Representation Error Research Articles

Psychophysical scaling reveals a unified theory of visual memory strength.

Almost all models of visual memory implicitly assume that errors in mnemonic representations are linearly related to distance in stimulus space. Here we show that neither memory nor perception are appropriately scaled in stimulus space; instead, they are based on a transformed similarity representation that is nonlinearly related to stimulus space. This result calls into question a foundational assumption of extant models of visual working memory. Once psychophysical similarity is taken into account, aspects of memory that have been thought to demonstrate a fixed working memory capacity of around three or four items and to require fundamentally different representations-across different stimuli, tasks and types of memory-can be parsimoniously explained with a unitary signal detection framework. These results have substantial implications for the study of visual memory and lead to a substantial reinterpretation of the relationship between perception, working memory and long-term memory.

A point‐based redesign algorithm for designing geometrically complex surfaces. A case study: Miralles's croissant paradox

This study explores the use of point clouds for both representation and genetic morphogenesis of complex geometry. The accurate representation of existing objects of complex curved geometry, which are subsequently geometrically modified by evolutionary morphogenetic processes, is analysed. To this end, as a method of representation and generation of complex geometries, a point-based genetic algorithm and the use of large unstructured point clouds are proposed. A study of convergence and diversity of the implemented algorithm is detailed, as well as a comparison with the Coyote optimisation algorithm in terms of representation error demonstrating its efficiency. Some commonly used three-dimensional formats in architecture, such as NURBS and polygon meshes, are analysed, and compared against point clouds. This study also includes an evaluation regarding whether the use of point clouds is a more suitable format for realistic representation, rationalisation and genetic morphogenesis.

Transfer Function-Guided Saliency-Aware Compression for Transmitting Volumetric Data

We introduce a transfer-function-guided three-dimensional (3-D) block-based saliency-aware compression scheme for volumetric data that is both content and spatially scalable. Salient 3-D volumetric blocks are identified and weighted with the help of a transfer function which is used to render the data. We describe our method in the form of a framework for processing, progressive transmission, and visualization of volumetric data on a target device, such as a mobile device with limited computational resources. In particular, we address the transmission bottleneck incurred when transferring 3-D volumetric data. Identified salient regions are progressively transmitted to the target device. The received data are rendered progressively in the respective order with a predefined or user-defined transfer function. Our method is developed with medical applications in mind, where preservation of all information is essential for clinical diagnosis. Because our method is integrated into a resolution scalable coding scheme with an integer wavelet transform of the image, it allows the rendering of each significant region at a different resolution up to fully lossless reconstruction. We perform a thorough qualitative and quantitative evaluation of the saliency detection method and the resulting saliency-aware compression schemes. Our results show reduced error in representation of the volumetric data with our method.

An [formula omitted]-DPG method for the convection–diffusion problem

Following Muga and van der Zee (Muga and van der Zee, 2015), we generalize the standard Discontinuous Petrov–Galerkin (DPG) method, based on Hilbert spaces, to Banach spaces. Numerical experiments using model 1D convection-dominated diffusion problem are performed and compared with Hilbert setting. It is shown that Banach-based method gives solutions less susceptible to Gibbs phenomenon. h-adaptivity is implemented with the help of the error representation function as error indicator.

Development of a Mesoscale Inversion System for Estimating Continental‐Scale CO2 Fluxes

AbstractComputational requirements often impose limitations on the spatial and temporal resolutions of atmospheric CO2 inversions, increasing aggregation and representation errors. This study enables higher spatial and temporal resolution inversions with spatial and temporal error structures similar to those used in other published inversions by representing the prior flux error covariances as a Kronecker product of spatial and temporal covariances and by using spectral methods for the spatial correlations. Compared to existing inversion systems that are forced to degrade the resolution of the problem in order to bring the dimensionality down to computationally tractable levels, this inversion framework is able to take advantage of mesoscale transport simulations and more of the complexity of spatial and temporal covariances in the surface CO2 fluxes. This approach was successfully implemented over one month with an identical‐twin observing system simulation experiment (OSSE) using a set of assumptions about the prior flux uncertainties compatible both with continental‐scale uncertainty estimates and with comparisons of vegetation models to flux towers. The demonstration illustrates the potential of the newly developed inversion system to use high‐temporal‐resolution information from the North American tower network, to extract high‐resolution information about CO2 fluxes that is inaccessible to coarser resolution inversion systems, and to simultaneously optimize an ensemble of prior estimates. This demonstration sets the stage for regional flux inversions that can take full advantage of the high‐resolution data available in tower CO2 records and mesoscale atmospheric transport reanalyses, include more realistic prior error structures, and explore specifying prior fluxes with ensembles.

