B-spline Filter Research Articles

Rational b-spline adaptive filter for active noise control of machinary noises

Spline adaptive filter has a different architecture than linear-in-parameter nonlinear filters like Volterra filter. There are various kinds of splines like Bezier spline, B-spline and rational B-spline. Rational B spline has weights associated with control points and hence, provides more flexibility than B-spline to create a curve. This paper presents development of rational b-spline adaptive filter for active noise control. Updating equations to update control points and weights of control points are derived. A simulation study is presented to study performance of proposed rational B-spline adaptive filter to reduce machinary noises. Performance of proposed rational B-spline filter are compared with B-spline filter and Bezier filter for active noise control of experimentally recorded noises of band-saw, CNC machine and compressor

Seismic time-frequency analysis via time-varying filtering based empirical mode decomposition method

We proposed a seismic time-frequency analysis method using time- varying filtering based empirical mode decomposition (TVF-EMD). TVF-EMD is a recently-developed signal decomposition method in the field of nonstationary signal processing. The method is suitable for chirp signals, which address the mode mixing problem. TVF-EMD decomposes the non-stationary signal into IMFs with fixed bandwidth and then applies the instantaneous amplitude, frequency, and phase to build the time-frequency spectrum based on the Hilbert transform. Different from empirical mode decomposition (EMD), TVF-EMD uses the time-varying B-spline filter and adaptively calculates the cut-off frequency at each moment for mode decomposition, which is suitable for non-stationary signal processing. Synthetic and field data examples demonstrate comparing with the conventional methods, TVF-EMD has better time-frequency concentration and is more suitable for processing.

Noise Reduction in Human Motion-Captured Signals for Computer Animation based on B-Spline Filtering.

Motion capturing is used to record the natural movements of humans for a particular task. The motions recorded are extensively used to produce animation characters with natural movements and for virtual reality (VR) devices. The raw captured motion signals, however, contain noises introduced during the capturing process. Therefore, the signals should be effectively processed before they can be applied to animation characters. In this study, we analyzed several common methods used for smoothing signals. The smoothed signals were then compared based on the smoothness metrics defined. It was concluded that the filtering based on the B-spline-based least square method could achieve high-quality outputs with predetermined continuity and minimal parameter adjustments for a variety of motion signals.

Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence

A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. These simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.

The Calculation of Roughness Uncertainty by Fitting B-Spline Filter Assessment Middle Lines

The roughness and uncertainty are important parameters of surface morphology. The least square middle line method is often used to estimate the roughness and its uncertainty. However, the roughness and its uncertainty obtained by the least square middle line method are inaccurate. This paper proposes a method to calculate exactly the roughness and its uncertainty by piecewise fitting the smooth B-spline filter assessment middle lines. A B-spline smoothing filter is selected to determine the assessment middle line of roughness. The B-spline filter can not only give the accurate roughness, but also obtain the smooth assessment middle line. The model of roughness uncertainty is proposed by piecewise fitting B-spline filter middle lines as the quadratic curves. The S-shaped test part is used to verify the model of roughness uncertainty.

Asymptotic error of cubic B-spline interpolation using prefiltering

A popular class of reconstruction filters that are used in signal and image processing is based on cubic B-splines. One reason for their popularity is the fact that they can be efficiently implemented. This is specifically true with modern GPUs where cubic B-spline filtering can be implemented by means of linearly interpolating texture fetches so that the actual number of memory accesses can be significantly reduced. The curve obtained from filtering with the cubic B-spline does in general not interpolate the original data set. The latter can however be achieved by applying a prefiltering step that transforms the original data set. We study the asymptotic behavior of the reconstruction error of the cubic B-spline interpolation filter using a state of the art method that is based on a Taylor series expansion and that was carefully adjusted to accommodate the infinite support of this reconstruction filter.

