Neural radiance fields (NeRFs) are a powerful tool for implicit scene representations, allowing for differentiable rendering and the ability to make predictions about previously unseen viewpoints. From a robotics perspective, there has been growing interest in object and scene-based localisation using NeRFs, with a number of recent works relying on sampling-based or Monte-Carlo localisation schemes. Unfortunately, these can be extremely computationally expensive, requiring multiple network forward passes to infer camera or object pose. To alleviate this, a variety of sampling strategies have been applied, many relying on keypoint recognition techniques from classical computer vision. This work conducts a systematic empirical comparison of these approaches and shows that in contrast to conventional feature matching approaches for geometry-based localisation, sampling-based localisation using NeRFs benefits significantly from stable features. Results show that rendering stable features can result in a tenfold reduction in the number of forward passes required, a significant speed improvement.
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Scale-free dynamics, formalized by selfsimilarity, provides a versatile paradigm massively and ubiquitously used to model temporal dynamics in real-world data. However, its practical use has mostly remained univariate so far. By contrast, modern applications often demand multivariate data analysis. Accordingly, models for multivariate selfsimilarity were recently proposed. Nevertheless, they have remained rarely used in practice because of a lack of available robust estimation procedures for the vector of selfsimilarity parameters. Building upon recent mathematical developments, the present work puts forth an efficient estimation procedure based on the theoretical study of the multiscale eigenstructure of the wavelet spectrum of multivariate selfsimilar processes. The estimation performance is studied theoretically in the asymptotic limits of large scale and sample sizes, and computationally for finite-size samples. As a practical outcome, a fully operational and documented multivariate signal processing estimation toolbox is made freely available and is ready for practical use on real-world data. Its potential benefits are illustrated in epileptic seizure prediction from multi-channel EEG data.
We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis: non--linearity and heteroscedasticity. The impact of heteroscedasticity on the precision of the estimators is well--known, however the conjunction of these two phenomena makes handling outliers more difficult. An iterative procedure to estimate the parameters of a heteroscedastic non--linear model is considered. The studied estimators combine weighted $MM-$regression estimators, to control the impact of high leverage points, and a robust method to estimate the parameters of the variance function.
Complex models are often used to understand interactions and drivers of human-induced and/or natural phenomena. It is worth identifying the input variables that drive the model output(s) in a given domain and/or govern specific model behaviors such as contextual indicators based on socio-environmental models. Using the theory of multivariate weighted distributions to characterize specific model behaviors, we propose new measures of association between inputs and such behaviors. Our measures rely on sensitivity functionals (SFs) and kernel methods, including variance-based sensitivity analysis. The proposed $\ell_1$-based kernel indices account for interactions among inputs, higher-order moments of SFs, and their upper bounds are somehow equivalent to the Morris-type screening measures, including dependent elementary effects. Empirical kernel-based indices are derived, including their statistical properties for the computational issues, and numerical results are provided.
Quadratic NURBS-based discretizations of the Galerkin method suffer from volumetric locking when applied to nearly-incompressible linear elasticity. Volumetric locking causes not only smaller displacements than expected, but also large-amplitude spurious oscillations of normal stresses. Continuous-assumed-strain (CAS) elements have been recently introduced to remove membrane locking in quadratic NURBS-based discretizations of linear plane curved Kirchhoff rods (Casquero et al., CMAME, 2022). In this work, we propose two generalizations of CAS elements (named CAS1 and CAS2 elements) to overcome volumetric locking in quadratic NURBS-based discretizations of nearly-incompressible linear elasticity. CAS1 elements linearly interpolate the strains at the knots in each direction for the term in the variational form involving the first Lam\'e parameter while CAS2 elements linearly interpolate the dilatational strains at the knots in each direction. For both element types, a displacement vector with C1 continuity across element boundaries results in assumed strains with C0 continuity across element boundaries. In addition, the implementation of the two locking treatments proposed in this work does not require any additional global or element matrix operations such as matrix inversions or matrix multiplications. The locking treatments are applied at the element level and the nonzero pattern of the global stiffness matrix is preserved. The numerical examples solved in this work show that CAS1 and CAS2 elements, using either two or three Gauss-Legrendre quadrature points per direction, are effective locking treatments since they not only result in more accurate displacements for coarse meshes, but also remove the spurious oscillations of normal stresses.