Jointly Learning the Discriminative Dictionary and Projection for Face Recognition

Recently, dictionary learning has become an active topic. However, the majority of dictionary learning methods directly employs original or predefined handcrafted features to describe the data, which ignores the intrinsic relationship between the dictionary and features. In this study, we present a method called jointly learning the discriminative dictionary and projection (JLDDP) that can simultaneously learn the discriminative dictionary and projection for both image-based and video-based face recognition. The dictionary can realize a tight correspondence between atoms and class labels. Simultaneously, the projection matrix can extract discriminative information from the original samples. Through adopting the Fisher discrimination criterion, the proposed framework enables a better fit between the learned dictionary and projection. With the representation error and coding coefficients, the classification scheme further improves the discriminative ability of our method. An iterative optimization algorithm is proposed, and the convergence is proved mathematically. Extensive experimental results on seven image-based and video-based face databases demonstrate the validity of JLDDP.

Minimum Eigenvector Collaborative Representation Discriminant Projection for Feature Extraction

High-dimensional signals, such as image signals and audio signals, usually have a sparse or low-dimensional manifold structure, which can be projected into a low-dimensional subspace to improve the efficiency and effectiveness of data processing. In this paper, we propose a linear dimensionality reduction method—minimum eigenvector collaborative representation discriminant projection—to address high-dimensional feature extraction problems. On the one hand, unlike the existing collaborative representation method, we use the eigenvector corresponding to the smallest non-zero eigenvalue of the sample covariance matrix to reduce the error of collaborative representation. On the other hand, we maintain the collaborative representation relationship of samples in the projection subspace to enhance the discriminability of the extracted features. Also, the between-class scatter of the reconstructed samples is used to improve the robustness of the projection space. The experimental results on the COIL-20 image object database, ORL, and FERET face databases, as well as Isolet database demonstrate the effectiveness of the proposed method, especially in low dimensions and small training sample size.

Blind Image Clustering for Camera Source Identification via Row-Sparsity Optimization

Given a set of images with the number of cameras providing those images unknown, how to blindly identify the sources of the images has been a critical problem in digital forensics. Although state-of-the-art methods have achieved impressive results, they have failed at suppressing outliers. When they deal with a noisy dataset, the performance is significantly degraded. To address this issue, we propose an optimization approach with sparsity constraints to simultaneously handle the how-many subproblem ( i.e. , the number of cameras) and the which-from-which subproblem ( i.e. , the image–camera relationship). In our approach, we first formulate the blind camera source clustering as a row-sparsity optimization problem, in which the representation errors are minimized and the outliers caused by noisy features are suppressed. Then, a new two-stage refinement method based on inter- and the intra-class differences is proposed to achieve a more accurate estimation of the number of cameras. Because strong sparsity constraints have been adopted and the interactive relationship among data points can be fully explored to distinguish the images originated from different cameras, the proposed method can effectively handle outliers. Extensive experiments on the popular Dresden dataset show that the proposed method outperforms existing methods in both identification accuracy and efficiency.

Generating Proxy SWOT Water Surface Elevations Using WRF‐Hydro and the CNES SWOT Hydrology Simulator

AbstractThe Surface Water Ocean Topography (SWOT) mission will launch in early 2022 to provide the first global inventory of terrestrial surface water. Although SWOT is primarily a research mission with key science objectives in both the oceanography and hydrology domains, SWOT data are expected to have application potential to address many societal needs. To identify SWOT applications, prepare for the use of SWOT data, and quantify SWOT impacts prior to launch, realistic proxy SWOT observations with representative measurement errors are required. This paper provides a step‐by‐step description of two methods for deriving proxy SWOT water surface elevations (WSEs) from an Observing System Simulation Experiment (OSSE) using the Weather Research and Forecasting hydrological extension package (WRF‐Hydro). The first, a basic method, provides a simple and efficient way to sample WRF‐Hydro output according to the SWOT orbit and add random white noise to simulate measurement error, similar to many previous approaches. An alternate method using the Centre National d'Etudes Spatiales (CNES) Large‐Scale SWOT Hydrology Simulator accounts for additional sources of measurement error and produces output in formats comparable to that expected from official SWOT products. The basic method is ideal for river hydrology applications in which a full representation of SWOT measurement errors and spatial resolution is unnecessary, whereas the CNES simulator approach is better‐suited for more rigorous scientific studies that require a comprehensive error budget.