Superconvergent error estimates for position-dependent smoothness-increasing accuracy-conserving (SIAC) post-processing of discontinuous Galerkin solutions

Superconvergence of discontinuous Galerkin methods is an area of increasing interest due to the ease with which higher order information can be extracted from the approximation. Cockburn, Luskin, Shu, and Suli showed that by applying a B-spline filter to the approximation at the final time, the order of accuracy can be improved from order k+1 to order 2k+1 in the L2-norm for linear hyperbolic equations with periodic boundary conditions (where k is the polynomial degree and h is the mesh element diameter) [Math. Comp. (2003)]. The applicability of this filter for linear hyperbolic problems with non-periodic boundary conditions was computationally extended and renamed a position-dependent smoothness-increasing accuracy-conserving (SIAC) filter by van Slingerland, Ryan, Vuik [SISC (2011)]. However, error estimates in the L2$-norm for this new position-dependent SIAC filter were never given. Furthermore, error estimates in the L-infinity-norm have not been established for the original kernel nor the position-dependent kernel. In this paper, for the first time we establish that it is possible to obtain order s, s=min{2k+1,2k + 2-\frac {d}{2}} accuracy in the L-infinity-norm for the position-dependent SIAC filter, where d is the dimension. Furthermore, we extend the error estimates given by Cockburn et al. so that they are applicable to the entire domain when implementing the position-dependent SIAC filter. We also computationally demonstrate the applicability of this filter for visualization of streamlines.

Topology optimization in B-spline space

In this paper, we present a new form of density based topology optimization where the design space is restricted to the B-spline space. An arbitrarily shaped design domain is embedded into a rectangular domain in which tensor-product B-splines are used to represent the density field. We show that, with proper choice of B-spline degrees and knot spans, the B-spline design space is free from checkerboards without extraneous filtering or penalty. We further reveal that the B-spline representation provides an intrinsic filter for topology optimization where the filter size is controlled by B-spline degrees and knot spans. This B-spline filter is effective in removing numerical artifacts and controlling minimal feature length in optimized structures when the B-spline basis functions span multiple analysis elements. We demonstrate that the B-spline filter is linear in storage cost and does not require neighboring element information. Further, this B-spline based density representation decouples the design representation of density distribution from the finite element mesh thus multi-resolution designs can be obtained without re-meshing the design domain. In particular, successive optimization with respect to design resolutions leads to topologically simple features obtainable in either coarse or fine design resolutions, thus achieving a form of mesh independency with respect to design representation. This approach is versatile in the sense a variety of finite element and isogeometric analysis techniques can be used for solution of equilibrium equations and a variety of projection methods can be used to approximate B-spline density in analysis. Numerical studies have been conducted over several representative topology optimization problems, including minimal compliance of MBB beams, compliant mechanism inverters, and heat conductions.

An Analytical Expression for Empirical Mode Decomposition Based on B-Spline Interpolation

Although empirical mode decomposition (EMD) lacks a rigorous theoretical basis, it has attracted much attention for analyzing nonstationary signals adaptively. In this paper, the EMD method is investigated from a digital signal processing perspective. Based on an analysis of extrema sampling and B-spline interpolation, we show that the upper and lower envelopes of signals are formed by a succession of three basic operations: decimation of local extrema, interpolation, and filtering by a B-spline filter. We then show that some aliasing noise can be suppressed by the mean of the envelopes, though the extrema sampling is a sub-Nyquist sampling. For uniformly spaced extrema of signals, we derive a general analytical expression of intrinsic mode functions (IMFs) extracted by the EMD method from signals.

MECHANICAL PULPING: Investigation of the surface topographical differences between the Cross Direction and the Machine Direction for newspaper and paperboard