Purpose: To provide a simulation framework for routine neuroimaging test data, which allows for "stress testing" of deep segmentation networks against acquisition shifts that commonly occur in clinical practice for T2 weighted (T2w) fluid attenuated inversion recovery (FLAIR) Magnetic Resonance Imaging (MRI) protocols. Approach: The approach simulates "acquisition shift derivatives" of MR images based on MR signal equations. Experiments comprise the validation of the simulated images by real MR scans and example stress tests on state-of-the-art MS lesion segmentation networks to explore a generic model function to describe the F1 score in dependence of the contrast-affecting sequence parameters echo time (TE) and inversion time (TI). Results: The differences between real and simulated images range up to 19 % in gray and white matter for extreme parameter settings. For the segmentation networks under test the F1 score dependency on TE and TI can be well described by quadratic model functions (R^2 > 0.9). The coefficients of the model functions indicate that changes of TE have more influence on the model performance than TI. Conclusions: We show that these deviations are in the range of values as may be caused by erroneous or individual differences of relaxation times as described by literature. The coefficients of the F1 model function allow for quantitative comparison of the influences of TE and TI. Limitations arise mainly from tissues with the low baseline signal (like CSF) and when the protocol contains contrast-affecting measures that cannot be modelled due to missing information in the DICOM header.
Surface parameterization plays a fundamental role in many science and engineering problems. In particular, as genus-0 closed surfaces are topologically equivalent to a sphere, many spherical parameterization methods have been developed over the past few decades. However, in practice, mapping a genus-0 closed surface onto a sphere may result in a large distortion due to their geometric difference. In this work, we propose a new framework for computing ellipsoidal conformal and quasi-conformal parameterizations of genus-0 closed surfaces, in which the target parameter domain is an ellipsoid instead of a sphere. By combining simple conformal transformations with different types of quasi-conformal mappings, we can easily achieve a large variety of ellipsoidal parameterizations with their bijectivity guaranteed by quasi-conformal theory. Numerical experiments are presented to demonstrate the effectiveness of the proposed framework.
We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in measurement models without parametric assumptions such as linearity or Gaussianity. Moreover, we do not assume the number of hidden variables is known, and we show that at most one unknown intervention per hidden variable is needed. This extends a recent line of work on learning causal representations from observations and interventions. The proofs are constructive and introduce two new graphical concepts -- imaginary subsets and isolated edges -- that may be useful in their own right. As a matter of independent interest, the proofs also involve a novel characterization of the limits of edge orientations within the equivalence class of DAGs induced by unknown interventions. These are the first results to characterize the conditions under which causal representations are identifiable without making any parametric assumptions in a general setting with unknown interventions and without faithfulness.
Suppose we want to construct some structure on a bounded-degree graph, e.g., an almost maximum matching, and we want to decide about each edge depending only on its constant-radius neighborhood. We examine and compare the strengths of different extensions of these local algorithms. A common extension is to use preprocessing, which means that we can make some calculation about the whole graph, and each local decision can also depend on this calculation. In this paper, we show that preprocessing is needless: if a nearly optimal local algorithm uses preprocessing, then the same can be achieved by a local algorithm without preprocessing, but with a global randomization.
Stochastic filtering is a vibrant area of research in both control theory and statistics, with broad applications in many scientific fields. Despite its extensive historical development, there still lacks an effective method for joint parameter-state estimation in SDEs. The state-of-the-art particle filtering methods suffer from either sample degeneracy or information loss, with both issues stemming from the dynamics of the particles generated to represent system parameters. This paper provides a novel and effective approach for joint parameter-state estimation in SDEs via Rao-Blackwellization and modularization. Our method operates in two layers: the first layer estimates the system states using a bootstrap particle filter, and the second layer marginalizes out system parameters explicitly. This strategy circumvents the need to generate particles representing system parameters, thereby mitigating their associated problems of sample degeneracy and information loss. Moreover, our method employs a modularization approach when integrating out the parameters, which significantly reduces the computational complexity. All these designs ensure the superior performance of our method. Finally, a numerical example is presented to illustrate that our method outperforms existing approaches by a large margin.
Novel categories are commonly defined as those unobserved during training but present during testing. However, partially labelled training datasets can contain unlabelled training samples that belong to novel categories, meaning these can be present in training and testing. This research is the first to generalise between what we call observed-novel and unobserved-novel categories within a new learning policy called open-set learning with augmented category by exploiting unlabelled data or Open-LACU. After surveying existing learning policies, we introduce Open-LACU as a unified policy of positive and unlabelled learning, semi-supervised learning and open-set recognition. Subsequently, we develop the first Open-LACU model using an algorithmic training process of the relevant research fields. The proposed Open-LACU classifier achieves state-of-the-art and first-of-its-kind results.
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