Using Spherical Harmonics in the Galactocentric Coordinate System to Study the Kinematics of Globular Star Clusters

The technique of spherical harmonics, both scalar and vector ones, has long been applied to analyze the astronomical data on a sphere, for example, in the representation of systematic errors, in stellar kinematics. Up to now, spherical harmonics have been used exclusively in heliocentric coordinate systems: the equatorial or Galactic one. To study the kinematics of the entire Galaxy (and not only the solar neighborhood), it is reasonable to pass to the Galactocentric coordinate system. The second release of the Gaia catalogue does not yet allow such an analysis to be performed for individual stars due to the relatively low accuracy of the parallaxes. However, such a study seems possible for globular star clusters, despite their small number. Although the kinematics of globular clusters was studied in detail in many papers, we want to test the method of analyzing the Galactocentric proper motions and radial velocities using spherical harmonics based on data from this catalogue.

Observer-Based Control for Uncertain Nonlinear Systems Applied to Continuous Biochemical Reactors

The purpose of this paper is to present an observer-based control design with application to continuous bioreactors. For this purpose, phenomenological bioreactor models were represented by identified linear models plus unknown modelling error terms. Therefore, an uncertainty-based observer with a polynomial structure capable of estimating the unknown modelling error of the reactor representation is coupled to a linear input-output controller. The proposed methodology was evaluated in a sulphate reduction bioprocess and an acetone-butanol-ethanol (ABE) fermentation process for butanol (biofuel) production, under continuous regimes. Experimentally validated mathematical models were considered for this purpose. A theoretical framework is presented to demonstrate the corresponding closed-loop stability of the systems, and numerical simulations were carried out to corroborate the satisfactory performance of the proposed methodology.

Optimality and Limitations of Audio-Visual Integration for Cognitive Systems.

Multimodal integration is an important process in perceptual decision-making. In humans, this process has often been shown to be statistically optimal, or near optimal: sensory information is combined in a fashion that minimizes the average error in perceptual representation of stimuli. However, sometimes there are costs that come with the optimization, manifesting as illusory percepts. We review audio-visual facilitations and illusions that are products of multisensory integration, and the computational models that account for these phenomena. In particular, the same optimal computational model can lead to illusory percepts, and we suggest that more studies should be needed to detect and mitigate these illusions, as artifacts in artificial cognitive systems. We provide cautionary considerations when designing artificial cognitive systems with the view of avoiding such artifacts. Finally, we suggest avenues of research toward solutions to potential pitfalls in system design. We conclude that detailed understanding of multisensory integration and the mechanisms behind audio-visual illusions can benefit the design of artificial cognitive systems.

Design and simulation of quantum-dot cellular automata serial decimal pipelined processor based on Turing machine model

The quantum-dot cellular automata (QCA) nanoscale computer technology is promising to overcome the limits of the microelectronic CMOS technology. Because the leading role of QCA wires, the serial data transfer/processing is preferable. The financial, Internet of Things, and control computer applications require direct processing of decimal information without representation and conversion errors. Because a QCA wire can be considered as a virtual tape with written binary symbols, a special version of Turing machine model can be used for a QCA computer implementation. Design of a novel QCA serial decimal pipelined processor based on the Turing machine model is presented. The processor uses the run-time tape reconfiguration for arithmetic processing of decimal operands encoded in the 5-bit Johnson-Mobius code. The proposed design demonstrates significant hardware simplification.

Modeling Spatial Heterogeneity in Surface Turbulent Heat Flux in the U.S. Southern Great Plains

AbstractAdvances in numerical modeling of cloud dynamics are driving a need for improved land model prediction at convective storm scales. In this study, satellite and ground‐based vegetation remote sensing data were combined with land model experiments to more accurately characterize land surface spatial heterogeneity in the Community Land Model (CLM4.0). The new subgrid classification of plant functional types (PFT) and leaf area index (LAI) enables consistent comparison between models and ground‐based flux measurements in the U.S. southern Great Plains. Errors in vegetation data sets (inferred from comparison between 250 m satellite and ground‐based LAI), while large, had less impact on the simulated characteristics of spatial heterogeneity compared to errors in model representation of surface energy partitioning (between latent and sensible heat flux) and its relationship to LAI. Predicted spatial heterogeneity in surface energy partitioning was enhanced after replacing soil and stomatal resistance parameters with a new set that better predicts the observed relationship to LAI. These modifications increase the number of smaller (mesoscale) dry land patches having higher sensible heat flux. The parameter experiments suggest that vegetation state and processes (transpiration) act to broaden the size spectrum of surface heat flux heterogeneity, which can influence clouds and convective initiation. Moreover, improvements in vegetation input data and model parameters had partially compensating effects on surface flux heterogeneity, indicating the importance of evaluating input data and parameterizations together to improve prediction at higher spatial resolutions.

