A Dual Domain Robust Reversible Watermarking Algorithm for Frame Grouping Videos Using Scene Smoothness

The proposed robust reversible watermarking algorithm addresses the compatibility challenges between robustness and reversibility in existing video watermarking techniques by leveraging scene smoothness for frame grouping videos.Grounded in the H.264 video coding standard,the algorithm first employs traditional robust watermark stitching technology to embed watermark information in the low-frequency coefficient domain of the U channel.Subsequently,it utilizes histogram migration techniques in the high-frequency coefficient domain of the U channel to embed auxiliary information,enabling successful watermark extraction and lossless recovery of the original video content.Experimental results demonstrate the algorithm’s strong imperceptibility,with each embedded frame in the experimental videos achieving a mean peak signal-to-noise ratio of 49.3830 dB and a mean structural similarity of 0.9996.Compared with the three comparison algorithms,the performance of the two experimental indexes is improved by 7.59%and 0.4%on average.At the same time,the proposed algorithm has strong robustness to both offline and online attacks:In the face of offline attacks,the average normalized correlation coefficient between the extracted watermark and the original watermark is 0.9989,and the average bit error rate is 0.0089.In the face of online attacks,the normalized correlation coefficient between the extracted watermark and the original watermark is 0.8840,and the mean bit error rate is 0.2269.Compared with the three comparison algorithms,the performance of the two experimental indexes is improved by 1.27%and 18.16%on average,highlighting the algorithm’s robustness.Furthermore,the algorithm exhibits low computational complexity,with the mean encoding and the mean decoding time differentials during experimental video processing being 3.934 and 2.273 s,respectively,underscoring its practical utility.

Smoothness加强的全局和局部显著目标检测

显著目标检测是计算机视觉的重要组成部分。针对基于对比度的方法存在的前景和背景容易被误检的问题,提出Smoothness加强的全局和局部显著目标检测的方法。在全局对比度检测过程中引入中心先验知识,在局部对比度检测过程中引入Compactness特征,再使用Smoothness特征加强全局的显著性及局部的显著性,最后将全局显著图和局部显著图进行线性融合。在MSRA-1000、ECSSD数据集上的评估中,该算法有更高的准确率,在CSSD数据集上能和最先进算法相媲美。实验表明,从全局和局部两个角度出发的显著性检测的方法能够有效的互补,Smoothness能够有效加强前景和背景的差异性,并且有效纠正一些误检现象,从而取得更好的结果。

Machine learning based online fault prognostics for nonstationary industrial process via degradation feature extraction and temporal smoothness analysis

Fault degradation prognostic, which estimates the time before a failure occurs and process breakdowns, has been recognized as a key component in maintenance strategies nowadays. Fault degradation processes are, in general,slowly varying and can be modeled by autoregressive models. However, industrial processes always show typical nonstationary nature, which may bring two challenges: how to capture fault degradation information and how to model nonstationary processes. To address the critical issues, a novel fault degradation modeling and online fault prognostic strategy is developed in this paper. First, a fault degradation-oriented slow feature analysis(FDSFA) algorithm is proposed to extract fault degradation directions along which candidate fault degradation features are extracted. The trend ability assessment is then applied to select major fault degradation features. Second, a key fault degradation factor(KFDF) is calculated to characterize the fault degradation tendency by combining major fault degradation features and their stability weighting factors. After that, a time-varying regression model with temporal smoothness regularization is established considering nonstationary characteristics. On the basis of updating strategy, an online fault prognostic model is further developed by analyzing and modeling the prediction errors. The performance of the proposed method is illustrated with a real industrial process.

Smoothness Prior Approach for Spectral Smoothing and Baseline Correction

Smoothness prior approach for spectral smoothing is investigated using Fourier frequency filter analysis.We show that the regularization parameter in penalized least squares could continuously control the bandwidth of low-pass filter.Besides,due to its property of interpolating the missing values automatically and smoothly,a spectral baseline correction algorithm based on the approach is proposed.This algorithm generally comprises spectral peak detection and baseline estimation.First,the spectral peak regions are detected and identified according to the second derivatives.Then,generalized smoothness prior approach combining identification information could estimate the baseline in peak regions.Results with both the simulated and real spectra show accurate baseline-corrected signals with this method.

