Abstract: Video frame interpolation typically involves two steps: motion estimation and pixel synthesis. Such a two-step approach heavily depends on the quality of motion estimation. This paper presents a robust video frame interpolation method that combines these two steps into a single process. Specifically, our method considers pixel synthesis for the interpolated frame as local convolution over two input frames. The convolution kernel captures both the local motion between the input frames and the coefficients for pixel synthesis. Our method employs a deep fully convolutional neural network to estimate a spatially-adaptive convolution kernel for each pixel. This deep neural network can be directly trained end to end using widely available video data without any difficult-to-obtain ground-truth data like optical flow. Our experiments show that the formulation of video interpolation as a single convolution process allows our method to gracefully handle challenges like occlusion, blur, and abrupt brightness change and enables high-quality video frame interpolation.

Abstract: Video frame interpolation typically involves two steps: motion estimation and pixel synthesis. Such a two-step approach heavily depends on the quality of motion estimation. This paper presents a robust video frame interpolation method that combines these two steps into a single process. Specifically, our method considers pixel synthesis for the interpolated frame as local convolution over two input frames. The convolution kernel captures both the local motion between the input frames and the coefficients for pixel synthesis. Our method employs a deep fully convolutional neural network to estimate a spatially-adaptive convolution kernel for each pixel. This deep neural network can be directly trained end to end using widely available video data without any difficult-to-obtain ground-truth data like optical flow. Our experiments show that the formulation of video interpolation as a single convolution process allows our method to gracefully handle challenges like occlusion, blur, and abrupt brightness change and enables high-quality video frame interpolation.

Abstract: In this paper an ordered multi-material SIMP (solid isotropic material with penalization) interpolation is proposed to solve multi-material topology optimization problems without introducing any new variables. Power functions with scaling and translation coefficients are introduced to interpolate the elastic modulus and the cost properties for multiple materials with respect to the normalized density variables. Besides a mass constraint, a cost constraint is also considered in compliance minimization problems. A heuristic updating scheme of the design variables is derived from the Kuhn-Tucker optimality condition (OC). Since the proposed method does not rely on additional variables to represent material selection, the computational cost is independent of the number of materials considered. The iteration scheme is designed to jump across the discontinuous point of interpolation derivatives to make stable transition from one material phase to another. Numerical examples are included to demonstrate the proposed method. Because of its conceptual simplicity, the proposed ordered multi-material SIMP interpolation can be easily embedded into any existing single material SIMP topology optimization codes.

Abstract: We propose Deep Feature Interpolation (DFI), a new data-driven baseline for automatic high-resolution image transformation. As the name suggests, DFI relies only on simple linear interpolation of deep convolutional features from pre-trained convnets. We show that despite its simplicity, DFI can perform high-level semantic transformations like make older/younger, make bespectacled, add smile, among others, surprisingly well–sometimes even matching or outperforming the state-of-the-art. This is particularly unexpected as DFI requires no specialized network architecture or even any deep network to be trained for these tasks. DFI therefore can be used as a new baseline to evaluate more complex algorithms and provides a practical answer to the question of which image transformation tasks are still challenging after the advent of deep learning.

Abstract: Pointwise GPS measurements of tropospheric zenith total delay can be interpolated to provide high resolution water vapor maps which may be used for correcting SAR images, for numeral weather prediction and for correcting Network Real-time Kinematic GPS observations. Several previous studies have addressed the importance of the elevation dependency of water vapor, but it is often a challenge to separate elevation-dependent tropospheric delays from turbulent components. In this paper, we present an iterative tropospheric decomposition interpolation model that decouples the elevation and turbulent tropospheric delay components. For a 150 km x 150 km California study region, we estimate real-time mode zenith total delays at 41 GPS stations over 1 year using the precise point positioning technique, and demonstrate that the decoupled interpolation model generates improved high resolution tropospheric delay maps compared with previous tropospheric turbulence and elevation dependent models. Cross validation of the GPS zenith total delays yields an RMS error of 4.6 mm with the decoupled interpolation model, compared with 8.4 mm with the previous model. On converting the GPS zenith wet delays to precipitable water vapor and interpolating to 1 km grid cells across the region, validations with the MODIS near-IR water vapor product show 1.7 mm RMS differences using the decoupled model, compared with 2.0 mm for the previous interpolation model. Such results are obtained without differencing the tropospheric delays or water vapor estimates in time or space, whilst the errors are similar over flat and mountainous terrain, as well as for both inland and coastal areas.

