Interpolation Of Sequences Research Articles

Kriging based sequence interpolation and probability distribution correction for gaussian wind field data reconstruction

Data reconstruction is an important research topic for missing data recovery and data supplement. Spatial interpolation is often used for data reconstruction. The interpolation for time series is usually conducted at each time point by common methods, which is sometimes inefficient. Additionally, statistical characteristics recovering may not be taken into account together during interpolation, which affects the utilization of data in structural design and safety assessment. In this paper, supposing that the data of a potential observation point are completely missing (no historical observation information at all), Kriging based Sequence Interpolation (KSI) combined with probability distribution correction is proposed for data reconstruction. KSI is proposed for two purposes. First, the primary interpolation results can be obtained by KSI, namely global interpolation once. Second, the Probability Density Function (PDF) of missing points can be reconstructed by KSI and subsequently provide a reference to correct the primary interpolation results. The proposed method is verified by both the simulated and field monitoring data, and the results show that the calculation efficiency is greatly improved compared with common methods. The fusion of data reconstruction and PDF reconstruction is novel and the effectiveness is verified via the structural dynamic response analysis. The RMS of structural displacement responses induced by the reconstructed wind load is almost coincide with that by the actual wind load.

Interpolation of Point Sequences with Extremum of Curvature by Log-aesthetic Curves with G2 continuity

Interpolation of Point Sequences with Extremum of Curvature by Log-aesthetic Curves with G2 continuity

Volumetric interpolation of tomographic sequences for accurate 3D reconstruction of anatomical parts

Background and objective:Tomographic sequences of biomedical images are commonly used to achieve a three-dimensional visualization of the human anatomy. In some cases, the number of images contained in the sequence is limited, e.g., in low-dose computed tomography acquired on neonatal patients, resulting in a coarse and inaccurate 3D reconstruction.Methods:In this paper, volumetric image interpolation methods, devised to increase the axial resolution of tomographic sequences and achieve a refined 3D reconstruction, are proposed and compared. The techniques taken into consideration are based on motion-compensated frame-interpolation concepts, which have been developed for video applications, mainly frame-rate conversion.Results: The performance of the proposed methods is quantitatively assessed by using sequences with a simulated low axial resolution obtained from the decimation of standard high-resolution computed tomography sequences. Real data with an actual low axial resolution have been used as well for a qualitative evaluation of the proposed methods.Conclusions:The experimental results demonstrate that the proposed methods enable an effective slice interpolation and that the achievable 3D models clearly benefit from the increased axial resolution.

Move blocked model predictive control with guaranteed stability and improved optimality using linear interpolation of base sequences

To mitigate the online computational load of model predictive control, move blocking, which parameterises either the input sequence or offset from the base sequence by fixing the decision variables over arbitrary time intervals, is commonly used. However, existing move blocking schemes use a fixed base sequence only and do not fully exploit the valuable properties from various base sequences. Thus, we propose the interpolated solution-based move blocking strategy which parameterises the offset from the convex combination of two complementary base sequences – infinite-horizon linear quadratic regulator solution and shifted previous solution – and optimises the interpolation parameter as an additional decision variable in the optimal control problem. This allows the controller to exploit the valuable properties from both solutions by choosing the optimal interpolation parameter and blocked offset according to the current state online. The proposed approach efficiently improves the optimality performance whileguaranteeing the recursive feasibility and closed-loop stability.

CR-Morph: Controllable Rigid Morphing for 2D Animation

This paper presents a rigidity-preserving morphing technique that blends a pair of 2D shapes in a controllable manner. The morphing is controllable in two aspects: 1) motion dynamics in the interpolation sequences can be effectively enhanced through an intuitive skeleton control and 2) not only the boundaries but also the interior features of the source and target shapes are precisely aligned during the morphing. We introduce a new compatible triangulation algorithm to decompose the source and target shapes into isomorphic triangles. Moreover, a robust and motion-controllable rigidity-preserving transformation scheme is proposed to blend the compatible triangulations, ultimately leading to a morphing sequence which is appearance-preserving and with the desired motion dynamics. Our approach constitutes a powerful and easy-to-use morphing tool for two-dimensional animation. We demonstrate its versatility, effectiveness and visual accuracy through a variety of examples and comparisons to prior work.

High-resolution lung MRI with Ultrashort-TE: 1.5 or 3 Tesla?

