Soil moisture sensor calibration based on the Multivariate Adaptive Regression Splines (MARSplines) model is studied in this paper. Different from the generic polynomial fitting methods, the MARSplines model is a non-parametric model, and it is able to model the complex relationship between the actual and measured soil moisture. Rao-1 algorithm is employed to tune the hyper-parameters of the calibration model and thus the performance of the proposed method is further improved. Data collected from four commercial soil moisture sensors is utilized to verify the effectiveness of the proposed method. To assess the calibration performance, the proposed model is compared with the model without using the temperature information. The numeric studies prove that it is promising to apply the proposed model for real applications.

The mean, median, and mode are usually calculated from univariate observations as the most basic representative values of a random variable. To measure the spread of the distribution, the standard deviation, interquartile range, and modal interval are also calculated. When we analyze continuous relations between a pair of random variables from bivariate observations, regression analysis is often used. By minimizing appropriate costs evaluating regression errors, we estimate the conditional mean, median, and mode. The conditional standard deviation can be estimated if the bivariate observations are obtained from a Gaussian process. Moreover, the conditional interquartile range can be calculated for various distributions by the quantile regression that estimates any conditional quantile (percentile). Meanwhile, the study of the modal interval regression is relatively new, and spline regression models, known as flexible models having the optimality on the smoothness for bivariate data, are not yet used. In this paper, we propose a modal interval regression method based on spline quantile regression. The proposed method consists of two steps. In the first step, we divide the bivariate observations into bins for one random variable, then detect the modal interval for the other random variable as the lower and upper quantiles in each bin. In the second step, we estimate the conditional modal interval by constructing both lower and upper quantile curves as spline functions. By using the spline quantile regression, the proposed method is widely applicable to various distributions and formulated as a convex optimization problem on the coefficient vectors of the lower and upper spline functions. Extensive experiments, including settings of the bin width, the smoothing parameter and weights in the cost function, show the effectiveness of the proposed modal interval regression in terms of accuracy and visual shape for synthetic data generated from various distributions. Experiments for real-world meteorological data also demonstrate a good performance of the proposed method.

It is important to consider curvature properties around the control points to produce natural-looking results in the vector illustration. C2 interpolating splines satisfy point interpolation with local support. Unfortunately, they cannot control the sharpness of the segment because it utilizes trigonometric function as blending function that has no degree of freedom. In this paper, we alternate the definition of C2 interpolating splines in both interpolation curve and blending function. For the interpolation curve, we adopt a rational Bézier curve that enables the user to tune the shape of curve around the control point. For the blending function, we generalize the weighting scheme of C2 interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-C2 features, such as cusps and fillets, without losing generality. In our experiment, we provide both quantitative and qualitative comparisons to existing parametric curve models and discuss the difference among them.

Curve extension is a useful function in shape modeling for cyberworlds, while a Ball B-spline Curve (BBSC) has its advantages in representing freeform tubular objects. In this paper, an extension algorithm for the BBSC with G2-continuity is investigated. We apply the extending method of B-Spline curves to the skeleton of the BBSC through generalizing a minimal strain energy method from 2D to 3D. And the initial value of the G2-continuity parameter for the skeleton is selected by minimizing the approximate energy function which is a problem with O(1) time complexity. The corresponding radius function of the control ball points is determined through applying the G2-continuity conditions for the skeleton to the scalar function. In order to ensure the radii of the control ball points are positive, we make a decision about the range of the G2-continuity parameter for the radius and then determine it by minimizing the strain energy in the affected area. Some experiments comparing our method with other methods are given. And at the same time, we present the advantage of our method in modeling flexibility from the aspects of the skeleton and radius. The results illustrate our method for extending the BBSC is effective.

Traditional face swapping technologies require that the faces of source images and target images have similar pose and appearance (usually frontal). For overcoming this limit in applications this paper presents a pose-free face swapping method based on personalized 3D face modeling. By using a deformable 3D shape morphable model, a photo-realistic 3D face is reconstructed from a single frontal view image. With the aid of the generated 3D face, a virtual source image of the person with the same pose as the target face can be rendered, which is used as a source image for face swapping. To solve the problem of illumination difference between the target face and the source face, a color transfer merging method is proposed. It outperforms the original color transfer method in dealing with the illumination gap problem. An experiment shows that the proposed face reconstruction method is fast and efficient. In addition, we have conducted experiments of face swapping in a variety of scenarios such as children's story book, role play, and face de-identification stripping facial information used for identification, and promising results have been obtained.