Abstract: A thorough review has been performed on interpolation methods to fill gaps in time-series, efficiency criteria, and uncertainty quantifications. On one hand, there are numerous available methods: interpolation, regression, autoregressive, machine learning methods, etc. On the other hand, there are many methods and criteria to estimate efficiencies of these methods, but uncertainties on the interpolated values are rarely calculated. Furthermore, while they are estimated according to standard methods, the prediction uncertainty is not taken into account: a discussion is thus presented on the uncertainty estimation of interpolated/extrapolated data. Finally, some suggestions for further research and a new method are proposed.

Abstract: The interpolation, prediction, and feature analysis of fine-gained air quality are three important topics in the area of urban air computing. The solutions to these topics can provide extremely useful information to support air pollution control, and consequently generate great societal and technical impacts. Most of the existing work solves the three problems separately by different models. In this paper, we propose a general and effective approach to solve the three problems in one model called the Deep Air Learning (DAL). The main idea of DAL lies in embedding feature selection and semi-supervised learning in different layers of the deep learning network. The proposed approach utilizes the information pertaining to the unlabeled spatio-temporal data to improve the performance of the interpolation and the prediction, and performs feature selection and association analysis to reveal the main relevant features to the variation of the air quality. We evaluate our approach with extensive experiments based on real data sources obtained in Beijing, China. Experiments show that DAL is superior to the peer models from the recent literature when solving the topics of interpolation, prediction, and feature analysis of fine-gained air quality.

Abstract: Given two consecutive frames, video interpolation aims at generating intermediate frame(s) to form both spatially and temporally coherent video sequences. While most existing methods focus on single-frame interpolation, we propose an end-to-end convolutional neural network for variable-length multi-frame video interpolation, where the motion interpretation and occlusion reasoning are jointly modeled. We start by computing bi-directional optical flow between the input images using a U-Net architecture. These flows are then linearly combined at each time step to approximate the intermediate bi-directional optical flows. These approximate flows, however, only work well in locally smooth regions and produce artifacts around motion boundaries. To address this shortcoming, we employ another U-Net to refine the approximated flow and also predict soft visibility maps. Finally, the two input images are warped and linearly fused to form each intermediate frame. By applying the visibility maps to the warped images before fusion, we exclude the contribution of occluded pixels to the interpolated intermediate frame to avoid artifacts. Since none of our learned network parameters are time-dependent, our approach is able to produce as many intermediate frames as needed. We use 1,132 video clips with 240-fps, containing 300K individual video frames, to train our network. Experimental results on several datasets, predicting different numbers of interpolated frames, demonstrate that our approach performs consistently better than existing methods.

Abstract: Electroencephalogram (EEG) signal is usually suffered from motion artifacts, generated randomly during signal acquisition timings. These artifacts sturdily affect the investigation and therefore, diagnosis of neural diseases from EEG signal. The artifact removal may cause loss of important information from the signal. Therefore, it is required to remove the motion artifacts and simultaneously preserve the desired information, which makes EEG artifact removal a vital task. Enhanced Empirical Mode Decomposition (EEMD) is the most widespread method used for artifact removal, as it is a data-driven based feature extraction method. In this research work the efficiency of various EEMD with different interpolation based artifact removal method have been compared. The EEMD is used to convert input single channel EEG signal to a multichannel signal, and in order to remove the randomness of motion artifact, CCA and DWT filtering were used successively. The performance of different interpolation based artifact removal methods have evaluated and results indicate that the proposed algorithm is suitable for use as a supplement to algorithms currently in use as it offers improvements in DSNR and various other performance parameters.