PurposeTo assess the influence of magnetic field strength and additionally of acquisition and reconstruction parameters on the quality of high-resolution lung MRI, using a prototype Ultrashort-TE (UTE) sequence. Materials and methodsThis prospective study received ethical approval and all participants provided written informed consent. From January to February 2018, images were obtained in 10 healthy volunteers at 1.5 T and 3 T with a prototypical free-breathing UTE spiral 3D-GRE sequence with volumetric interpolation (VIBE) sequence and near-millimeter resolution. Five sequences were acquired to assess the effects of magnetic field strength (1.5 vs 3 T), voxel resolution (1.2 vs 1.0mm3), number of spiral interleaves (464 vs 264) and iterative reconstruction (iterative self-consistent parallel imaging reconstruction [SPIRiT] versus Non-Uniform Fourier Transform [NUFFT]) on image quality. Image quality was assessed by two independent observers. They evaluated the proportion of detected airways from the trachea down to the subsegmental level and placed ROI in the lung parenchyma, airways and vessels to calculate signal-to noise (SNR) and contrast-to-noise (CNR) ratios. Continuous variables were expressed as mean ± standard deviation and were compared by t-test. ResultsNearly complete visualization of the segmental bronchi (94 ± 12 to 99 ± 3%) was obtained with all sequences. Acquisition at 3 T (p < 0.001), use of a fewer spiral interleaves (p < 0.001) and NUFFT reconstruction (p < 0.001) all resulted in a significantly lower visibility of the subsegmental bronchi, while a smaller voxel size improved their visibility (p = 0.001). SNR and CNR were significantly lower at 3 T (140.2 ± 19.9 vs 190.2 ± 34.8, p < 0.001; and 5.7 ± 2.4vs 10.8 ± 2.8, p < 0.001, respectively). ConclusionsUsing equivalent acquisition and reconstruction parameters, image quality was lower at 3 T than at 1.5 T with decreased visibility of the subsegmental bronchi and lower SNR and CNR values.

Master of Puppets: An Animation-by-Demonstration Computer Puppetry Authoring Framework

This paper presents Master of Puppets (MOP), an animation-by-demonstration framework that allows users to control the motion of virtual characters (puppets) in real time. In the first step, the user is asked to perform the necessary actions that correspond to the character’s motions. The user’s actions are recorded, and a hidden Markov model is used to learn the temporal profile of the actions. During the runtime of the framework, the user controls the motions of the virtual character based on the specified activities. The advantage of the MOP framework is that it recognizes and follows the progress of the user’s actions in real time. Based on the forward algorithm, the method predicts the evolution of the user’s actions, which corresponds to the evolution of the character’s motion. This method treats characters as puppets that can perform only one motion at a time. This means that combinations of motion segments (motion synthesis), as well as the interpolation of individual motion sequences, are not provided as functionalities. By implementing the framework and presenting several computer puppetry scenarios, its efficiency and flexibility in animating virtual characters is demonstrated.

Topology Optimization of Multiple Materials Compliant Mechanisms Based on Sequence Interpolation Model and Multigrid Method

Topology Optimization of Multiple Materials Compliant Mechanisms Based on Sequence Interpolation Model and Multigrid Method

Symmetric contours and convergent interpolation

The essence of Stahl–Gonchar–Rakhmanov theory of symmetric contours as applied to the multipoint Padé approximants is the fact that given a germ of an algebraic function and a sequence of rational interpolants with free poles of the germ, if there exists a contour that is “symmetric” with respect to the interpolation scheme, does not separate the plane, and in the complement of which the germ has a single-valued continuation with non-identically zero jump across the contour, then the interpolants converge to that continuation in logarithmic capacity in the complement of the contour. The existence of such a contour is not guaranteed. In this work we do construct a class of pairs interpolation scheme/symmetric contour with the help of hyperelliptic Riemann surfaces (following the ideas of Nuttall and Singh, 1977; Baratchart and Yattselev, 2009). We consider rational interpolants with free poles of Cauchy transforms of non-vanishing complex densities on such contours under mild smoothness assumptions on the density. We utilize ∂̄-extension of the Riemann–Hilbert technique to obtain formulae of strong asymptotics for the error of interpolation.

