A disposition of interpolation techniques

A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated values, 3) incorporation of ancillary information, and 4) incorporation of process knowledge. The described methods include inverse distance weighting, nearest neighbour methods, geostatistical interpolation methods, Kalman filter methods, Bayesian Maximum Entropy methods, etc. The applicability of methods in aggregation (upscaling) and disaggregation (downscaling) is discussed. Software for interpolation is described. The application of interpolation techniques is illustrated in two case studies: temporal interpolation of indicators for ecological water quality, and spatio-temporal interpolation and aggregation of pesticide concentrations in Dutch surface waters. A valuable next step will be to construct a decision tree or decision support system, that guides the environmental scientist to easy-to-use software implementations that are appropriate to solve their interpolation problem. Validation studies are needed to assess the quality of interpolated values, and the quality of information on uncertainty provided by the interpolation method

Temporal Interpolation via Motion Field Prediction

Navigated 2D multi-slice dynamic Magnetic Resonance (MR) imaging enables high contrast 4D MR imaging during free breathing and provides in-vivo observations for treatment planning and guidance. Navigator slices are vital for retrospective stacking of 2D data slices in this method. However, they also prolong the acquisition sessions. Temporal interpolation of navigator slices an be used to reduce the number of navigator acquisitions without degrading specificity in stacking. In this work, we propose a convolutional neural network (CNN) based method for temporal interpolation via motion field prediction. The proposed formulation incorporates the prior knowledge that a motion field underlies changes in the image intensities over time. Previous approaches that interpolate directly in the intensity space are prone to produce blurry images or even remove structures in the images. Our method avoids such problems and faithfully preserves the information in the image. Further, an important advantage of our formulation is that it provides an unsupervised estimation of bi-directional motion fields. We show that these motion fields can be used to halve the number of registrations required during 4D reconstruction, thus substantially reducing the reconstruction time.Comment: Submitted to 1st Conference on Medical Imaging with Deep Learning (MIDL 2018), Amsterdam, The Netherland

Enhancing spatial accuracy of mobile phone data using multi-temporal dasymetric interpolation

Novel digital data sources allow us to attain enhanced knowledge about locations and mobilities of people in space and time. Already a fast-growing body of literature demonstrates the applicability and feasibility of mobile phone-based data in social sciences for considering mobile devices as proxies for people. However, the implementation of such data imposes many theoretical and methodological challenges. One major issue is the uneven spatial resolution of mobile phone data due to the spatial configuration of mobile network base stations and its spatial interpolation. To date, different interpolation techniques are applied to transform mobile phone data into other spatial divisions. However, these do not consider the temporality and societal context that shapes the human presence and mobility in space and time. The paper aims, first, to contribute to mobile phone-based research by addressing the need to give more attention to the spatial interpolation of given data, and further by proposing a dasymetric interpolation approach to enhance the spatial accuracy of mobile phone data. Second, it contributes to population modelling research by combining spatial, temporal and volumetric dasymetric mapping and integrating it with mobile phone data. In doing so, the paper presents a generic conceptual framework of a multi-temporal function-based dasymetric (MFD) interpolation method for mobile phone data. Empirical results demonstrate how the proposed interpolation method can improve the spatial accuracy of both night-time and daytime population distributions derived from different mobile phone data sets by taking advantage of ancillary data sources. The proposed interpolation method can be applied for both location- and person-based research, and is a fruitful starting point for improving the spatial interpolation methods for mobile phone data. We share the implementation of our method in GitHub as open access Python code.Peer reviewe

A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects

Temporal characteristics are prominently evident in a substantial volume of knowledge, which underscores the pivotal role of Temporal Knowledge Graphs (TKGs) in both academia and industry. However, TKGs often suffer from incompleteness for three main reasons: the continuous emergence of new knowledge, the weakness of the algorithm for extracting structured information from unstructured data, and the lack of information in the source dataset. Thus, the task of Temporal Knowledge Graph Completion (TKGC) has attracted increasing attention, aiming to predict missing items based on the available information. In this paper, we provide a comprehensive review of TKGC methods and their details. Specifically, this paper mainly consists of three components, namely, 1)Background, which covers the preliminaries of TKGC methods, loss functions required for training, as well as the dataset and evaluation protocol; 2)Interpolation, that estimates and predicts the missing elements or set of elements through the relevant available information. It further categorizes related TKGC methods based on how to process temporal information; 3)Extrapolation, which typically focuses on continuous TKGs and predicts future events, and then classifies all extrapolation methods based on the algorithms they utilize. We further pinpoint the challenges and discuss future research directions of TKGC

Interpolating fields of carbon monoxide data using a hybrid statistical-physical model

Atmospheric Carbon Monoxide (CO) provides a window on the chemistry of the atmosphere since it is one of few chemical constituents that can be remotely sensed, and it can be used to determine budgets of other greenhouse gases such as ozone and OH radicals. Remote sensing platforms in geostationary Earth orbit will soon provide regional observations of CO at several vertical layers with high spatial and temporal resolution. However, cloudy locations cannot be observed and estimates of the complete CO concentration fields have to be estimated based on the cloud-free observations. The current state-of-the-art solution of this interpolation problem is to combine cloud-free observations with prior information, computed by a deterministic physical model, which might introduce uncertainties that do not derive from data. While sharing features with the physical model, this paper suggests a Bayesian hierarchical model to estimate the complete CO concentration fields. The paper also provides a direct comparison to state-of-the-art methods. To our knowledge, such a model and comparison have not been considered before.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS168 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The physical mandate for belief-goal psychology

This article describes a heuristic argument for understanding certain physical systems in terms of properties that resemble the beliefs and goals of folk psychology. The argument rests on very simple assumptions. The core of the argument is that predictions about certain events can legitimately be based on assumptions about later events, resembling Aristotelian ‘final causation’; however, more nuanced causal entities (resembling fallible beliefs) must be introduced into these types of explanation in order for them to remain consistent with a causally local Universe

Modeling and interpolation of the ambient magnetic field by Gaussian processes

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.Comment: 17 pages, 12 figures, to appear in IEEE Transactions on Robotic

Real-time modelling and interpolation of spatio-temporal marine pollution

Due to the complexity of the interactions involved in various dynamic systems, known physical, biological or chemical laws cannot adequately describe the dynamics behind these processes. The study of these systems thus depends on measurements often taken at various discrete spatial locations through time by noisy sensors. For this reason, scientists often necessitate interpolative, visualisation and analytical tools to deal with the large volumes of data common to these systems. The starting point of this study is the seminal research by C. Shannon on sampling and reconstruction theory and its various extensions. Based on recent work on the reconstruction of stochastic processes, this paper develops a novel real-time estimation method for non- stationary stochastic spatio-temporal behaviour based on the Integro-Di erence Equation (IDE). This meth- odology is applied to collected marine pollution data from a Norwegian fjord. Comparison of the results obtained by the proposed method with interpolators from state-of-the-art Geographical Information System (GIS) packages will show, that signifi cantly superior results are obtained by including the temporal evolution in the spatial interpolations.peer-reviewe