Pointwise Approach Research Articles

NeRF-NQA: No-Reference Quality Assessment for Scenes Generated by NeRF and Neural View Synthesis Methods.

Neural View Synthesis (NVS) has demonstrated efficacy in generating high-fidelity dense viewpoint videos using a image set with sparse views. However, existing quality assessment methods like PSNR, SSIM, and LPIPS are not tailored for the scenes with dense viewpoints synthesized by NVS and NeRF variants, thus, they often fall short in capturing the perceptual quality, including spatial and angular aspects of NVS-synthesized scenes. Furthermore, the lack of dense ground truth views makes the full reference quality assessment on NVS-synthesized scenes challenging. For instance, datasets such as LLFF provide only sparse images, insufficient for complete full-reference assessments. To address the issues above, we propose NeRF-NQA, the first no-reference quality assessment method for densely-observed scenes synthesized from the NVS and NeRF variants. NeRF-NQA employs a joint quality assessment strategy, integrating both viewwise and pointwise approaches, to evaluate the quality of NVS-generated scenes. The viewwise approach assesses the spatial quality of each individual synthesized view and the overall inter-views consistency, while the pointwise approach focuses on the angular qualities of scene surface points and their compound inter-point quality. Extensive evaluations are conducted to compare NeRF-NQA with 23 mainstream visual quality assessment methods (from fields of image, video, and light-field assessment). The results demonstrate NeRF-NQA outperforms the existing assessment methods significantly and it shows substantial superiority on assessing NVS-synthesized scenes without references. An implementation of this paper are available at https://github.com/VincentQQu/NeRF-NQA.

Listwise Generative Retrieval Models via a Sequential Learning Process

Recently, a novel generative retrieval (GR) paradigm has been proposed, where a single sequence-to-sequence model is learned to directly generate a list of relevant document identifiers (docids) given a query. Existing GR models commonly employ maximum likelihood estimation (MLE) for optimization: This involves maximizing the likelihood of a single relevant docid given an input query, with the assumption that the likelihood for each docid is independent of the other docids in the list. We refer to these models as the pointwise approach in this article. While the pointwise approach has been shown to be effective in the context of GR, it is considered sub-optimal due to its disregard for the fundamental principle that ranking involves making predictions about lists. In this article, we address this limitation by introducing an alternative listwise approach, which empowers the GR model to optimize the relevance at the docid list level. Specifically, we view the generation of a ranked docid list as a sequence learning process: At each step, we learn a subset of parameters that maximizes the corresponding generation likelihood of the i th docid given the (preceding) top i -1 docids. To formalize the sequence learning process, we design a positional conditional probability for GR. To alleviate the potential impact of beam search on the generation quality during inference, we perform relevance calibration on the generation likelihood of model-generated docids according to relevance grades. We conduct extensive experiments on representative binary and multi-graded relevance datasets. Our empirical results demonstrate that our method outperforms state-of-the-art GR baselines in terms of retrieval performance.

Deep calibration with random grids

We propose a neural network-based approach to calibrating stochastic volatility models, which combines the pioneering grid approach by Horvath et al. [Deep learning volatility: A deep neural network perspective on pricing and calibration in (rough) volatility models. Quant. Finance, 2021, 21(1), 11–27]. with the pointwise two-stage calibration of Bayer and Stemper [Deep calibration of rough stochastic volatility models. Working Paper, arXiv:1810.03399, 2018] and Liu et al. [A neural network-based framework for financial model calibration. J. Math. Ind., 2019, 9(1), 1–28]. Our methodology inherits robustness from the former while not suffering from the need for interpolation/extrapolation techniques, a clear advantage ensured by the pointwise approach. The crucial point to the entire procedure is the generation of implied volatility surfaces on random grids, which one dispenses to the network in the training phase. We support the validity of our calibration technique with several empirical and Monte Carlo experiments for the rough Bergomi and Heston models under a simple but effective parametrization of the forward variance curve. The approach paves the way for valuable applications in financial engineering—for instance, pricing under local stochastic volatility models—and extensions to the fast-growing field of path-dependent volatility models.