We developed a novel movement-imagery-based brain-computer interface (BCI) for untrained subjects without employing machine learning techniques. The development of BCI consisted of several steps. First, spline Laplacian analysis was performed. Next, time-frequency analysis was applied to determine the optimal frequency range and latencies of the electroencephalograms (EEGs). Finally, trials were classified as right or left based on β-band event-related synchronization using the cumulative distribution function of pretrigger EEG noise. To test the performance of the BCI, EEGs during the execution and imagination of right/left wrist-bending movements were measured from 63 locations over the entire scalp using eight healthy subjects. The highest classification accuracies were 84.4% and 77.8% for real movements and their imageries, respectively. The accuracy is significantly higher than that of previously reported machine-learning-based BCIs in the movement imagery task (paired t-test, p < 0.05). It has also been demonstrated that the highest accuracy was achieved even though subjects had never participated in movement imageries.

This paper introduces a tensorial representation of multiple cameras with arbitrary curvilinear motions. It enables us to define a multilinear relationship among image points derived from non-rigid object motions viewed from multiple cameras with arbitrary curvilinear motions. We show the new multilinear relationship is useful for generating images and reconstructing 3D non-rigid object motions viewed from cameras with arbitrary curvilinear motions. The method is tested in real image sequences.

This paper presents a low complexity partially folded architecture of transposed FIR filter and cubic B-spline interpolator for ATSC terrestrial broadcasting systems. By using the multiplexer, the proposed FIR filter and interpolator can provide high clock frequency and low hardware complexity. A binary representation method was used for designing the high order FIR filter. Also, in order to compensate the truncation error of FIR filter outputs, a fixed-point range detection method was used. The proposed partially folded architecture was designed and implemented with 90-nm CMOS technology that had a supply voltage of 1.1 V. The implementation results show that the proposed architectures have 12% and 16% less hardware complexity than the other kinds of architecture. Also, both the filter and the interpolator operate at a clock frequency of 200 MHz and 385 MHz, respectively.

Pen-input is not a new means for CAD designers, in particular, in the concept design phase. Meanwhile, B-Splines are well known curve and surface design tool in 3D shape modeling in the final modeling stages in which neat curves and surfaces should be produced. In this paper, an intuitive B-Spline design method that can be used for the CAD systems both in conceptual modeling phase and in later design phases is proposed. Unlike the control point based interactive modification schemes for the B-spline curves and surfaces, we extend what has been called the "touch-and-replace" method used for poly-line modification in the late 1980s to B-Splines; our approach uses successive pen strokes to modify the final shape of the existing B-Spline curves and surfaces. We also show related user test results in this paper as an empirical proof.

A procedure is developed to construct a time-limited pulse for its use in the short-range impulse radio communications. The even-numbered shifts of the pulse constitute a train of overlapping pulses. The pulses are intentionally made orthogonal to the second derivative of one another. This orthogonality makes it possible to detect the received pulses, which are assumed to be the second derivative of the transmitted pulses, by means of correlation with the original pulses. An example pulse is presented that complies with the FCC regulation for indoor ultra-wide bandwidth radio communications.

Grey model (abbreviated as GM), which is based on Deng's grey theory, has been established as a prediction model. At present, it has been widely applied in many research fields to solve efficiently the predicted problems of uncertainty systems. However, this model has irrational problems concerning the calculation of derivative and background value z since the predicted accuracy of GM is unsatisfying when original data shows great randomness. In particular, the predicted accuracy falls in case of higher-order derivative or multivariate greatly. In this paper, the new calculation methods of derivative and background value z are first proposed to enhance the predicted power according to cubic spline function. The newly generated model is defined as 3spGM. To further improve predicted accuracy, Taylor approximation method is then applied to 3spGM model. We call the improved version as T-3spGM. Finally, the effectiveness of the proposed model is validated with three real cases.

This paper presents a method for lossy compression of digital video data by parametric line and Natural cubic spline approximation. The method estimates the variation of pixel values in the temporal dimension by taking group of pixels together as keyblocks and interpolating them in Euclidean space. Break and fit criterion is used to minimize the number of keyblocks required for encoding and decoding of approximated data. Each group of pixels at fixed spatial location is encoded/decoded independently. The proposed method can easily be incorporated in the existing video data compression techniques based on Discrete Cosine Transform or Wavelet Transform.

An experimental test has been done on the suitability of box splines for the estimation of color images from their observation through the honeycomb color filter. The estimation is made by following the framework of consistent sampling by Unser and Aldroubi. Numerical evaluation of the estimation errors has shown that the best estimation may be made by choosing the box splines which are twice locally averaged along each of the three axes consisting of the unilateral triangular mesh. A close look at estimated images has indicated that those box splines are almost free from directional jaggy noises that the traditional B-splines suffer from.

