Search Results (26)

Several important functions, including the gamma function, as well as several infinite sums, admit integral representations involving the Hankel contour. In addition, the large t asymptotic analysis of several recently derived identities satisfied by the Riemann zeta function requires the computation of the asymptotic form of certain integrals which also involve the Hankel contour; these integrals depend on a real parameter, $\alpha$. A rigorous asymptotic technique is presented here for computing such integrals to all orders. For certain values of $\alpha$, the relevant formula, in addition to an asymptotic series of explicit terms, also contains a specific integral. It is shown that, remarkably, the leading behavior of this integral can be written in the form of the leading order of the Bleistein integral. The latter integral arises in the implementation of the classical steepest descent method in the case that the stationary point coincides with one of the boundary points of the integral under consideration. Full article

The increase in global air traffic volumes has significant economic and ecological impacts. A key factor in this context is the development of the noise situation around airports. However, assessing the development of the noise situation at multiple airports simultaneously and in detail requires comprehensive calculations. Therefore, there is a strong need for a simple method to evaluate how the growth of air traffic affects the noise impact around airports, especially under considerations of different what-if scenarios. This can be achieved by assigning a noise-equivalent value to each aircraft that represents its noise impact. These noise points indicate how many movements of a reference aircraft would be required to produce approximately the same noise impact as one movement of the aircraft under consideration. The concept allows for an easy and quick assessment of aircraft noise by summing such noise points, because, as shown in this study, the noise point sum can directly be related to a change in noise levels and contour area. This article presents a promising method for determining noise points and applies it to aircraft groups from a recently proposed database of the German aircraft noise calculation method AzB. The noise point concept is verified at various airports, demonstrating its effectiveness in representing noise situations and developments. The differences of analyzed contour areas obtained via noise calculations and via the noise point concept remain below 3.6% over a generic 30-year forecast. Full article

Background/Objectives: A common approach to investigating visual form processing is through studying responses to visual stimuli that comprise illusory contours. Such stimuli induce contours where none exist physically and thus reveal the constructive nature of visual perception and the conditions that engender it. The present work used IC stimuli to study the development of visual form detection and extraction in infants and adults. Methods: Infant and adult participants viewed square stimulus forms with either real or illusory contours, while their looking behavior was measured with an eye tracker. Fixations of the stimuli were coded by region, distinguishing between the contours of the forms and within the forms themselves. Fixations were summed by region, and fixations on forms were interpreted to index the detection of coherent, whole forms. Fixations on contours (real and illusory) were interpreted to index the extraction of form edges. Results: Total form fixations differed by age. For real contours, fixations by infants exceeded those by adults; when contours were illusory, adult fixations were greater than those of infants. Contour fixations were similar between ages. Infants and adults both looked more at contours when illusory than when real. Conclusions: Together, the results provide new conclusions about change and continuity in the visual analysis of form and contour. The results suggest that the visual detection and binding of simple form structure appears to develop between infancy and adulthood. However, the exploration of contours that support the extraction of form contours from backgrounds appears to change little between infancy and adulthood. Full article

Aiming at the problems of the imprecise safety distance standards for low-altitude UAVs within complex low-altitude environments and the difficulty of managing heterogeneous vehicles, a UAV safety interval calibration method based on random heading is proposed. Firstly, a UAV clustering model based on K-Means++ was established for the performance characteristics of UAVs, using evaluation indexes such as contour coefficient, sum of squares of errors, Davidson–Bourdain index, etc. Then, combining this with the characteristics of UAVs with random heading, a UAV safety interval calibration model based on random heading was constructed, and the conflict probability and airspace utilization rate were determined and metered for UAV safety interval calibration. The experimental results showed that the profile coefficient, sum of squares of errors, and Davidson–Berding index of the iteratively optimized UAV clustering were optimized by 53.9%, 55.6%, and 46.6%, respectively, compared with the initial clustering results, and that the safe intervals calibrated in the experimental environment of a single category of UAVs were also applicable to the fusion airspace environment after validation. The research results can provide a theoretical basis and methodological support for the safety interval calibration of UAVs in low-altitude fusion operations. Full article

In this paper, the authors approach the problem of boundary condition synthesis (also defined as field continuation) in a doubly connected domain by the use of a Neural Network-based approach. In this innovative method, given a field problem (magnetostatic, in the test case shown here), a set of Finite Element Method simulations is performed in order to define the training set (in terms of the potential over a domain) by solving the direct problem; subsequently, the Neural Network is trained to perform the boundary condition synthesis. The performances of different Neural Networks are compared, showing the accuracy and computational efficiency of the method. Moreover, domains externally bounded by two different kinds of polygonal contours (L-shaped and three-segments, respectively) are considered. As for the latter, the effect of the concavity/convexity of the boundary is deeply investigated. To sum up, a classical field continuation problem turns out to be revisited and solved with an innovative approach, based on deep learning. Full article