Central limit theorem for bifurcating markov chains under L2-ergodic conditions

AbstractBifurcating Markov chains (BMCs) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMCs under $L^2$ -ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As an application, we study the elementary case of a symmetric bifurcating autoregressive process, which justifies the nontrivial hypothesis considered on the kernel transition of the BMCs. We illustrate in this example the phase transition observed in the fluctuations.

Ray-based cable and obstacle interference-free workspace for cable-driven parallel robots

A low computational cost and generalized ray-based interference-free workspace (IFW) analysis method for arbitrary types of CDPRs is proposed in this paper. This work extends the existing ray-based method (RBM) properties to solve the ray-based workspace under cable–cable and cable–obstacle interference-free conditions. The proposed method covers a broader range of obstacles defined by polynomial surfaces than existing methods. After determining the IFW, the ray-based workspace under different workspace conditions can be combined. Path planning can be performed similarly to the existing point-wise approach but with guaranteed connectivity inside the available workspace. Meanwhile, the proposed approach can simultaneously handle different CDPRs with translation and orientation.

Linear inviscid damping for shear flows near Couette in the 2D stably stratified regime

We investigate the linear stability of shears near the Couette flow for a class of 2D incompressible stably stratified fluids. Our main result consists of nearly optimal decay rates for perturbations of stationary states whose velocities are monotone shear flows $(U(y),0)$ and have an exponential density profile. In the case of the Couette flow $U(y)=y$, we recover the rates predicted by Hartman in 1975, by adopting an explicit point-wise approach in frequency space. As a by-product, this implies optimal decay rates as well as Lyapunov instability in $L^2$ for the vorticity. For the previously unexplored case of more general shear flows close to Couette, the inviscid damping results follow by a weighted energy estimate. Each outcome concerning the stably stratified regime applies to the Boussinesq equations as well. Remarkably, our results hold under the celebrated Miles-Howard criterion for stratified fluids.

Human health risk exposure and ecological risk assessment of potentially toxic element pollution in agricultural soils in the district of Frydek Mistek, Czech Republic: a sample location approach

BackgroundHuman activities considerably contribute to polluting potentially toxic element (PTEs) levels in soils, especially agricultural soils. The consistent introduction of PTEs in the environment and the soil pose health-related risks to humans, flora and fauna. One hundred and fifteen samples were collected in the district of Frydek Mistek (Czech Republic) in a regular grid form. The soil samples were air-dried, and the concentrations of PTEs (i.e. lead, arsenic, chromium, nickel, manganese, cadmium, copper, and zinc) were determined by ICP-OES (inductively coupled plasma optical emission spectrometry). The purpose of this study is to create digitized soil maps that expose the human-related health risks posed by PTEs, estimate pollution indices, ascertain the spatially distributed patterns of PTEs, source apportionment and quantify carcinogenic and non-carcinogenic health risks using the sample location approach.ResultsThe results revealed that the pollution assessment of the soils in the study area using diverse pollution assessment indexes (pollution index, pollution load index, ecological risk and risk index), based on the application of the local background value and the European average value, displayed a range of pollution levels due to differences in the threshold limits from differing geochemical background levels. The principal components analysis and positive matrix factorization, respectively, identified the sources of pollution and the distribution of PTE sources. Mapping the health index and total carcinogenic risk highlighted hotspots of areas within the study area that require immediate remediation. The self-organizing map (SeOM) revealed a diversified colour pattern for the factor scores. A single neuron exhibited a high hotspot in all factor loadings on different blocks of neurons. Children’s CDItotal (Chronic Daily Intake total) values for non-carcinogenic risk and carcinogenic risk were found to be greater than adults’, as were their HQ (hazard quotients) and CR (carcinogenic risk) values. According to the health index of non-carcinogenic risk, 6.1% of the study area sampled posed a potential risk to children rather than adults. Corresponding to the sampled pointwise health risk assessment, 13.05% of the sampled locations are carcinogenic to children. The estimated health risk in the agricultural soil was high, with both carcinogenic and non-carcinogenic risks that could threaten persons living in the study area, particularly children.ConclusionIn general, the continuous application of agriculturally related inputs such as phosphate fertilizers and other anthropogenic activities (e.g., steel industry) can increase the level of PTEs in soils. The use of mean, maximum, and minimum values in health risk estimation does not provide a comprehensive picture of a research area’s health state. This study recommends using a sampled pointwise or location health risks assessment approach, which allows researchers to identify high-risk environments that exceeds the recommended threshold as well as areas on the verge of becoming high risk, allowing for rapid remedial action.