This paper presents a computational approach to the imaging of a partially immersed conducting cylinder. Both cubic-spline method and trigonometric series for shape description are used and compared. Based on the boundary condition and the recorded scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The genetic algorithm is employed to find out the global extreme solution of the object function. It is found that the shape described by Fourier series can be reconstructed by cubic-spline. In the opposite case, the shape described by cubic-spline and reconstructed by Fourier series expansion will fail. Even when the initial guess is far away from the exact one, the cubic-spline expansion and genetic algorithm can avoid the local extreme and converge to a global extreme solution. Numerical results are given to show that the shape description by using cubic-spline method is much better than that by the Fourier series. In addition, the effect of Gaussian noise on the reconstruction is investigated.

The present paper discusses a new construction of UWB pulses within the framework of soft-spectrum adaptation. The employed basis functions are B-splines having the following properties: (i) The B-splines are time-limited piecewise polynomials. (ii) The first-order B-splines are rectangular pulses and they converge band-limited functions at the limit that their order tends to infinity. (iii) There are an analog circuit and a fast digital filter for the generation of B-splines. Simple application of Gram-Schmidt orthonormalization process to the shifted B-splines results in a few basic pulses, which are well time-limited and have a broad band width, but do not comply with the FCC spectral mask. A constrained approximation technique is proposed for adaptively designing pulses so that they approximate target frequency characteristics. At the cost of using eleven shifted B-splines, an example set of four pulses comforting the FCC spectral mask is obtained.

In this paper, an adaptive bound reduced-form genetic algorithm (ABRGA) to tune the control points of B-spline neural networks is proposed. It is developed not only to search for the optimal control points but also to adaptively tune the bounds of the control points of the B-spline neural networks by enlarging the search space of the control points. To improve the searching speed of the reduced-form genetic algorithm (RGA), the ABRGA is derived, in which better bounds of control points of B-spline neural networks are determined and paralleled with the optimal control points searched. It is shown that better efficiency is obtained if the bounds of control points are adjusted properly for the RGA-based B-spline neural networks.

A digital/analog hybrid system is presented which implements the cardinal polynomial spline interpolation of arbitrary degree. Based on the fact that the (m-1)st derivative of a spline of degree m-1 is a staircase function, this system generates a cardinal spline of degree m-1 by m-1 cascaded integrators with a staircase function input. A given sequence of sampled values are transformed by a digital filter into coefficients for the B-spline representation of the spline interpolating the sampled values. The values of its (m-1)st derivative with respect to time are computed by the recurrence formula interpreting differentiation of the spline as difference of the coefficients. Then a digital-to-analog converter generates a staircase function representing the (m-1)st derivative, which is integrated by a cascade of m-1 analog integrators to make the expected spline. In order to cope with the offset errors involved in the integrators, a dynamical sampled-data control is attached. An analog-to-digital converter is employed to sample the output of the cascaded integrators. Target state of the cascaded integrators at each sampling instance is computed from the coefficients for the B-spline representation. The state error between the target and the estimated is compensated by feeding back a weighted sum of the state error to the staircase input.

A new approach to correcting the array amplitude failure by a combination of B-spline techniques and genetic algorithms is proposed. Some array elements indicate the control knots for a B-spline curve by their nominal positions and amplitudes; others distribute the excitation amplitudes according to the sampling points on the curve. The inherent smoothness of the B-spline curves reduce the effect of excessive coupling between adjacent elements. Genetic algorithms are used to search for a quasi-optimized B-spline curve to produce the ultimate amplitude distribution for correcting the array failure. To demonstrate the method's effectiveness, simulation results for correcting failures with three- and four-element failures are presented.

Obtaining a linearizing feedback and a coordinate transformation map is very difficult, even though the system is feedback linearizable. It is known that finding a desired transformation map and feedback is equivalent to finding an integrating factor for an annihilating one-form for single input nonlinear systems. It is also known that such an integrating factor can be approximated using the simple C.I.R method and tensor product splines. In this paper, it is shown that m integrating factors can always be approximated whenever a nonlinear system with m inputs is feedback linearizable. Next, m zero-forms can be constructed by utilizing these m integrating factors and the same methodology in the single input case. Hence, the coordinate transformation map is obtained.

A numerical model of thin-film transistors for circuit simulation has been developed. This model utilizes three schemes. First, the spline interpolation with transformation by y=x+log(x) achieves excellent preciseness for both on-current and off-current simultaneously. Second, the square polynomial supplement solves an anomaly near the points where drain voltage equal to zero. Third, the linear extrapolation achieves continuities of the current and its derivatives as a function of voltages out of the area where the spline interpolation is performed, and improves convergence during circuit simulation.