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral Tf（x1,x2）=p.v.∫∫R^n1＋n2 Ω（y′1,y′2）h（｜y1｜,｜y2｜）/｜y1｜^n1｜y2｜^n2 f（x1-y1,x2-y2）dy1dy2maps from Sp,q^α1,α2F（R^n1×R^n2）boundedly to itself for 1 〈 p, q 〈 ∞, α1, α2 ∈R.

Greedy Algorithm in m-Term Approximation for Periodic Besov Class with Mixed Smoothness

Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m -term approximation with regard to tensor product wavelet-type basis is pro-posed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the L q norm. Moreover, it depends only on the expansion of function f by tensor pro-duct wavelet-type basis, but neither on q nor on any special features of f.

SMOOTHNESS INDICATOR OF WENO SCHEME FOR RESOLVING SHORT WAVE

Based on the traditional fifth-order weighted essentially non-oscillatory(WENO)scheme,a smoothness indicator is introduced to improve the capability of WENO schemes for resolving short waves.In the construction of the new smoothness indicator,the proportion of the first-order term in the original smoothness indicator is reduced by replacing the square of the first-order term with the product of the first-order and the third-order terms.To preserve the fifth-order of convergence rate,the smoothness indicator is combined with the method of Borges,et al.The numerical results show that the proposed schemes are more suitable for simulating turbulent flows or aeroacoustics problems than the previous fifth-order WENO schemes,thanks to its improved resolution on short waves.

Automatic Assessment of Fabric Smoothness Grade Using Double CCD Grating Projection

Automatically assessing fabric smoothness grade is very important in the evaluation of fabric appearance.A system for objectively evaluating the fabric smoothness grade based on a grating projection unit and double colored CCD(short form of charge coupled device) was constructed in this paper.Two images captured by different CCD compensated each other which reduced the influence of noises.The application of the four-step phase-shifting method enabled the calculation of the exact phase in a point easy and quick.A large amount of 3D points with three coordinates X,Y and Z were obtained precisely making the definition and calculation of fabric smoothness characters easy.Then four parameters which intuitively denoted the fabric smoothness degree were obtained.Finally,a proper neural network was built,which successfully performed the fabric smoothness classification.The experimental results show that the system is applicable for all the fabric whatever pattern or color.The experimental grades provided by this grating projection system are also highly consistent with the subjective results.

Application of Rough Sets to Evaluate Fabric Smoothness Grade

For garment or fabric appearance, the cloth smoothness grade is one of the most important performance factors in textile and garment community. In this paper, on the base of Rough Set Theory,a new objective method for fabric smoothness grade evaluation was constructed. The objective smoothness grading model took the parameters of 120 AATCC replicas' point-sampled models as the conditional attributes and formed the smoothness grading decision table. Then, NS discretization method and genetic algorithm reduction method were used in the attributes discretization and feature reduction. Finally, the grading model was expressed as simple and intuitional classification rules. The simulation results show the validity of the fabric smoothness grading system which is built on the use of rough sets.

GLOBAL SMOOTHNESS PRESERVATION BY BIVARIATE INTERPOLATION OPERATORS

Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity.

CHARACTERIZATION OF HLDER SPACES CORRESPONDING TO DITZIAN-TOTIK MODULUS OF SMOOTHNESS

For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, and the isomorphism is given by the cofficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density . In case ∧a,p is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented.

Equivalence of <i>K</i>-Functionals and Modulus of Smoothness Generated by a Generalized Dunkl Operator on the Real Line

This paper is intended to establish the equivalence between K-functionals and modulus of smoothness tied to a Dunkl type operator on the real line.

Equivalence between Modulus of Smoothness and K-Functional on Rotation Group SO(3)

In this paper we obtain the equivalence between modulus of smoothness and K-functional on rotation group SO(3).

A real-time data smoothness method based on xPC-Target

A method of real-time data smoothness which is applied in a hardware-in-the-loop （HIL） simulation platform for a plug-in hybrid electric vehicle synthetical power device is described. The input signal of the platform comes from a AC/DC switch power with output containing noises. A linear slide average arithmetic is applied to smooth the noises. To average a certain number input sample signals, this method can decrease the noises voltage level, which meet the requirement of the simulation platform. The efficiency and signal delay time are presented to describe the result of this method, and a statistical index is used to judge the arithmetic＇ s efficiency. The tests results show that the arithmetic fit the requirement of the HIL simulation platform.

A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS

In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].

