Photometric stereo refers to the process to compute the 3D shape of an object using information on illumination and reflectance from several input images from the same point of view. The most often used reflectance model is the Lambertian reflectance, however this does not include specular highlights in input images. In this paper we consider the arising non-linear optimisation problem when employing Blinn-Phong reflectance for modeling specular effects. To this end we focus on the regularising Levenberg-Marquardt scheme. We show how to derive an explicit bound that gives information on the convergence reliability of the method depending on given data, and we show how to gain experimental evidence of numerical correctness of the iteration by making use of the Scherzer condition. The theoretical investigations that are at the heart of this paper are supplemented by some tests with real-world imagery.
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We develop scalable randomized kernel methods for jointly associating data from multiple sources and simultaneously predicting an outcome or classifying a unit into one of two or more classes. The proposed methods model nonlinear relationships in multiview data together with predicting a clinical outcome and are capable of identifying variables or groups of variables that best contribute to the relationships among the views. We use the idea that random Fourier bases can approximate shift-invariant kernel functions to construct nonlinear mappings of each view and we use these mappings and the outcome variable to learn view-independent low-dimensional representations. Through simulation studies, we show that the proposed methods outperform several other linear and nonlinear methods for multiview data integration. When the proposed methods were applied to gene expression, metabolomics, proteomics, and lipidomics data pertaining to COVID-19, we identified several molecular signatures forCOVID-19 status and severity. Results from our real data application and simulations with small sample sizes suggest that the proposed methods may be useful for small sample size problems. Availability: Our algorithms are implemented in Pytorch and interfaced in R and would be made available at: //github.com/lasandrall/RandMVLearn.
Adhesive joints are increasingly used in industry for a wide variety of applications because of their favorable characteristics such as high strength-to-weight ratio, design flexibility, limited stress concentrations, planar force transfer, good damage tolerance, and fatigue resistance. Finding the optimal process parameters for an adhesive bonding process is challenging: the optimization is inherently multi-objective (aiming to maximize break strength while minimizing cost), constrained (the process should not result in any visual damage to the materials, and stress tests should not result in failures that are adhesion-related), and uncertain (testing the same process parameters several times may lead to different break strengths). Real-life physical experiments in the lab are expensive to perform. Traditional evolutionary approaches (such as genetic algorithms) are then ill-suited to solve the problem, due to the prohibitive amount of experiments required for evaluation. Although Bayesian optimization-based algorithms are preferred to solve such expensive problems, few methods consider the optimization of more than one (noisy) objective and several constraints at the same time. In this research, we successfully applied specific machine learning techniques (Gaussian Process Regression) to emulate the objective and constraint functions based on a limited amount of experimental data. The techniques are embedded in a Bayesian optimization algorithm, which succeeds in detecting Pareto-optimal process settings in a highly efficient way (i.e., requiring a limited number of physical experiments).
To date, query performance prediction (QPP) in the context of content-based image retrieval remains a largely unexplored task, especially in the query-by-example scenario, where the query is an image. To boost the exploration of the QPP task in image retrieval, we propose the first benchmark for image query performance prediction (iQPP). First, we establish a set of four data sets (PASCAL VOC 2012, Caltech-101, ROxford5k and RParis6k) and estimate the ground-truth difficulty of each query as the average precision or the precision@k, using two state-of-the-art image retrieval models. Next, we propose and evaluate novel pre-retrieval and post-retrieval query performance predictors, comparing them with existing or adapted (from text to image) predictors. The empirical results show that most predictors do not generalize across evaluation scenarios. Our comprehensive experiments indicate that iQPP is a challenging benchmark, revealing an important research gap that needs to be addressed in future work. We release our code and data as open source at //github.com/Eduard6421/iQPP, to foster future research.
Accurate time series forecasting is critical for a wide range of problems with temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the performance of a single predictor can be highly variable due to shifts in the underlying data distribution. This paper proposes a new methodology for building robust ensembles of time series forecasting models. Our approach utilizes Adaptive Robust Optimization (ARO) to construct a linear regression ensemble in which the models' weights can adapt over time. We demonstrate the effectiveness of our method through a series of synthetic experiments and real-world applications, including air pollution management, energy consumption forecasting, and tropical cyclone intensity forecasting. Our results show that our adaptive ensembles outperform the best ensemble member in hindsight by 16-26% in root mean square error and 14-28% in conditional value at risk and improve over competitive ensemble techniques.
