Use Of Spline Interpolation Research Articles

Spline Interpolation and Deep Neural Networks as Feature Extractors for Signature Verification Purposes

Digital security in modern systems very often uses biometric, and increasingly, new implementations appear. Such applications can be found everywhere, even when picking up the package from courier, we certify its receipt through our signature on the tablet. However, verification of this form is not one of the simplest elements in information processing systems. Given the different sizes, angles, or writing conditions that may affect its stability, new methods to evaluate signatures are constantly needed. In this article, we propose the use of spline interpolation and two types of artificial neural networks to verify the identity of a person based on selected local and global features extracted from the image of a signature. Global features are extracted concerning interpolation and graphic processing methods, while local features are verified using convolutional neural networks. Both sets of features are used in the identity verification process. The article presents the model of the operation together with experiments, taking into account various parameters of the proposed extraction. We have reached an accuracy of 87.7% on the SVC2004 database.

Recommendations for motion correction of infant fNIRS data applicable to multiple data sets and acquisition systems

Despite motion artifacts are a major source of noise in fNIRS infant data, how to approach motion correction in this population has only recently started to be investigated. Homer2 offers a wide range of motion correction methods and previous work on simulated and adult data suggested the use of Spline interpolation and Wavelet filtering as optimal methods for the recovery of trials affected by motion. However, motion artifacts in infant data differ from those in adults’ both in amplitude and frequency of occurrence. Therefore, artifact correction recommendations derived from adult data might not be optimal for infant data. We hypothesized that the combined use of Spline and Wavelet would outperform their individual use on data with complex profiles of motion artifacts. To demonstrate this, we first compared, on infant semi-simulated data, the performance of several motion correction techniques on their own and of the novel combined approach; then, we investigated the performance of Spline and Wavelet alone and in combination on real cognitive data from three datasets collected with infants of different ages (5, 7 and 10 months), with different tasks (auditory, visual and tactile) and with different NIRS systems. To quantitatively estimate and compare the efficacy of these techniques, we adopted four metrics: hemodynamic response recovery error, within-subject standard deviation, between-subjects standard deviation and number of trials that survived each correction method. Our results demonstrated that (i) it is always better correcting for motion artifacts than rejecting the corrupted trials; (ii) Wavelet filtering on its own and in combination with Spline interpolation seems to be the most effective approach in reducing the between- and the within-subject standard deviations. Importantly, the combination of Spline and Wavelet was the approach providing the best performance in semi-simulation both at low and high levels of noise, also recovering most of the trials affected by motion artifacts across all datasets, a crucial result when working with infant data.

Test of an equal taxon–weight modification of Middeldorp's pollen density dating on data from varved sediments of Lake Gościąż, Poland

The cores from the varved sediments of Lake Gościąż enable testing of methods, based on pollen concentration, to reconstruct the time-basis of a palynological data set. The sediments' varves or annual laminae were counted and their thicknesses measured, and the pollen content was recorded at known intervals with regard to depth and time. In the present study, we have treated this pollen record as if the sediments were not annually laminated and as if, consequently, the time-basis of the pollen record was unknown. We reconstructed several different time-bases by means of two methods using pollen concentration, namely pollen density dating (PDD) according to Middeldorp and a modification of that method, which gives all included arboreal pollen-taxa the same weight: equal taxon–weight modification (ETW). After reconstructing these time-bases we compared them with the varve time-basis. We conclude that both PDD and ETW result in good time-bases. Our modification improves the performance of Middeldorp's method, largely because of the use of spline interpolation instead of a polynomial regression of varve age on pollen variables. An advantage of ETW over PDD is that ETW using a spline produces a good approximation of arboreal influx, preserving both trends and short-term variability, whereas PDD results in an arboreal influx being an unnaturally smooth function of time.

The Use of Spline Interpolation in Semi-Lagrangian Transport Models

The accuracy of interpolating semi-Lagrangian (SL) discretization methods depends on the choice of the interpolating function. Results from barotropic transport simulations on the sphere are presented, using either bicubic Lagrangian or bicubic spline SL discretization. The spline-based scheme is shown to generate excessively noisy fields in these simulations. The two methods are then tested in a one-dimensional advection problem. The damping and dispersion relations for the schemes are examined. The analysis and numerical experiments suggest that the excessive noise found in the spline-based simulations is a consequence of insufficient damping of the small scales for small and near-integer values of the Courant number. Inspection of the local Courant number for the two-dimensional spline-based simulation confirms this hypothesis. This noise can be controlled by adding a scale-selective diffusion term to the spline-based scheme, while retaining its excellent dispersion characteristics.

Use of Spline Interpolation in Slope Stability Analysis

Abstract: Spline Interpolation is a numerical procedure which is widely used to contour variables from irregularly spaced data. It has been shown that, under specific criteria, Spline Interpolation is equivalent to a well known estimation technique known as Kriging. Unlike Kriging, Spline Interpolation does not require a preliminary structural analysis. However, as a result, one should expect that the estimates obtained from Spline Interpolation are not as accurate as those obtained from Kriging. This paper examines the role of the Spline Interpolation technique in the prediction of pore‐water pressures in limit equilibrium slope stability analyses. The pore‐water pressures of interest are those at the base of a slice when the factor of safety is estimated using the method of slices and limit equilibrium techniques.The results of the study show that the Spline Interpolation technique is more accurate than the 4‐Way Interpolation technique. However, the Spline Interpolation technique requires significant computing time and computer memory. As a result, the number of known data points which can be analyzed (on a microcomputer) within a slope stability computer program is somewhat limited.

Iso‐solid diagrams of fat blends from thermal analysis data

AbstractThe use of spline interpolation between solid fat index (SFI) values obtained from calorimetric experiments to determine iso‐solid data is described. Computer programs control both the sampling of the data from the calorimeter and the calculation of iso‐solid values. This approach allows us to plot iso‐solid diagrams fully automa‐tically. Examples for cocoa butter/milk fat mixtures are given.