Site representativity of AERONET and GAW remotely sensed aerosol optical thickness and absorbing aerosol optical thickness observations

Abstract. Remote sensing observations from the AERONET (AErosol RObotic NETwork) and GAW (Global Atmosphere Watch) networks are intermittent in time and have a limited field of view. A global high-resolution simulation (Goddard Earth Observing System Model (GEOS-5) Nature Run) is used to conduct an OSSE (observing system simulation experiment) for AERONET and GAW observations of AOT (aerosol optical thickness) and AAOT (absorbing aerosol optical thickness) and estimate the spatiotemporal representativity of individual sites for larger areas (from 0.5 to 4∘ in size). GEOS-5 NR and the OSSE are evaluated and have shown to have sufficient skill, although daily AAOT variability is significantly underestimated, while the frequency of AAOT observations is overestimated (both resulting in an underestimation of temporal representativity errors in AAOT). Yearly representation errors are provided for a host of scenarios: varying grid-box size, temporal collocation protocols and site altitudes are explored. Monthly representation errors show correlations from month to month, with a pronounced annual cycle that suggests temporal averaging may not be very successful in reducing multi-year representation errors. The collocation protocol for AEROCOM (AEROsol Comparisons between Observations and Models) model evaluation (using daily data) is shown to be suboptimal and the use of hourly data is advocated instead. A previous subjective ranking of site spatial representativity (Kinne et al., 2013) is analysed and a new objective ranking proposed. Several sites are shown to have yearly representation errors in excess of 40 %. Lastly, a recent suggestion (Wang et al., 2018) that AERONET observations of AAOT suffer a positive representation bias of 30 % globally is analysed and evidence is provided that this bias is likely an overestimate (the current paper finds 4 %) due to methodological choices.

Tracking multiple construction workers through deep learning and the gradient based method with re-matching based on multi-object tracking accuracy

Multiple construction worker tracking is an active research area critical to the planning of the job site. Challenges in multiple construction worker tracking include miss detection and mismatch due to occlusion and identity switches. To the best knowledge of the authors, the mismatch is not reported in the literature of construction for image based single camera multiple worker tracking. As a result, the mismatch should be taken into account through a representative performance index such as the Multi-Object Tracking Accuracy (MOTA). This work aims to improve the performance of the current multiple worker tracking through an approach composed of three stages: detection, matching and re-matching. In the detection stage, the deep learning detector, Mask R-CNN, is utilized. In the matching stage, we attempt to track workers between consecutive image frames through a gradient based method with feature based comparison. Several cost means and matching methods have been experimented for model selection. Trajectories of tracking objects are derived in this stage. The best cost measurements and matching methods are recommended. Trajectories of tracking objects could be interrupted because of miss detection or mismatch. We call those broken trajectories, without matched detections, orphans. In the re-matching stage, we attempt to recover unmatched detections in the current frame with previous orphans based on extracted features. A competitive MOTA of 56.7% was obtained from the proposed approach over MOTA of 55.9% from the state-of-the-art Detect-And-Track model on a human tracking benchmark dataset. On construction job sites, we have tested the approach with 4 testing videos, resulting in a total MOTA of 81.8%, average MOTA per video of 79.0% and standard deviation of 13.0%, while the maximum and minimum MOTAs are 96.0% and 69.0%, respectively. As a result, the proposed work could potentially provide better multiple worker tracking on the construction job site. Additionally, to have a better representation of the tracking errors, this work suggests to utilize the MOTA for multiple construction worker tracking.

Fraction Sense: An Analysis of Preservice Mathematics Teachers’ Cognitive Obstacles

Research on cognitive obstacles related to fraction sense in preservice mathematics teachers is significant, because their success depends on their skills. The acquisition of fraction sense is a complicated problem requiring a strategy to solve it. This study presents cognitive obstacles with fraction sense tests in preservice who will teach in secondary schools. It focuses on the following categories of cognitive obstacles: epistemological (language representation, tendency to generalise and rely on intuition) and didactic (less meaningful learning, and strategy). This paper takes a qualitative descriptive approach to examine 20 preservice mathematics teachers. The preservice teachers who encountered cognitive obstacles related to fraction sense testing were then grouped based on the similarity of their answers, and seven of them were selected to be interviewed. The research findings showed that five preservice teachers had overlapping obstacles: language representation and tendency to generalise; tendency to generalise and less meaningful learning; language representation, tendency to rely on intuition and trial and error strategy in; language representation and trial and error; and language representation and tendency to rely on intuition.