Abstract: Design of multiscale structures is a challenging task due to a vast design space of both materials and structures. Consideration of load uncertainty adds another level of complexity. In this paper, a robust concurrent TO (topology optimization) approach is developed for designing multiscale structures composed of multiple porous materials under random field loading uncertainty. To determine the optimal distribution of the porous materials at the macro/structural scale, our key idea is to employ the discrete material optimization method to interpolate the material properties for multiple porous materials. In addition, for the first time we interpret the interpolation schemes in the existing concurrent TO model of porous material with a clear physical meaning by putting forward a SIMP-like single interpolation scheme. This scheme integrates the SIMP (Solid Isotropic Material with Penalization) at the microscale and PAMP (Porous Anisotropic Material with Penalization) at the macroscale into a single equation. Efficient uncertainty characterization and propagation methods based on K-L expansion and linear superposition are introduced, and several important improvements in objective function evaluation and sensitivity analysis are presented. Improved sensitivity analysis equations are derived for volume preserving filtering, which is employed to deal with numerical instabilities at the macro and micro scales in the robust concurrent TO model. Measures to ensure manufacturability and to improve analysis accuracy and efficiency are devised. 2D and 3D examples demonstrate the effectiveness of the proposed approach in simultaneously obtaining robust optimal macro structural topology and material microstructural topologies.

Abstract: The spatial distribution of precipitation is an important aspect of water-related research. The use of different interpolation schemes in the same catchment may cause large differences and deviations from the actual spatial distribution of rainfall. Our study analyzes different methods of spatial rainfall interpolation at annual, daily, and hourly time scales to provide a comprehensive evaluation. An improved regression-based scheme is proposed using principal component regression with residual correction (PCRR) and is compared with inverse distance weighting (IDW) and multiple linear regression (MLR) interpolation methods. In this study, the meso-scale catchment of the Fuhe River in southeastern China was selected as a typical region. Furthermore, a hydrological model HEC-HMS was used to calculate streamflow and to evaluate the impact of rainfall interpolation methods on the results of the hydrological model. Results show that the PCRR method performed better than the other methods tested in the study and can effectively eliminate the interpolation anomalies caused by terrain differences between observation points and surrounding areas. Simulated streamflow showed different characteristics based on the mean, maximum, minimum, and peak flows. The results simulated by PCRR exhibited the lowest streamflow error and highest correlation with measured values at the daily time scale. The application of the PCRR method is found to be promising because it considers multicollinearity among variables.

Abstract: Rainfall data in continuous space provide an essential input for most hydrological and water resources planning studies. Spatial distribution of rainfall is usually estimated using ground-based point rainfall data from sparsely positioned rain-gauge stations in a rain-gauge network. Kriging has become a widely used interpolation method to estimate the spatial distribution of climate variables including rainfall. The objective of this study is to evaluate three geostatistical (ordinary kriging (OK), ordinary cokriging (OCK), kriging with an external drift (KED)) and two deterministic (inverse distance weighting, radial basis function) interpolation methods for enhanced spatial interpolation of monthly rainfall in the Middle Yarra River catchment and the Ovens River catchment in Victoria, Australia. Historical rainfall records from existing rain-gauge stations of the catchments during 1980-2012 period are used for the analysis. A digital elevation model of each catchment is used as the supplementary information in addition to rainfall for the OCK and KED methods. The prediction performance of the adopted interpolation methods is assessed through cross-validation. Results indicate that the geostatistical methods outperform the deterministic methods for spatial interpolation of rainfall. Results also indicate that among the geostatistical methods, the OCK method is found to be the best interpolator for estimating spatial rainfall distribution in both the catchments with the lowest prediction error between the observed and estimated monthly rainfall. Thus, this study demonstrates that the use of elevation as an auxiliary variable in addition to rainfall data in the geostatistical framework can significantly enhance the estimation of rainfall over a catchment.

Abstract: In this article, a special point is found for the interpolation approximation of the linear combination of multi-term fractional derivatives. The derived numerical differentiation formula can achieve at least second order accuracy. Then the formula is used to numerically solve the time multi-term and distributed-order fractional sub-diffusion equations. Several unconditionally stable and convergent difference schemes are presented. The stability and convergence of the difference schemes are discussed. Some numerical examples are provided to show the efficiency of the proposed difference schemes.