On the k-smoothness and k-strong Smoothness

In this paper, by normwe give a sufficient and necessary condition of k-smooth points and k-strong smooth points.

Smoothness-oriented path optimization for robotic milling processes

Industrial robots are increasingly used for five-axis machining operations, where the rotation of the end effector along the toolaxis direction is functionally redundant. This functional redundancy should be carefully resolved when planning the robot path according to the tool path generated by a computer-aided manufacturing(CAM) system. Improper planning of the redundancy may cause drastic variations of the joint motions, which could significantly decrease the machining efficiency as well as the machining accuracy. To tackle this problem, this paper presents a new optimization-based methodology to globally resolve the functional redundancy for the robotic milling process. Firstly, a global performance index concerning the smoothness of the robot path at the joint acceleration level is proposed. By minimizing the smoothness performance index while considering the avoidance of joint limits and the singularity and the constraint of the stiffness performance, the resolution of the redundancy is formulated as a constrained optimization problem. To efficiently solve the problem, the sequential linearization programming method is employed to improve the initial solution provided by the conventional graph-based method. Then, simulations for a given tool path are presented. Compared with the graph-based method, the proposed method can generate a smoother robot path in which a significant reduction of the magnitude of the maximum joint acceleration is obtained, resulting in a smoother tool-tip feedrate profile. Finally, the experiment on the robotic milling system is also presented. The results show that the optimized robot path of the proposed method obtains better surface quality and higher machining efficiency, which verifies the effectiveness of the proposed method.

Non-Linear Approximation of Functions with Mixed Smoothness by Sets of Finite Pseudo-Dimension

In this paper, the non-linear approximation on the class of multivariate functions with bounded mixed derivatives is investigated, and the asymptotic degree of the non-linear width on this class is determined.

Hrmander Type Theorem for Fourier Multipliers with Optimal Smoothness on Hardy Spaces of Arbitrary Number of Parameters

The main purpose of this paper is to establish the HSrmander-Mihlin type theorem for Fourier multipliers with optimal smoothness on k-parameter Hardy Spaces for k≥ 3 using the multi- parameter Littlewood-Paley theory. For the sake of convenience and simplicity, we only consider the case k 3, and the method works for all the cases k ≥ 3： Tmf（x1,x2,x3） =1/（（2π）＋n1＋n2＋n3） ∫ R n1×R n2×R n3 m（ξ）f（ξ）e 2π ix.ξ dξ. where x = （x1,x2,x3） ∈ Rn1 × Rn2 × R n3 and ξ = （ξ1,ξ2,ξ3） ∈ R n1 × Rn2 ×R n3. One of our main results is the following： Assume that m（ξ） is a function on Rn1＋n2＋n3 satisfying sup j,k,l ∈Z ｜｜mj,k,l｜｜ W（s1,s2,s3）〈∞ with si 〉 ni（1/p-1/2） for 1 ≤ i ≤ 3. Then Tm is bounded from HP（R n1 × R n2 ×R n3） to HP（R n1 ×R n2 × R n3） for all 0 〈 p ≤ 1 and ｜｜Tm｜｜ Hp→Hp≤ sup j,k,l∈Z ｜｜mj,k,l｜｜ W（s1,s2,s3） Moreover, the smoothness assumption on sl for 1 ≤ i ≤ 3 is optimal. Here we have used the notations mj,k,l （ξ）= m（2 j ξ1,2 k ξ2, 2 l ξ3） ψ（ξ1） ψ（ξ2） ψ（ξ3） and ψ（ξi） is a suitable cut-off function on R ni for 1 ≤ i ≤ 3, and W（s1,s2,s3） is a three-parameter Sobolev space on R n × R n2 × Rn 3. Because the Fefferman criterion breaks down in three parameters or more, we consider the Lp boundedness of the Littlewood-Paley square function of T mf to establish its boundedness on the multi-parameter Hardy spaces.

Pointwise Characterizations of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness and Their Applications

In this article,the authors first establish the point wise characterizations of Besov and Triebel-Lizorkin spaces with generalized smoothness on R;via the Hajlasz gradient sequences,which serve as a way to extend these spaces to more general metric measure spaces.Moreover,on metric spaces with doubling measures,the authors further prove that the Besov and the Triebel-Lizorkin spaces with generalized smoothness defined via Hajlasz gradient sequences coincide with those defined via hyperbolic fillings.As an application,some trace theorems of these spaces on Ahlfors regular spaces are established.