An Efficient Compression Method of Hyperspectral Images Based on Compressed Sensing and Joint Optimization

Compressed sensing provides the possibility of efficient compression of massive hyperspectral data. However, the existing methods often use the organization pattern of image blocks in sparse representation, and cannot make full use of inter spectral correlation. The separate retrieval of dictionary and measurement matrix also restricts the processing efficiency. To solve these problems, a novel and efficient hyperspectral image compression method based on compressed sensing and joint optimization is proposed in this paper. In sparse representation, the data organization pattern on spectral dimension is adopted to better express the correlation between spectra and improve the efficiency of operation. On the dictionary and measurement matrix, a joint optimization algorithm is proposed, which synchronously inhibits the sparse representation error and the reconstruction error. Experimental results show that compared with similar methods, the reconstruction error of this method is increased by 3 dB and the number of iterations is reduced by seven times, and the compression rate can reach 1/18.

Increasing the Space–Time Resolution of Mapped Sea Surface Height From Altimetry

AbstractWe present a mapping methodology to improve the resolution of gridded sea surface height (SSH) from multisatellite along‐track measurements, and apply it in the California Current system. This is motivated by the upcoming Surface Water and Ocean Topography (SWOT) satellite mission, which will collect novel high‐resolution wide‐swath SSH measurements. The calibration/validation of SWOT will be in the California Current and requires independent observations of SSH spatial variability. Our objective was to discover how far we could push the space–time resolution of SSH maps based on the existing altimetry constellation. Currently, the best SSH maps for the region are from AVISO's global product based on optimal interpolation (OI). Our methodology is based on 2‐D variational analysis (2DVAR), and we address some limitations of the AVISO OI global parameterization that restrict the resolution. Key improvements are (1) use of a background field incorporating mesoscale information, as opposed to a long‐term mean field; (2) optimized regional parameters; and (3) a representation error term in the observational error covariance matrix to account for the spread of measurements in time. Using a suite of independent remote and in situ observations, we show the 2DVAR method can produce higher‐resolution SSH maps in the California Current region that successfully capture smaller‐scale ocean features than AVISO, at the expense of an increase in noise.

Representing model uncertainty for global atmospheric CO<sub>2</sub> flux inversions using ECMWF-IFS-46R1

Abstract. Atmospheric flux inversions use observations of atmospheric CO2 to provide anthropogenic and biogenic CO2 flux estimates at a range of spatio-temporal scales. Inversions require prior flux, a forward model and observation errors to estimate posterior fluxes and uncertainties. Here, we investigate the forward transport error and the associated biogenic feedback in an Earth system model (ESM) context. These errors can occur from uncertainty in the initial meteorology, the analysis fields used, or the advection schemes and physical parameterisation of the model. We also explore the spatio-temporal variability and flow-dependent error covariances. We then compare the error with the atmospheric response to uncertainty in the prior anthropogenic emissions. Although transport errors are variable, average total-column CO2 (XCO2) transport errors over anthropogenic emission hotspots (0.1–0.8 ppm) are comparable to, and often exceed, prior monthly anthropogenic flux uncertainties projected onto the same space (0.1–1.4 ppm). Average near-surface transport errors at three sites (Paris, Caltech and Tsukuba) range from 1.7 to 7.2 ppm. The global average XCO2 transport error standard deviation plateaus at ∼0.1 ppm after 2–3 d, after which atmospheric mixing significantly dampens the concentration gradients. Error correlations are found to be highly flow dependent, with XCO2 spatio-temporal correlation length scales ranging from 0 to 700 km and 0 to 260 min. Globally, the average model error caused by the biogenic response to atmospheric meteorological uncertainties is small (<0.01 ppm); however, this increases over high flux regions and is seasonally dependent (e.g. the Amazon; January and July: 0.24±0.18 ppm and 0.13±0.07 ppm). In general, flux hotspots are well-correlated with model transport errors. Our model error estimates, combined with the atmospheric response to anthropogenic flux uncertainty, are validated against three Total Carbon Observing Network (TCCON) XCO2 sites. Results indicate that our model and flux uncertainty account for 21 %–65 % of the total uncertainty. The remaining uncertainty originates from additional sources, such as observation, numerical and representation errors, as well as structural errors in the biogenic model. An underrepresentation of transport and flux uncertainties could also contribute to the remaining uncertainty. Our quantification of CO2 transport error can be used to help derive accurate posterior fluxes and error reductions in future inversion systems. The model uncertainty diagnosed here can be used with varying degrees of complexity and with different modelling techniques by the inversion community.