Abstract: Shape correspondence is an important and challenging problem in geometry processing. Generalized map representations, such as functional maps, have been recently suggested as an approach for handling difficult mapping problems, such as partial matching and matching shapes with high genus, within a generic framework. While this idea was shown to be useful in various scenarios, such maps only provide low frequency information on the correspondence. In many applications, such as texture transfer and shape interpolation, a high quality pointwise map that can transport high frequency data between the shapes is required. We name this problem map deblurring and propose a robust method, based on a smoothness assumption, for its solution. Our approach is suitable for non-isometric shapes, is robust to mesh tessellation and accurately recovers vertex-to-point, or precise, maps. Using the same framework we can also handle map denoising, namely improvement of given pointwise maps from various sources. We demonstrate that our approach outperforms the state-of-the-art for both deblurring and denoising of maps on benchmarks of non-isometric shapes, and show an application to high quality intrinsic symmetry computation.

Abstract: Majority of tool-paths for high-speed machining is composed of series of short linear segments, so-called G01 moves. This discrete tool-path format limits the achievable speed and accuracy of CNC machines. To generate continuous feed motion along sharp cornered tool-paths, most NC systems smooth corners locally using a pre-specified curve or a spline and slow down to be able to change the feed direction within machine kinematic limits. Path speed is dramatically reduced for accuracy if sharp corners are within close vicinity. This paper proposes a new real-time interpolation algorithm for NC systems to generate continuous rapid feed motion along short segmented linear tool-paths by smoothing local and adjacent corners that are within close vicinity. Instead of locally modifying the corner geometry with a spline, the proposed algorithm directly blends axis velocities between consecutive linear segments based on the jerk limited acceleration profile (JLAP) and generates cornering trajectories within user-specified contour errors and kinematic limits of the drives. A novel Look-Ahead Windowing (LAW) technique is developed to plan tangential feed profile with uninterrupted acceleration to continuously smooth the path. The feed profile is optimized to generate rapid motion along overlapping adjacent corners. Simulation and experimental results demonstrate effectiveness of the proposed method to interpolate accurate Cartesian high-speed motion along short-segmented tool-paths for machining free-form surfaces found in dies, molds and aerospace parts.

Abstract: Inspired by the nonlocal methods in image processing and the point integral method, we introduce a novel weighted nonlocal Laplacian method to compute a continuous interpolation function on a point cloud in high dimensional space. The numerical results in semi-supervised learning and image inpainting show that the weighted nonlocal Laplacian is a reliable and efficient interpolation method. In addition, it is fast and easy to implement.

Abstract: This study introduces a procedure to obtain all interpolating functions, y = f ( x ) , subject to linear constraints on the function and its derivatives defined at specified values. The paper first shows how to express these interpolating functions passing through a single point in three distinct ways: linear, additive, and rational. Then, using the additive formalism, interpolating functions with linear constraints on one, two, and n points are introduced as well as those satisfying relative constraints. In particular, for expressions passing through n points, a generalization of the Waring’s interpolation form is introduced. An alternative approach to derive additive constraint interpolating expressions is introduced requiring the inversion of a matrix with dimensions equally the number of constraints. Finally, continuous and discontinuous interpolating periodic functions passing through a set of points with specified periods are provided. This theory has already been applied to obtain least-squares solutions of initial and boundary value problems applied to nonhomogeneous linear differential equations with nonconstant coefficients.

Abstract: We present the SnapNet system, which provides accurate real-time map matching for cellular-based trajectory traces. Such traces are characterized by input locations that are far from the actual road segment, errors on the order of kilometers, back-and-forth transitions, and highly sparse input data. SnapNet applies a series of filters to handle the noisy locations and an interpolation stage to address the data sparseness. At the core of SnapNet is a novel incremental HMM algorithm that combines digital map hints in the estimation process and a number of heuristics to reduce the noise and provide real-time estimations. Evaluation of SnapNet using actual traces from different cities covering more than 400 km shows that it can achieve a precision and recall of more than 90% under noisy coarse-grained input location estimates. This maps to over 97% and 34% enhancement in precision and recall, respectively, when compared to the traditional HMM map-matching algorithms. Moreover, SnapNet has a latency of 0.58 ms per location estimate.

