MERSI II but worse than VIIRS. Furthermore, we found that the residual error in remote sensing reflectance exponentially decreased as the measurement signal-to-noise ratio (MSNR) increased. Because of this exponential relationship, the MSNR should not be lower than 181 to achieve the &#x003C;5&#x0025; uncertainty goal of remote sensing reflectance at 443 nm that NASA proposed. Our results suggest that the TCO algorithm is an effective approach for comprehensively estimating and comparing instrument performance.