Real time paper surface-web measurement is one of the challenging research fields. The traditional laboratory method has many limitations and is unable to measure the entire tambour during the manufacturing process. It has been necessary to develop an online technique that could measure the surface topography in real time. An optical technique was developed, based on laser triangulation, and is applied to develop a new prototype device, which characterizes high speed paper-web surfaces over a wide scale of spatial wavelengths spectrum and computes the surface roughness in real time. The used multi channel pulsed laser diode, source of illumination onto the paper-web, is of benefit due to its low coherence length and is capable to deliver a powerful burst of light beam over a 1 µs duration, which delivers energy of 100 µJ per pulse. The short exposure time avoids blurriness in the acquired images which could possible due to the high speed and vibrations on the paper-web.The laser beam is shaped into a narrow line-of-light using cylindrical lenses and is projected onto a paper-web surface, which covers a physical length of about 210 mm. The created line-of-light cross section full width at half maximum, FWHM Gaussian distribution, is 2-3 pixels on the image. The line-of-light is projected onto the paper-web perpendicular to the plane of the surface. The low angled, low specular, reduced coherence length, scattered reflected laser line is captured by the 3 CCD sensors, which are synchronized with the laser source. The low specular light ensures to avoid saturation of the imaging sensors if the surface is very smooth, and obliquely captures the z-directional fine feature of the surface.The scattered phenomenon of the reflected light is responsible for the surface irregularity measurements. The basic image processing algorithm is applied in order to remove noise and cropped the images widthwise so that only pixels above a preset threshold gray level can be processed, which enables efficient real time measurement. The image is transformed into a 1D array using the center of gravity, COG. The accuracy and precision of the COG depends on the line-of-light FWHM, which, in turn, is responsible for the accuracy, noise and the resolution of the developed technique. The image subpixel resolution achieved is 0.01 times a pixel and uuncertainty in the raw data is 0.43 µm while it is 0.05 µm in the rms roughness.The signal processing steps combining the B-Spline filter and the filter in the spatial frequency domain were employed in order to separate roughness, waviness, and form and position error in the raw profile. The prototype is designed to measure online surface roughness and to characterize surface in a spatial wavelength spectrum from 0.09 to 30 mm, which is extendable to any required spatial range in order to cover a wide scale surface feature such as micro roughness, macro roughness and waviness. It is proven that exploitation of a simple laser triangulation technique could lead to an improvement in the overall quality and efficiency in the paper and paperboard industries and it can also be of potential interest for the other surface characterization problems.

Research on Interpolation Methods in Medical Image Processing

Image interpolation is widely used for the field of medical image processing. In this paper, interpolation methods are divided into three groups: filter interpolation, ordinary interpolation and general partial volume interpolation. Some commonly-used filter methods for image interpolation are pioneered, but the interpolation effects need to be further improved. When analyzing and discussing ordinary interpolation, many asymmetrical kernel interpolation methods are proposed. Compared with symmetrical kernel ones, the former are have some advantages. After analyzing the partial volume and generalized partial volume estimation interpolations, the new concept and constraint conditions of the general partial volume interpolation are defined, and several new partial volume interpolation functions are derived. By performing the experiments of image scaling, rotation and self-registration, the interpolation methods mentioned in this paper are compared in the entropy, peak signal-to-noise ratio, cross entropy, normalized cross-correlation coefficient and running time. Among the filter interpolation methods, the median and B-spline filter interpolations have a relatively better interpolating performance. Among the ordinary interpolation methods, on the whole, the symmetrical cubic kernel interpolations demonstrate a strong advantage, especially the symmetrical cubic B-spline interpolation. However, we have to mention that they are very time-consuming and have lower time efficiency. As for the general partial volume interpolation methods, from the total error of image self-registration, the symmetrical interpolations provide certain superiority; but considering the processing efficiency, the asymmetrical interpolations are better.

An Evaluation of Prefiltered B-Spline Reconstruction for Quasi-Interpolation on the Body-Centered Cubic Lattice

In this paper, we demonstrate that quasi-interpolation of orders two and four can be efficiently implemented on the Body-Centered Cubic (BCC) lattice by using tensor-product B-splines combined with appropriate discrete prefilters. Unlike the nonseparable box-spline reconstruction previously proposed for the BCC lattice, the prefiltered B-spline reconstruction can utilize the fast trilinear texture-fetching capability of the recent graphics cards. Therefore, it can be applied for rendering BCC-sampled volumetric data interactively. Furthermore, we show that a separable B-spline filter can suppress the postaliasing effect much more isotropically than a nonseparable box-spline filter of the same approximation power. Although prefilters that make the B-splines interpolating on the BCC lattice do not exist, we demonstrate that quasi-interpolating prefiltered linear and cubic B-spline reconstructions can still provide similar or higher image quality than the interpolating linear box-spline and prefiltered quintic box-spline reconstructions, respectively.