Abstract: While the recent theory of compressed sensing provides an opportunity to overcome the Nyquist limit in recovering sparse signals, a solution approach usually takes the form of an inverse problem of an unknown signal, which is crucially dependent on specific signal representation. In this paper, we propose a drastically different two-step Fourier compressive sampling framework in a continuous domain that can be implemented via measurement domain interpolation, after which signal reconstruction can be done using classical analytic reconstruction methods. The main idea originates from the fundamental duality between the sparsity in the primary space and the low-rankness of a structured matrix in the spectral domain, showing that a low-rank interpolator in the spectral domain can enjoy all of the benefits of sparse recovery with performance guarantees. Most notably, the proposed low-rank interpolation approach can be regarded as a generalization of recent spectral compressed sensing to recover large classes of finite rate of innovations (FRI) signals at a near-optimal sampling rate. Moreover, for the case of cardinal representation, we can show that the proposed low-rank interpolation scheme will benefit from inherent regularization and an optimal incoherence parameter. Using a powerful dual certificate and the golfing scheme, we show that the new framework still achieves a near-optimal sampling rate for a general class of FRI signal recovery, while the sampling rate can be further reduced for a class of cardinal splines. Numerical results using various types of FRI signals confirm that the proposed low-rank interpolation approach offers significantly better phase transitions than conventional compressive sampling approaches.

Abstract: We investigate the use of parabolic interpolation in data hiding and propose a novel data hiding algorithm with high capacity based on interpolated image. Specifically, the proposed algorithm creates an interpolated image from input image by parabolic interpolation, and embeds secret bits into interpolated pixels in terms of the relation between the interpolated value and the mean value. Ten standard benchmark images are taken as test images for validating efficiency of our algorithm. The results illustrate that our algorithm has better performances than some popular data hiding methods in embedding capacity and visual quality with respect to PSNR and SSIM.

Abstract: Spare-view sampling and its associated iterative image reconstruction in computed tomography have actively investigated. Sparse-view CT technique is a viable option to low-dose CT, particularly in cone-beam CT (CBCT) applications, with advanced iterative image reconstructions with varying degrees of image artifacts. One of the artifacts that may occur in sparse-view CT is the streak artifact in the reconstructed images. Another approach has been investigated for sparse-view CT imaging by use of the interpolation methods to fill in the missing view data and that reconstructs the image by an analytic reconstruction algorithm. In this study, we developed an interpolation method using convolutional neural network (CNN), which is one of the widely used deep-learning methods, to find missing projection data and compared its performances with the other interpolation techniques.

Abstract: Room Impulse Responses (RIRs) are typically measured using a set of microphones and a loudspeaker. When RIRs spanning a large volume are needed, many microphone measurements must be used to spatially sample the sound field. In order to reduce the number of microphone measurements, RIRs can be spatially interpolated. In the present study, RIR interpolation is formulated as an inverse problem. This inverse problem relies on a particular acoustic model capable of representing the measurements. Two different acoustic models are compared: the plane wave decomposition model and a novel time-domain model, which consists of a collection of equivalent sources creating spherical waves. These acoustic models can both approximate any reverberant sound field created by a far-field sound source. In order to produce an accurate RIR interpolation, sparsity regularization is employed when solving the inverse problem. In particular, by combining different acoustic models with different sparsity promoting regularizations, spatial sparsity, spatio-spectral sparsity, and spatio-temporal sparsity are compared. The inverse problem is solved using a matrix-free large-scale optimization algorithm. Simulations show that the best RIR interpolation is obtained when combining the novel time-domain acoustic model with the spatio-temporal sparsity regularization, outperforming the results of the plane wave decomposition model even when far fewer microphone measurements are available.

Abstract: In recent years, quantum image processing is one of the most active fields in quantum computation and quantum information. Image scaling as a kind of image geometric transformation has been widely studied and applied in the classical image processing, however, the quantum version of which does not exist. This paper is concerned with the feasibility of the classical bilinear interpolation based on novel enhanced quantum image representation (NEQR). Firstly, the feasibility of the bilinear interpolation for NEQR is proven. Then the concrete quantum circuits of the bilinear interpolation including scaling up and scaling down for NEQR are given by using the multiply Control-Not operation, special adding one operation, the reverse parallel adder, parallel subtractor, multiplier and division operations. Finally, the complexity analysis of the quantum network circuit based on the basic quantum gates is deduced. Simulation result shows that the scaled-up image using bilinear interpolation is clearer and less distorted than nearest interpolation.