Building 3D subsurface models conforming to seismic structural and stratigraphic features

Subsurface modeling from seismic and borehole data is important for reservoir prediction, geophysical exploration, and production. A reasonable model should honor borehole rock properties and conform to seismic structural and stratigraphic features. Such a subsurface model can be difficult to build in cases complicated by faults and unconformities. Automatic and semiautomatic methods have been proposed to build subsurface models from seismic and borehole data; however, seismic structural and stratigraphic features and borehole measurements are not fully used in most methods. I have developed a workflow to fully use seismic and borehole data to build subsurface models that honor borehole measurements and conform to seismic horizons, faults, unconformities, and stratigraphic features such as channels. In this workflow, I first automatically remove the faulting and folding in seismic and borehole data and map them into an unfaulted and flattened space, in which seismic reflectors and borehole measurements corresponding to the same geologic layers are horizontally aligned. I then build a subsurface model in this unfaulted and flattened space by computing a sequence of 2D horizontal interpolations of borehole data. Each horizontal interpolation is guided by the stratigraphic features apparent in the corresponding horizontal seismic slice, so that the interpolant conforms to the seismic stratigraphic features. I finally map the interpolated model back into the input space and obtain a subsurface model that honors the seismic and borehole data. I demonstrate the proposed workflow using synthetic and real examples complicated by faults and unconformities.

Interpolation of stationary sequences observed with a noise

Interpolation of stationary sequences observed with a noise

Context-Aware Computer Aided Inbetweening.

This paper presents a context-aware computer aided inbetweening (CACAI) technique that interpolates planar strokes to generate inbetween frames from a given set of key frames. The inbetweening is context-aware in the sense that not only the stroke's shape but also the context (i.e., the neighborhood of a stroke) in which a stroke appears are taken into account for the stroke correspondence and interpolation. Given a pair of successive key frames, the CACAI automatically constructs the stroke correspondence between them by exploiting the context coherence between the corresponding strokes. Meanwhile, the construction algorithm is able to incorporate the user's interaction with ease and allows the user more effective control over the correspondence process than existing stroke matching techniques. With a one-to-one stroke correspondence, the CACAI interpolates the shape and context between the corresponding strokes for the generation of intermediate frames. In the interpolation sequence, both the shape of individual strokes and the spatial layout between them are well retained such that the feature characteristics and visual appearance of the objects in the key frames can be fully preserved even when complex motions are involved in these objects. We have developed a prototype system to demonstrate the ease of use and effectiveness of the CACAI.

An algorithm for the discretization of an ideal projector

Ideal interpolation is a generalization of the univariate Hermite interpolation. It is well known that every univariate Hermite interpolant is a pointwise limit of some Lagrange interpolants. However, a counterexample provided by Shekhtman Boris shows that, for more than two variables, there exist ideal interpolants that are not the limit of any Lagrange interpolants. So it is natural to consider: Given an ideal interpolant, how to find a sequence of Lagrange interpolants (if any) that converge to it. The authors call this problem the discretization for ideal interpolation. This paper presents an algorithm to solve the discretization problem. If the algorithm returns “True”, the authors get a set of pairwise distinct points such that the corresponding Lagrange interpolants converge to the given ideal interpolant.

Minimax interpolation of sequences with stationary increments and cointegrated sequences

We consider the problem of optimal estimation of the linear functional $A_{N}\xi ={\sum _{k=0}^{N}}a(k)\xi (k)$ depending on the unknown values of a stochastic sequence $\xi (m)$ with stationary increments from observations of the sequence $\xi (m)+\eta (m)$ at points of the set $\mathbb{Z}\setminus \{0,1,2,\dots ,N\}$, where $\eta (m)$ is a stationary sequence uncorrelated with $\xi (m)$. We propose formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functional in the case of spectral certainty, where spectral densities of the sequences are exactly known. We also consider the problem for a class of cointegrated sequences. We propose relations that determine the least favorable spectral densities and the minimax spectral characteristics in the case of spectral uncertainty, where spectral densities are not exactly known while a set of admissible spectral densities is specified.

Topological Indices and Interpolation of Sequences

In this paper, some topological indices of benzenoid graphs and mathematical graphs are computed, using the interpolation of sequences.