Multi-camera 3D object detection for autonomous driving is a challenging problem that has garnered notable attention from both academia and industry. An obstacle encountered in vision-based techniques involves the precise extraction of geometry-conscious features from RGB images. Recent approaches have utilized geometric-aware image backbones pretrained on depth-relevant tasks to acquire spatial information. However, these approaches overlook the critical aspect of view transformation, resulting in inadequate performance due to the misalignment of spatial knowledge between the image backbone and view transformation. To address this issue, we propose a novel geometric-aware pretraining framework called GAPretrain. Our approach incorporates spatial and structural cues to camera networks by employing the geometric-rich modality as guidance during the pretraining phase. The transference of modal-specific attributes across different modalities is non-trivial, but we bridge this gap by using a unified bird's-eye-view (BEV) representation and structural hints derived from LiDAR point clouds to facilitate the pretraining process. GAPretrain serves as a plug-and-play solution that can be flexibly applied to multiple state-of-the-art detectors. Our experiments demonstrate the effectiveness and generalization ability of the proposed method. We achieve 46.2 mAP and 55.5 NDS on the nuScenes val set using the BEVFormer method, with a gain of 2.7 and 2.1 points, respectively. We also conduct experiments on various image backbones and view transformations to validate the efficacy of our approach. Code will be released at //github.com/OpenDriveLab/BEVPerception-Survey-Recipe.
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud of data points is obtained by sampling from a possibly uncountable superposition of Gaussian distributions, whose variance has a generic probability density $\varrho$. Our analysis covers therefore a large family of data distributions, including the case of power-law-tailed distributions with no covariance. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation, and the dependence of the separability transition on the distribution scale parameters.
The propagation of charged particles through a scattering medium in the presence of a magnetic field can be described by a Fokker-Planck equation with Lorentz force. This model is studied both, from a theoretical and a numerical point of view. A particular trace estimate is derived for the relevant function spaces to clarify the meaning of boundary values. Existence of a weak solution is then proven by the Rothe method. In the second step of our investigations, a fully practicable discretization scheme is proposed based on implicit time-stepping through the energy levels and a spherical-harmonics finite-element discretization with respect to the remaining variables. A full error analysis of the resulting scheme is given, and numerical results are presented to illustrate the theoretical results and the performance of the proposed method.
Dynamic Movement Primitives (DMP) have found remarkable applicability and success in various robotic tasks, which can be mainly attributed to their generalization, modulation and robustness properties. Nevertheless, the spatial generalization of DMP can be problematic in some cases, leading to excessive or unnatural spatial scaling. Moreover, incorporating intermediate points (via-points) to adjust the DMP trajectory, is not adequately addressed. In this work we propose an improved online spatial generalization, that remedies the shortcomings of the classical DMP generalization, and moreover allows the incorporation of dynamic via-points. This is achieved by designing an online adaptation scheme for the DMP weights which is proved to minimize the distance from the demonstrated acceleration profile in order to retain the shape of the demonstration, subject to dynamic via-point and initial/final state constraints. Extensive comparative simulations with the classical and other DMP variants are conducted, while experimental results validate the applicability and efficacy of the proposed method.
Model-free data-driven computational mechanics, first proposed by Kirchdoerfer and Ortiz, replaces phenomenological models with numerical simulations based on sample data sets in strain-stress space. Recent literature extended the approach to inelastic problems using structured data sets, tangent space information, and transition rules. From an application perspective, the coverage of qualified data states and calculating the corresponding tangent space is crucial. In this respect, material symmetry significantly helps to reduce the amount of necessary data. This study applies the data-driven paradigm to elasto-plasticity with isotropic hardening. We formulate our approach employing Haigh-Westergaard coordinates, providing information on the underlying material yield surface. Based on this, we use a combined tension-torsion test to cover the knowledge of the yield surface and a single tensile test to calculate the corresponding tangent space. The resulting data-driven method minimizes the distance over the Haigh-Westergaard space augmented with directions in the tangent space subject to compatibility and equilibrium constraints.
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently used for the approximation of statistical moments, is combined with a suitable deterministic discretisation method in physical space and time. Under the assumption that numerical densities and temperatures are bounded in probability, we prove the convergence of random finite volume solutions to a statistical strong solution by applying genuine stochastic compactness arguments. Further, we show the convergence and error estimates for the Monte Carlo estimators of the expectation and deviation. We present several numerical results to illustrate the theoretical results.
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