Causal Cubic Splines: Formulations, Interpolation Properties and Implementations

The paper presents two formulations of causal cubic splines with equidistant knots. Both are based on a causal direct B-spline filter with parallel or cascade implementation. In either implementation, the causal part of the impulse response is realized with an efficient infinite-impulse-response (IIR) structure, while only the anticausal part is approximated with a finite-order finite-impulse-response (FIR) filter. Resulting cubic coefficients are computed from the causal B-spline coefficients by using a third-order output FIR filter with either single-input multiple-output (SIMO) or multiple-input multiple-output (MIMO) structure, depending on the chosen formulation of the cubic spline. The paper demonstrates and proves that the properties of the resulting causal splines are quite different, whether they are based on a more popular B-spline formulation, or a bit neglected tridiagonal matrix formulation. It is shown that the proposed low-complexity but accurate causal interpolators can be realized for many practical applications with the delay of only a few samples.

북동태평양 KR1 광구 수심자료의 지형분석 : 웨이브렛 필터의 적용

2-D wavelet analysis is applied to bathymetric data from the KR1 area of Korea Deepsea Mining Area. The wavelet analysis is one of the quantitative methods to analyze the topography. The wavelet allows us to create filters to select for topography in a continuous variety of shapes, sizes, and orientation. The 2-D Linear B-spline filter, 100 BS and 100 NF, is convolved with bathymetric data to identify the location of abyssal hills and abyssal troughs in bathymetry. In addition, the 2-D derivative of Cubic B-spline filter, 60 BS and 60 NF, is applied to bathymetric data to find the slope of abyssal hill in bathymetry. These filters were rotated <TEX>$5^{\circ}$</TEX> counterclockwise from NS to match the dominant orientation of seafloor lineament. Both filters result in good match with abyssal hills, troughs, and slopes. This method can apply to fault, fold, and other lineament structures description with variable size. The result of application shows that wavelet analysis of bathymetric data could be used with fundamental data of geophysical analysis.

Fractional Time-Shift B-Spline Filter

The fractional time-shift operators are essential devices in processing and adjustment of signals in modern communication systems. This letter introduces the fractional time-shift B-spline filter. The filter produces a time-shift Delta isin [0,1], which is an arbitrary fraction of the sampling period. We describe the construction and parallel implementation of the fractional time-shift filter. We give several of its applications (differentiator, integrator, and correlator) in numerical and statistical signal processing and in adaptive time-shift adjustments.

Generation of Stratified Samples for B-Spline Pixel Filtering

B-spline filter kernels have proved useful in many pixel-sampling applications. A cubic B-spline filter kernel, having a width of four pixels, is particularly effective. In distribution ray tracing, pixel filters are evaluated implicitly by having the density of sampling proportional to the filter value. In this work we present a simple method to generate random samples having an underlying B-spline density function. To reduce error it is important to stratify the samples, akin to jittering for uniform sampling. We provide an algebraic and a numerical technique for doing this for B-spline kernels of degree 1, 2, and 3.

A simple smoothing spline, III

Computational methods for spline smoothing are studied in the context of the linear smoothing spline. Comparisons are made between two efficient methods for computing the estimator using band-limited basis functions and the Kalman filter. In particular, the Kalman filter approach is shown to be an efficient method for computing under the Kimeldorf-Wahba representation for the estimator. Run time comparisons are made between band-limited B-spline and Kalman filter based algorithms.

Efficient implementation of all-digital interpolation

B-splines are commonly used for continuous representation of discrete time signals. This kind of representation proves to be very useful in applications such as image interpolation, rotation and edge detection. In all these applications, the first step is to compute the B-spline coefficients of the signal, and this involves the use of an IIR noncausal filter called the direct B-spline filter. The signal reconstruction is achieved using the indirect B-spline filter, which in many applications operates at a higher rate. In this paper, we introduce a simplified implementation of the signal reconstruction part that will significantly reduce the overall complexity. We also show that the direct B-spline filter can safely be replaced with a short FIR filter, without compromising the performance of the traditional method. Numerous examples show both visually and numerically that the differences between this method and the traditional one are indeed very small. Finally, we report the performance of these newly proposed methods in other image processing applications such as edge detection and least squares approximation.

Cubic splines for image interpolation and digital filtering

This paper presents the use of B-splines as a tool in various digital signal processing applications. The theory of B-splines is briefly reviewed, followed by discussions on B-spline interpolation and B-spline filtering. Computer implementation using both an efficient software viewpoint and a hardware method are discussed. Finally, experimental results are presented for illustrative purposes in two-dimensional image format. Applications to image and signal processing include interpolation, smoothing, filtering, enlargement, and reduction.