Fast parametric curve matching (FPCM) for automatic spike detection

Epilepsy is a widely spread neurological disease, whose treatment often requires resection of the pathological cortical tissue. Interictal spike analysis observed in the non-invasively collected EEG or MEG data offers an attractive way to localize epileptogenic cortical structures for surgery planning purposes. Interictal spike detection in lengthy multichannel data is a daunting task that is still often performed manually. This frequently limits such an analysis to a small portion of the data which renders the appropriate risks of missing the potentially epileptogenic region. While a plethora of automatic spike detection techniques have been developed each with its own assumptions and limitations, non of them is ideal and the best results are achieved when the output of several automatic spike detectors are combined. This is especially true in the low signal-to-noise ratio conditions. To this end we propose a novel biomimetic approach for automatic spike detection based on a constrained mixed spline machinery that we dub as fast parametric curve matching (FPCM). Using the peak-wave shape parametrization, the constrained parametric morphological model is constructed and convolved with the observed multichannel data to efficiently determine mixed spline parameters corresponding to each time-point in the dataset. Then the logical predicates that directly map to verbalized text-book like descriptions of the expected interictal event morphology allow us to accomplish the spike detection task. The results of simulations mimicking typical low SNR scenario show the robustness and high ROC AUC values of the FPCM method as compared to the spike detection performed using more conventional approaches such as wavelet decomposition, template matching or simple amplitude thresholding. Applied to the real MEG and EEG data from the human patients and to rat ECoG data, the FPCM technique demonstrates reliable detection of the interictal events and localization of epileptogenic zones concordant with independent conclusions made by the epileptologist. Since the FPCM is computationally light, tolerant to high amplitude artifacts and flexible to accommodate verbalized descriptions of the arbitrary target morphology, it may complement the existing arsenal of means for analysis of noisy interictal datasets.

Efficient Intersection Computation of the Bezier and Hermite Curves with Axis Aligned Bounding Box

Cubic parametric curves are used in many applications including the CAD/CAM systems. Especially the Hermite, Bezier and Coons formulations of a cubic parametric curve are used in E2 and E3 space. This paper presents efficient algorithm for the intersection computation of a cubic parametric curve with the Axis Aligned Bounding Box (AAB Box). Usual solution is to represent the cubic curve by a polyline, i.e. actually by sampled points of the given curve. However, this approach is dependent on the sampling frequency and can lead to problems especially in CAD/CAM systems and numerically controlled machines use.

Shape optimization of magnetorheological damper piston based on parametric curve for damping force augmentation

Making full use of the magnetically controllable rheological properties of magnetorheological (MR) fluid, MR actuators have been applied in many engineering fields. To adapt to different application scenarios, parameters of MR actuators often need to be optimized. Previous MR actuator optimization was focused on finding optimal combinations of geometric dimensions and physical parameters that meet certain requirements. The parts with optimized dimensions were still in regular shape, which might not bring optimal damping performance. Therefore, in this paper, shape optimization of MR damper piston based on parametric curve is performed for the first time. First, the regional magnetic saturation problem in the previous prototype is stated. Then, the MR damper with normal piston is simulated as a reference. Later, Bezier curve, one of the typical parametric curves, is used to form the piston with optimized parameters, and the MR damper with optimized piston is also simulated. Finally, prototypes of the MR dampers with normal and optimized pistons are fabricated and tested. Compared with the MR damper with normal piston, the one with optimized piston has larger field dependent force and total damping force under relatively large current, with about 52% and 24% maximum increasing percentage, respectively. The controllable force range of the MR damper with optimized piston is also larger than that with normal piston.

Determining implicit equation of conic section from quadratic rational Bézier curve using Gröbner basis

The Gröbner Basis is a subset of finite generating polynomials in the ideal of the polynomial ring k[x 1,…,xn ]. The Gröbner basis has a wide range of applications in various areas of mathematics, including determining implicit polynomial equations. The quadratic rational Bézier curve is a rational parametric curve that is generated by three control points P 0(x 0,y 0), P 1(xi ,yi ), P 2(x 2,y 2) in ℝ2 and weights ω 0, ω 1, ω 2, where the weights ω i are corresponding to control points Pi (xi, yi ), for i = 0,1, 2. According to Cox et al (2007), the quadratic rational Bézier curve can represent conic sections, such as parabola, hyperbola, ellipse, and circle, by defining the weights ω 0 = ω 2 = 1 and ω 1 = ω for any control points P 0(x 0, y 0), P 1(x 1, y 1), and P 2(x 2, y 2). This research is aimed to obtain an implicit polynomial equation of the quadratic rational Bézier curve using the Gröbner basis. The polynomial coefficients of the conic section can be expressed in the term of control points P 0(x 0, y 0), P 1(x 1, y 1), P 2(x 2, y 2) and weight ω, using Wolfram Mathematica. This research also analyzes the effect of changes in weight ω on the shape of the conic section. It shows that parabola, hyperbola, and ellipse can be formed by defining ω = 1, ω > 1, and 0 < ω < 1, respectively.

Design of a Bézier-Profile Plate for Closely Spaced Multimodal Vibration Energy Harvesting

A cubic Bézier-profile plate for multimodal vibration energy harvesting was developed. The design of the plate was based on an optimization procedure in which the profile of the plate was optimized via the parameters of a cubic Bézier curve to meet the requirements. The multimodal energy harvesting of the plate exploited its first bending mode and its first twisting mode. The conversion of vibration energy into electrical energy was by electromagnetic induction with a magnet attached to a corner of the plate. These two closely spaced vibration modes achieved the multi-modal energy harvesting of the device. Prototypes of the device were manufactured using a numerical-control machining process. The experimental results were in good agreement with the design specifications. With the same base lengths, height, and thickness, the maximum von Mises stress of the proposed plate was much lower due to its bell-shaped profile. The cubic Bézier curve chosen for the plate profile was effective for design of the closely-spaced multimodal vibration energy harvester. With the flexibility of its controllable parametric curve, a high design freedom of the energy harvester with specified frequency ratios could be achieved.

Parametric Design and Optimization of the Profile of Autonomous Underwater Helicopter Based on NURBS

Autonomous Underwater Helicopter (AUH) is a disk-shaped Autonomous Underwater Vehicle (AUV), and it has comparative advantage of near-bottom hovering and whole-direction turn-around ability over the traditional slender AUV. An optimization design of its irregular geometric profile is essential to improve its hydrodynamic performance. A parametric representation of its profile is proposed in this paper using Non-Uniform Rational B-spline (NURBS) curve. The parametric representation of AUH profile is described with two decision variables and several data points. Based on this parametric curve, Computational Fluid Dynamics (CFD) simulation is carried out to evaluate its hydrodynamic performance with various parameters. A predication model is established over variables’ design space using Kriging surrogate model with CFD simulation results and a Genetic Algorithm (GA) procedure is conducted to find optimal design variables, which can produce an optimum lift-drag ratio. CFD verification results confirm that AUH profile with optimized design variables can increase its lift-drag ratio by 2.11 times compared with that of non-optimized ones. It demonstrates that the parametric representation and optimization procedure of AUH profile proposed in this paper is feasible, and it has a great potential in improving AUH’s performance.