Regional Mean Sea Surface and Mean Dynamic Topography Models Around Malaysian Seas Developed From 27 Years of Along-Track Multi-Mission Satellite Altimetry Data

Contemporary Universiti Teknologi Malaysia 2020 Mean Sea Surface (UTM20 MSS) and Mean Dynamic Topography (UTM20 MDT) models around Malaysian seas are introduced in this study. These regional models are computed via scrutinizing along-track sea surface height (SSH) points and specific interpolation methods. A 1.5-min resolution of UTM20 MSS is established by integrating 27 years of along-track multi-mission satellite altimetry covering 1993–2019 and considering the 19-year moving average technique. The Exact Repeat Mission (ERM) collinear analysis, reduction of sea level variability of geodetic mission (GM) data, crossover adjustment, and data gridding are presented as part of the MSS computation. The UTM20 MDT is derived using a pointwise approach from the differences between UTM20 MSS and the local gravimetric geoid. UTM20 MSS and MDT reliability are validated with the latest Technical University of Denmark (DTU) and Collecte Localisation Services (CLS) models along with coastal tide gauges. The findings presented that the UTM20, CLS15, and DTU18 MSS models exhibit good agreement. Besides, UTM20 MDT is also in good agreement with CLS18 and DTU15 MDT models with an accuracy of 5.1 and 5.5 cm, respectively. The results also indicate that UTM20 MDT statistically achieves better accuracy than global models compared to tide gauges. Meanwhile, the UTM20 MSS accuracy is within 7.5 cm. These outcomes prove that UTM20 MSS and MDT models yield significant improvement compared to the previous regional models developed by UTM, denoted as MSS1 and MSS2 in this study.

On second solutions of the sixth-order nonlinear mathematical model with measured derivatives

In the present paper the sixth-order nonlinear mathematical model with nonsmooth solutions is studied. We consider a case, when the problem is guaranteed to have one solution and investigate the question on the presence of one more. Using the pointwise approach of Yu. V. Pokorny, which has shown its effectiveness in analyzing models of the second and fourth orders, sufficient conditions of the existence of the second solution for the sixth-order model with derivatives with respect to measure are obtained.

Non-ideal surface modelling approach for enabling uncertainty representation

Non-ideal models have gained considerable attention in the design stage for evaluating product functionality and performance considering the realistic conditions of the product surface. The performance evaluation generally involves deriving the statistical distributions of certain key characteristics, such as gaps and distances, based on numerous assembly process simulations, thus necessitating a large number of samples of non-ideal surfaces. The traditional practice for generating such samples is to model the systematic and random deviations of each point on the part surface. It is difficult, however, to represent the randomness of the real surface formation mechanism using this point-wise approach, thus leading to significant computational cost. As a result, this technique hinders the wider adoption of specified surface randomness representations in performance simulation and analysis.The deviation modes that feature non-ideal surfaces are dominated by manufacturing error factors, which could be systematically represented by corresponding mode functions. Furthermore, the variations in the manufacturing process inevitably cause randomness in surface deviations. In this paper, this randomness is defined as the uncertainty of non-ideal surfaces and reflected by the randomness of deviation mode function coefficients. A conceptual non-ideal surface error model that characterises the uncertainty of non-ideal surfaces through the random distributions of mode function coefficients as represented in phase space is therefore proposed. The phase space is a multi-dimensional space, in which each point denotes a group of mode function coefficients that determines a certain non-ideal surface sample. Following the distribution law of coefficients, a number of non-ideal surface samples can be generated by phase space sampling. This method reduces the problem from modelling an infinite number of surface points to modelling a finite coefficient dimension of points in the compact phase space. It thus enables the efficient modelling of non-ideal surfaces that reflect realistic errors resulting from the manufacturing process and facilitates the product performance analysis under the effect of surface randomness. To verify the method, a case study involving a tapered surface manufactured by the taper-turning process is presented. The phase space and error model are discussed with respect to typical manufacturing error factors in this process.

Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems

Point-block matrices arise naturally in multiphysics problems when all variables associated with a mesh point are ordered together, and are different from the general block matrices since the sizes of the blocks are so small one can often invert some of the diagonal blocks explicitly. Motivated by the recent works of Chow and Patel and Chow et al., we propose an efficient incomplete LU (ILU) preconditioner for point-block matrices targeting applications on GPU. The construction of the preconditioner involves two critical steps: (1) the initial guessing of values for the lower and upper triangular matrices; and (2) several sweeps of asynchronous updating of the triangular matrices. Three representative problems are studied to show the advantage of the proposed point-block approach over the standard point-wise approach in terms of the number of GMRES iterations and also the total compute time. Moreover, we compare the proposed algorithm with the level-scheduling based parallel algorithm employed in NVIDIA’s cuSPARSE library as well as the serial method implemented in Intel MKL library, and the experiments show that a 2×–5× speedup can be achieved over the block-based ILU( p) factorizations from the cuSPARSE library.

On the growth speed of own values for the fourth order spectral problem with Radon–Nikodim derivatives

In the present paper, the growth rate of eigenvalues for the fourth-order spectral problem with nonsmooth solutions is obtained. It arises when we apply the Fourier method to the mathematical model, describing small free vibrations of a mechanical system consisting of pivotally connected rods. We assume that at the connection points there are springs that respond to rotation, while the system is in the external environment with localized features, leading to a loss of smoothness of the solution. The analysis of the problem is based on the pointwise approach proposed by Yu. V. Pokorny, and proved to be effective in studying linear boundary problems of the second and fourth orders with continuous solutions (an exact parallel with oscilation theory of ordinary differential equations is constructed).

Nonlinear sixth order models with nonsmooth solutions and monoton nonlinearity

The sixth-order nonlinear spectral problem with nonsmooth solutions is studied. It is proved that the set of non-negative values for which the nonlinear spectral problem has at least one non-trivial non-negative solution is nonempty and coincides with a certain interval. We use the pointwise approach proposed by Yu. V. Pokorny analyzing solutions to a boundary value problem. This approach shown to be effective in the study of the second-order problems. Based on the previously obtained estimates of the Green’s function of the boundary-value problem, it was possible to show that the operator inverting the studied nonlinear problem, representable as a superposition of completely continuous and continuous operators, acts from the cone of nonnegative continuous functions to a narrower set. The last fact allows us to prove the uniqueness of a solution of a nonlinear boundary value problem using the theory of spaces with a cone.

Statistical hypothesis testing in wavelet analysis: theoretical developments and applications to Indian rainfall

Abstract. Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity (e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arclength, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.

Gravity Field Model Determination Based on GOCE Satellite Point-Wise Accelerations Estimated from Onboard Carrier Phase Observations

GPS-based, satellite-to-satellite tracking observations have been extensively used to elaborate the long-scale features of the Earth’s gravity field from dedicated satellite gravity missions. We proposed compiling a satellite gravity field model from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite accelerations directly estimated from the onboard GPS data using the point-wise acceleration approach, known as the carrier phase differentiation method. First, we composed the phase accelerations from the onboard carrier phase observations based on the sixth-order seven-point differentiator, which can eliminate the carrier phase ambiguity for Low Earth Orbiter (LEO). Next, the three-dimensional (3D) accelerations of the GOCE satellite were estimated from the derived phase accelerations as well as GPS satellite ephemeris and precise clock products. Finally, a global gravity field model up to the degree and order (d/o) 130 was compiled from the 71 days and nearly 2.5 years of 3D satellite accelerations. We also recovered three gravity field models up to d/o 130 from the accelerations derived by differentiating the kinematic orbits of European Space Agency (ESA), Graz, and School of Geodesy and Geomatics (SGG), which was the orbit differentiation method. We analyzed the accuracies of the derived accelerations and the recovered gravity field models based on the carrier phase differentiation method and orbit differentiation method in time, frequency, and spatial domain. The results showed that the carrier phase derived acceleration observations had better accuracy than those derived from kinematic orbits. The accuracy of the recovered gravity field model based on the carrier phase differentiation method using 2.5 years observations was higher than that of the orbit differentiation solutions for degrees greater than 70, and worse than Graz-orbit solution for degrees less than 70. The cumulative geoid height errors of carrier phase, ESA-orbit, and Graz-orbit solutions up to degree and order 130 were 17.70cm, 21.43 cm, and 22.11 cm, respectively.

