Weighted Quasi-Interpolant Spline Approximations of Planar Curvilinear Profiles in Digital Images

The approximation of curvilinear profiles is very popular for processing digital images and leads to numerous applications such as image segmentation, compression and recognition. In this paper, we develop a novel semi-automatic method based on quasi-interpolation. The method consists of three steps: a preprocessing step exploiting an edge detection algorithm; a splitting procedure to break the just-obtained set of edge points into smaller subsets; and a final step involving the use of a local curve approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), chosen for its robustness to data perturbation. The proposed method builds a sequence of polynomial spline curves, connected C0 in correspondence of cusps, G1 otherwise. To curb underfitting and overfitting, the computation of local approximations exploits the supervised learning paradigm. The effectiveness of the method is shown with simulation on real images from various application domains.

Adjustable Piecewise Quartic Hermite Spline Curve with Parameters

In this paper, the quartic Hermite parametric interpolating spline curves are formed with the quartic Hermite basis functions with parameters, the parameter selections of the spline curves are investigated, and the criteria for the curve with the shortest arc length and the smoothest curve are given. When the interpolation conditions are set, the proposed spline curves not only achieve C1-continuity but also can realize shape control by choosing suitable parameters, which addressed the weakness of the classical cubic Hermite interpolating spline curves.

C˜2 Continuous Cubic Hermite Interpolation Splines with Second-Order Elliptic Variation

In order to solve the deficiency of Hermite interpolation spline with second-order elliptic variation in shape control and continuity, c-2 continuous cubic Hermite interpolation spline with second-order elliptic variation was designed. A set of cubic Hermite basis functions with two parameters was constructed. According to this set of basis functions, the three-order Hermite interpolation spline curves were defined in segments 02, and the parameter selection scheme was discussed. The corresponding cubic Hermite interpolation spline function was studied, and the method to determine the residual term and the best interpolation function was given. The results of an example show that when the interpolation conditions remain unchanged, the cubic Hermite interpolation spline curves not only reach 02 continuity, but also can use the parameters to control the shape of the curves locally or globally. By determining the best values of the parameters, the cubic Hermite interpolation spline function can get a better interpolation effect, and the smoothness of the interpolation spline curve is the best.

Association of age with the timing of acute spine surgery–effects on neurological outcome after traumatic spinal cord injury

Purpose To investigate the association of age with delay in spine surgery and the effects on neurological outcome after traumatic spinal cord injury (SCI). Methods Ambispective cohort study (2011–2017) in n = 213 patients consecutively enrolled in a Level I trauma center with SCI care in a metropolitan region in Germany. Age-related differences in the injury to surgery interval and conditions associated with its delay (> 12 h after SCI) were explored using age categories or continuous variables and natural cubic splines. Effects of delayed surgery or age with outcome were analyzed using multiple logistic regression. Results The median age of the study population was 58.8 years (42.0–74.6 IQR). Older age (≥ 75y) was associated with a prolonged injury to surgery interval of 22.8 h (7.2–121.3) compared to 6.6 h (4.4–47.9) in younger patients (≤ 44y). Main reasons for delayed surgery in older individuals were secondary referrals and multimorbidity. Shorter time span to surgery (≤ 12 h) was associated with higher rates of ASIA impairment scale (AIS) conversion (OR 4.22, 95%CI 1.85–9.65), as mirrored by adjusted spline curves (< 20 h 20–25%, 20–60 h 10–20%, > 60 h < 10% probability of AIS conversion). In incomplete SCI, the probability of AIS conversion was lower in older patients [e.g., OR 0.09 (0.02–0.44) for’45-59y’ vs.’ ≤ 44y’], as confirmed by spline curves (< 40y 20–80%, ≥ 40y 5–20% probability). Conclusion Older patient age complexifies surgical SCI care and research. Tackling secondary referral to Level I trauma centers and delayed spine surgery imposes as tangible opportunity to improve the outcome of older SCI patients.

Constant Force Compliant Mechanisms Without Preloading

A constant force compliant mechanism generates an output force that keeps invariant in a large range of input displacement. Because of the constant force feature and the merits of compliant mechanisms, they are utilized in many applications. A problem in the current constant force compliant mechanisms is their preloading range that is a certain starting range of the input displacement. In the preloading displacement, the output force of a constant force compliant mechanism does not have the desired value. It goes up from zero value. The preloading displacement often occupies one quarter or more of the entire input displacement range, which weakens the performance of constant force compliant mechanisms. The preloading issue is eradicated in this research by using prebuckled beams as components for constructing constant force compliant mechanisms. It is difficult to synthesize constant force compliant mechanisms that are composed of prebuckled beams because of the intertwined force, buckling and deflection characteristics. In this research, the undeformed beams are represented by spline curves and controlled by its interpolation points. The synthesis of constant force compliant mechanisms is systemized as optimizing the design parameters of the composed prebuckled beams. Fully compliant constant force compliant mechanisms are synthesized without preloading. The synthesis solutions are validated by experimental results.

Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map

This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves.

Object-based tracking and nowcasting of gust fronts

&lt;p&gt;Thunderstorm gust fronts threaten human safety and property, especially in industries such as aviation and construction. The ability to predict the precise time and location of gust front arrivals would mitigate risk and reduce damage.&amp;#160;&lt;/p&gt;&lt;p&gt;Existing methods for nowcasting gust front locations are based on detecting the gust fronts from individual Doppler weather radars or scanning lidars. Even though these methods are locally effective, they have so far not been applied to large-scale radar mosaics to generate forecasts that could benefit society at large. To address this gap, an object-based method is proposed for nowcasting gust fronts by any number of ground-based Doppler weather radars. &amp;#160;&lt;/p&gt;&lt;p&gt;The gust fronts are first detected from the radar measurements and presented as objects consisting of spline curves. Given the one-dimensional geometry of the curves, existing object-based tracking methods, designed for tracking thunderstorms and based on two-dimensional polygons, cannot be applied to the gust front objects. Instead, a tracking method is formulated that matches multiple observations of the same gust front based on the location and length of the curves. The tracking considers possible splitting and merging of the gust front objects. After matching the gust front instances between consecutive timesteps, the location of the gust front is nowcast with a Kalman filter algorithm. &amp;#160;&lt;/p&gt;&lt;p&gt;The methodology is demonstrated with case studies of gust fronts related to mesoscale convective systems (MCS) in Finland. MCSs occur frequently in Finland during summer and cause significant wind and other storm-related damage. Spatially and temporally accurate forecasting of MCS events would aid preparedness and reduce the risk posed to society. The methodology presented in this work can be used to nowcast the gust front trajectory and thus increase preparedness especially for the wind damage related to MCS events. The methodology can also be combined with existing object-based methods for nowcasting convective storm cells, to create comprehensive hazard forecasting systems for thunderstorms.&lt;/p&gt;