Study of blocking effect elimination methods by means of intraframe video sequence interpolation

The paper deals with image interpolation methods and their applicability to eliminate some of the artifacts related to both the dynamic properties of objects in video sequences and algorithms used in the order of encoding steps. The main drawback of existing methods is the high computational complexity, unacceptable in video processing. Interpolation of signal samples for blocking - effect elimination at the output of the convertion encoding is proposed as a part of the study. It was necessary to develop methods for improvement of compression ratio and quality of the reconstructed video data by blocking effect elimination on the borders of the segments by intraframe interpolating of video sequence segments. The main point of developed methods is an adaptive recursive algorithm application with adaptive-sized interpolation kernel both with and without the brightness gradient consideration at the boundaries of objects and video sequence blocks. Within theoretical part of the research, methods of information theory (RD-theory and data redundancy elimination), methods of pattern recognition and digital signal processing, as well as methods of probability theory are used. Within experimental part of the research, software implementation of compression algorithms with subsequent comparison of the implemented algorithms with the existing ones was carried out. Proposed methods were compared with the simple averaging algorithm and the adaptive algorithm of central counting interpolation. The advantage of the algorithm based on the adaptive kernel size selection interpolation is in compression ratio increasing by 30%, and the advantage of the modified algorithm based on the adaptive interpolation kernel size selection is in the compression ratio increasing by 35% in comparison with existing algorithms, interpolation and quality of the reconstructed video sequence improving by 3% compared to the one compressed without interpolation. The findings will be widely used in video processing tasks, various codecs of video compression and streaming systems.

A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic dimension cause an explosion of the computational effort. We propose and analyze a multilevel version of the stochastic collocation method that, as is the case for multilevel Monte Carlo (MLMC) methods, uses hierarchies of spatial approximations to reduce the overall computational complexity. In addition, our proposed approach utilizes, for approximation in stochastic space, a sequence of multidimensional interpolants of increasing fidelity which can then be used for approximating statistics of the solution as well as for building high-order surrogates featuring faster convergence rates. A rigorous convergence and computational cost analysis of the new multilevel stochastic collocation method is provided in the case of elliptic equations, demonstrating its advantages compared to standard single-level stochastic collocation approximations as well as MLMC methods. Numerical results are provided that illustrate the theory and the effectiveness of the new multilevel method.

Impact and management of physiological calibration in spectral analysis of blood pressure variability.

Physiological calibration (Physiocal) improves the quality of continuous blood pressure (BP) signal from finger. However, the effects of Physiocal on spectral characteristics of systolic BP (SBP) variability are not well-known. We tested the hypothesis that the use of Physiocal may alter the results on SBP variability when compared with BP recording without Physiocal. Continuous BP was recorded simultaneously from fingers of both arms during 10-min standing by two Nexfin devices, one with (ON) and the other without (OFF) Physiocal (n = 19). Missing SBP values in ON signal were linearly interpolated over Physiocal sequences (ONinter). The OFF signal was analyzed without any corrections (OFFreference) and after linear interpolation of corresponding sequences when Physiocal appeared in the ON signal (OFFinter). Mean low frequency power of SBP oscillations (LFSBP, 0.04–0.15 Hz) did not differ between the OFFreference, OFFinter, and ONinter. However, LFSBP deviated more from OFFreference when analyzed from ONinter compared with the analysis from OFFinter [median (interquartile range): 14.7 (4.6–38.6) vs. 0.9 (0.5–1.8) %, p < 0.05]. In conclusion, the use of Physiocal had a significant effect on the spectral SBP variability that overwhelms the impact of linear interpolation of short data sequences. Therefore, caution is needed when comparing SBP variability between BP datasets acquired with and without Physiocal.

On recursion-free Horn clauses and Craig interpolation

One of the main challenges in software verification is efficient and precise analysis of programs with procedures and loops. Interpolation methods remain among the most promising techniques for such verification. To accommodate the demands of various programming language features, over the past years several extended forms of interpolation have been introduced. We give a precise ontology of such extended interpolation methods, and investigate the relationship between interpolation and fragments of constrained recursion-free Horn clauses. We also introduce a new notion of interpolation, disjunctive interpolation, which solves a more general class of problems in one step compared to previous notions of interpolants, such as tree interpolants or inductive sequences of interpolants. We present algorithms and complexity for construction of interpolants, as well as the corresponding decision problems for recursion-free Horn fragments. Finally, we give an extensive empirical evaluation using a solver for (recursive) Horn problems, in particular comparing the performance of tree interpolation and disjunctive interpolation for constraints modelling software verification tasks.

Convergence of Wachspress coordinates: from polygons to curved domains

Given a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al., we show that the corresponding sequences of Wachspress interpolants and mappings converge as 𝓞(h 2) for a sampling step size h of the boundary curve of the domain as h → 0. Several examples are shown to numerically validate the results and to visualise the behaviour of discrete interpolants and mappings as they converge to their smooth counterparts. Empirically, the same convergence order is observed also for mean value coordinates. Moreover, our numerical tests suggest that the convergence of interpolants and mappings is uniform both in the Wachspress and mean value cases.