Pointwise SAR image change detection using stereo-graph cuts with spatio-temporal information

ABSTRACTIn this letter, a pointwise approach using stereo-graph cuts (SGC) with spatio-temporal information is proposed for synthetic aperture radar (SAR) image change detection. The SGC is based on stereo-graph, which is designed to connect the local maximum pixels on two SAR images and can be used to capture the spatio-temporal information. With the support of stereo-graph, a novel SGC energy function is presented to quantify the spatio-temporal information and implicitly measure the difference information between the SAR images. Therefore, the change detection results can be obtained by minimizing the energy function with graph cuts technology. Experimental results on real SAR datasets confirm the validity of the proposed approach in which SGC and spatio-temporal information offer great contributions on improving the robustness and accuracy of detection.

Piecewise supervised deep hashing for image retrieval

In this paper, we propose a novel hash code generation method based on convolutional neural network (CNN), called the piecewise supervised deep hashing (PSDH) method to directly use a latent layer data and the output layer result of the classification network to generate a two-segment hash code for every input image. The first part of the hash code is the class information hash code, and the second part is the feature message hash code. The method we proposed is a point-wise approach and it is easy to implement and works very well for image retrieval. In particular, it performs excellently in the search of pictures with similar features. The more similar the images are in terms of color and geometric information and so on, the better it will rank above the search results. Compared with the hashing method proposed so far, we keep the whole hashing code search method, and put forward a piecewise hashing code search method. Experiments on three public datasets demonstrate the superior performance of PSDH over several state-of-art methods.

Pointwise SAR image change detection based on stereograph model with multiple-span neighbourhood information

ABSTRACTIn this article, a novel pointwise approach is proposed for change detection in bi-temporal synthetic aperture radar (SAR) images using stereograph model. Due to the fact that SAR image suffers from the speckle noise, a pointwise approach based on a set of characteristic points only, not on the whole pixels, seems to be more efficient. Moreover, the correlations of neighbourhood points which have different locations in bi-temporal SAR images should be studied to repress the speckle in change detection. Therefore, the stereograph model, which extends the graph model to three-dimensional space, is designed to connect the local maximum pixels on bi-temporal SAR images and can be used to capture the multiple-span neighbourhood information from the edges. Furthermore, a specialized change measure function is presented to quantify the neighbourhood information from stereograph model, and thus, a novel nondense difference image (NDI) is generated. Finally, a traditional classification method is used to analyse the NDI into changed class and unchanged class. Experiments on real SAR images show that the proposed NDI can improve separability between changed and unchanged areas, and the final results possess high accuracy and strong noise immunity for change detection tasks with noise-contaminated SAR images.

A Pointwise Approach to Dose-Response Meta-Analysis of Aggregated Data

In a two-stage dose-response meta-analysis a common functional relationship is applied to each study and an overall curve is obtained by combining study-specific dose-response coefficients. Possible limitations are: 1) a common dose-response model may have a poor fit in some of the studies; 2) combining dose-response coefficients discard information about study-specific exposure range. A pointwise approach for meta-analysis may overcome those limitations by combining predicted relative risks for a fine grid of exposure values based on potentially different dose-response models.We described how to flexibly model the dose-response association in a single study using fractional polynomials and spline, and how to present the combined results from study-specific analyses.The strategy is illustrated using aggregated data derived from the Surveillance, Epidemiology, and End Results program, with results compared to the corresponding analysis based on individual data.Another example on milk consumption and all-cause mortality is used to show the advantages of the pointwise approach regarding flexibility in the dose-response analyses, limitations of extrapolations, and informativeness in presenting pooled results.Application of the proposed strategy may improve dose-response meta-analysis of observational studies in case of particularly heterogeneous exposure distributions.

A pointwise approach to rigidity of almost graphical self-shrinking solutions of mean curvature flows

We prove rigidity of any properly immersed noncompact Lagrangian shrinker with single valued Lagrangian angle for Lagrangian mean curvature flows. Our pointwise approach also provides an elementary proof to the known rigidity results for graphical and almost graphical shrinkers of mean curvature flows.