Median based algorithm for sub-pixel estimation of extrema positions of diffuse light reflection signal

It has been proposed to utilize the median algorithm for determination of the extrema positions of diffuse light reflectance intensity distribution by a discrete signal of a photodiode linear array. The algorithm formula has been deduced on the base of piecewise-linear interpolation for signal representation by cumulative function. It has been shown that this formula is much simpler for implementation than known centroid algorithm and the noise immune Blais and Rioux detector algorithm. Also, the methodical systematic errors for zero noise as well as the random errors for full common mode additive noises and uncorrelated noises have been estimated and compared for mentioned algorithms. In these terms, the proposed median algorithm is proportionate to Blais and Rioux algorithm and considerably better then centroid algorithm.

MODELING OF ASYMPTOTICALLY OPTIMAL PIECEWISE LINEAR INTERPOLATION OF PLANE PARAMETRIC CURVES

Context. Piecewise linear approximation of curves has a large number of applications in computer algorithms, as the reconstruction of objects of complex shapes on monitors, CNC machines and 3D printers. In many cases, it is required to have the smallest number of segments for a given accuracy. Objective. The objective of this paper is to improve the method of asymptotically optimal piecewise linear interpolation of plane parametric curves. This improvement is based to research influence of the method parameters and algorithms to distributions of approximation errors. Method. An asymptotically optimal method of curves interpolation is satisfied to the condition of minimum number of approximation units. Algorithms for obtaining the values of the sequence of approximation nodes are suggested. This algorithm is based on numerical integration of the nodes regulator function with linear and spline interpolation of its values. The method of estimating the results of the curve approximation based on statistical processing of line segments sequence of relative errors is substantiated. Modeling of real curves approximation is carried out and influence of the sampling degree of integral function – the nodes regulator on distribution parameters of errors is studied. The influence is depending on a method of integral function interpolation. Results. Research allows to define necessary the number of discretization nodes of the integral function in practical applications. There have been established that with enough sampling points the variance of the error’s distribution stabilizes and further increasing this number does not significantly increase the accuracy of the curve approximation. In the case of spline interpolation of the integral function, the values of the distribution parameters stabilized much faster, which allows to reduce the number of initial sampling nodes by 5–6 times having similar accuracy. Conclusions. Modelling of convex planar parametric curves reconstruction by an asymptotically optimal linear interpolation algorithm showed acceptable results without exceeding the maximum errors limit in cases of a sufficient discretization of the integral function. The prospect of further research is to reduce the computational complexity when calculating the values of the integral distribution function by numerical methods, and to use discrete analogues of derivatives in the expression of this function.

Features of a real-time s-shaped acceleration/deceleration curve constructing with piecewise linear interpolation of complex-shaped surfaces

In this paper we considered the problem of an s-shaped acceleration/deceleration curve constructing in real time with linear-spline interpolation, taking into account given constraints on the contour acceleration, jerk, and feed rate. The input data for the s-curve were defined in the lookahead algorithm and the geometric smoothing module. The choice of a particular acceleration/deceleration strategy depends on the segment length, the allowable feed rates at the segment junction, and the given kinematic constraints. Each trajectory segment can have a maximum of seven time intervals and their rounding will produce inaccuracies when forming the velocity profile. Therefore, to compensate for rounding errors, the method of half division was applied, which made it possible to remove gaps in the velocity contour. The experimental data obtained indicate the correctness of the chosen approach for its implementation as part of the CNC for high-speed machining of surfaces with complex shapes. Key words Feed-rate planning algorithm, s-shaped acceleration/deceleration, trajectory smoothing, numerical control system, real-time, frame preview algorithm. Acknowledgements The research was carried out with financial support of Ministry of Science and Higher Education of Russian Federation in the frame of state assignment (project no.FSFS-2020-0031).

An Electrochemical Enzyme Biosensor for Ammonium Detection in Aquaculture Using Screen-Printed Electrode Modified by Gold Nanoparticle/Polymethylene Blue

A SPEC/AuNPs/PMB modified electrode was prepared by electrodeposition and electro-polymerization. The electrochemical behavior of reduced nicotinamide adenine dinucleotide (NADH) on the surface of the modified electrode was studied by cyclic voltammetry. A certain amount of substrate and glutamate dehydrogenase (GLDH) were coated on the modified electrode to form a functional enzyme membrane. The ammonia nitrogen in the water sample could be calculated indirectly by measuring the consumption of NADH in the reaction. The results showed that the strength of electro-catalytic current signal was increased by two times; the catalytic oxidation potential was shifted to the left by 0.5 V, and the anti-interference ability of the sensor was enhanced. The optimum substrate concentration and enzyme loading were determined as 1.3 mM NADH, 28 mM α-Ketoglutarate and 2.0 U GLDH, respectively. The homemade ceramic heating plate controlled the working electrode to work at 37 °C. A pH compensation algorithm based on piecewise linear interpolation could reduce the measurement error to less than 3.29 μM. The biosensor exhibited good linearity in the range of 0~300 μM with a detection limit of 0.65 μM NH4+. Compared with standard Nessler’s method, the recoveries were 93.71~105.92%. The biosensor was found to be stable for at least 14 days when refrigerated and sealed at 4 °C.

SNR improvement based on piecewise linear interpolation

Interpolation improves the resolution of the curve. Based on the stationary characteristics of the signal and the non-stationary characteristics of the noise, the theoretical proof indicates that the piecewise linear interpolation can improve the signal-to-noise ratio, which is further confirmed by simulation results.

Interp-SUM: Unsupervised Video Summarization with Piecewise Linear Interpolation

This paper addresses the problem of unsupervised video summarization. Video summarization helps people browse large-scale videos easily with a summary from the selected frames of the video. In this paper, we propose an unsupervised video summarization method with piecewise linear interpolation (Interp-SUM). Our method aims to improve summarization performance and generate a natural sequence of keyframes with predicting importance scores of each frame utilizing the interpolation method. To train the video summarization network, we exploit a reinforcement learning-based framework with an explicit reward function. We employ the objective function of the exploring under-appreciated reward method for training efficiently. In addition, we present a modified reconstruction loss to promote the representativeness of the summary. We evaluate the proposed method on two datasets, SumMe and TVSum. The experimental result showed that Interp-SUM generates the most natural sequence of summary frames than any other the state-of-the-art methods. In addition, Interp-SUM still showed comparable performance with the state-of-art research on unsupervised video summarization methods, which is shown and analyzed in the experiments of this paper.

A numerical method for two-dimensional Hammerstein integral equations

"In this paper we investigate a collocation method for the approximate solution of Hammerstein integral equations in two dimensions. As in [8], col- location is applied to a reformulation of the equation in a new unknown, thus reducing the computational cost and simplifying the implementation. We start with a special type of piecewise linear interpolation over triangles for a refor- mulation of the equation. This leads to a numerical integration scheme that can then be extended to any bounded domain in R2, which is used in collocation. We analyze and prove the convergence of the method and give error estimates. As the quadrature formula has a higher degree of precision than expected with linear interpolation, the resulting collocation method is superconvergent, thus requiring fewer iterations for a desired accuracy. We show the applicability of the proposed scheme on numerical examples and discuss future research ideas in this area."