Background: The need for frequent blood glucose (BG) monitoring and the inconveniences associated with self-monitoring of BG (SMBG) have driven the development of non-invasive approaches. Methods: This prospective study aimed to investigate the accuracy of glucose level calculation using the near-infrared spectroscopy (NIRS) technology Glucube^® system. People with Type 1 diabetes, Type 2 diabetes, prediabetes, and normal glucose metabolism were included. Over one week, individuals performed glucose measurements with the Glucube^® system and capillary blood fingersticks with a standard glucometer (Ascensia Contour^® Next). To assess the impact of the improvement in dexterity, the accuracy variables were compared with the point-of-care (POC) glucometer Accu-Chek^® Inform II in a one-week sub-study. Results: Overall, 105 subjects (mean age 53.8 ± 13.8 years, 50.5% female) participated, resulting in 1914 paired glucose measurements between 49 and 331 mg/dL. Total mean absolute relative difference (MARD) was 20.3%, MARD for values >100 mg/dL was 18.3%, and mean absolute deviation (MAD) for values <100 mg/dL was 24.9%. A total of 97.3% of measurements fell within A+B Parkes zones, and 58.8%, 76.9%, and 88.1% within +−20%, +−30%, or +−40% error, respectively. On completion, 62 participants (59%) fulfilled the one-week prospective sub-study. In this subgroup, the total MARD was reduced between day 1 and day 8 from 22.8 to 18.3% (p = 0.068). The percentages within Zone A were 51.6 vs. 61.2%, Zone B 46.8 vs. 33.9%, and Zone C 1.6 vs. 4.8%, and the sum of Parkes Zones A+B was 98.4 vs. 95.2% (p = 0.311) for day 1 and day 8, respectively. Conclusions: Glucube^® is a novel non-invasive system based on NIRS technology for monitoring blood glucose levels. Its promising capabilities support further research. Full article

Our study focuses on the governing equation of a finitely deformed flexible rod with strain waves. By utilizing the well-known Ablowita–Ramani–Segur (ARS) algorithm, we prove that the equation is non-integrable in the Painlevé sense. Based on the bifurcation theory for planar dynamical systems, we modify an auxiliary equation method to obtain a new systematic and effective method that can be used for a wide class of non-linear evolution equations. This method is summed up in an algorithm that explains and clarifies the ease of its applicability. The proposed method is successfully applied to construct wave solutions. The developed solutions are grouped as periodic, solitary, super periodic, kink, and unbounded solutions. A graphic representation of these solutions is presented using a $3D$ representation and a $2D$ representation, as well as a $2D$ contour plot. Full article

Purpose: When autocontouring based on artificial intelligence (AI) is used in the radiotherapy (RT) workflow, the contours are reviewed and eventually adjusted by a radiation oncologist before an RT treatment plan is generated, with the purpose of improving dosimetry and reducing both interobserver variability and time for contouring. The purpose of this study was to evaluate the results of application of a commercial AI-based autocontouring for RT, assessing both geometric accuracies and the influence on optimized dose from automatically generated contours after review by human operator. Materials and Methods: A commercial autocontouring system was applied to a retrospective database of 40 patients, of which 20 were treated with radiotherapy for prostate cancer (PCa) and 20 for head and neck cancer (HNC). Contours resulting from AI were compared against AI contours reviewed by human operator and human-only contours using Dice similarity coefficient (DSC), Hausdorff distance (HD), and relative volume difference (RVD). Dosimetric indices such as D_mean, D_0.03cc, and normalized plan quality metrics were used to compare dose distributions from RT plans generated from structure sets contoured by humans assisted by AI against plans from manual contours. The reduction in contouring time obtained by using automated tools was also assessed. A Wilcoxon rank sum test was computed to assess the significance of differences. Interobserver variability of the comparison of manual vs. AI-assisted contours was also assessed among two radiation oncologists for PCa. Results: For PCa, AI-assisted segmentation showed good agreement with expert radiation oncologist structures with average DSC among patients ≥ 0.7 for all structures, and minimal radiation oncology adjustment of structures (DSC of adjusted versus AI structures ≥ 0.91). For HNC, results of comparison between manual and AI contouring varied considerably e.g., 0.77 for oral cavity and 0.11–0.13 for brachial plexus, but again, adjustment was generally minimal (DSC of adjusted against AI contours 0.97 for oral cavity, 0.92–0.93 for brachial plexus). The difference in dose for the target and organs at risk were not statistically significant between human and AI-assisted, with the only exceptions of D_0.03cc to the anal canal and D_mean to the brachial plexus. The observed average differences in plan quality for PCa and HNC cases were 8% and 6.7%, respectively. The dose parameter changes due to interobserver variability in PCa were small, with the exception of the anal canal, where large dose variations were observed. The reduction in time required for contouring was 72% for PCa and 84% for HNC. Conclusions: When an autocontouring system is used in combination with human review, the time of the RT workflow is significantly reduced without affecting dose distribution and plan quality. Full article

Face images in the logarithmic space can be considered as a sum of the texture component and lighting map component according to Lambert Reflection. However, it is still not easy to separate these two parts, because face contour boundaries and lighting change boundaries are difficult to distinguish. In order to enhance the separation quality of these to parts, this paper proposes an illumination standardization algorithm based on extreme L0 Gaussian difference regularization constraints, assuming that illumination is massively spread all over the image but illumination change boundaries are simple, regular, and sparse enough. The proposed algorithm uses an iterative L0 Gaussian difference smoothing method, which achieves a more accurate lighting map estimation by reserving the fewest boundaries. Thus, the texture component of the original image can be restored better by simply subtracting the lighting map estimated. The experiments in this paper are organized with two steps: the first step is to observe the quality of the original texture restoration, and the second step is to test the effectiveness of our algorithm for complex face classification tasks. We choose the facial expression classification in this step. The first step experimental results show that our proposed algorithm can effectively recover face image details from extremely dark or light regions. In the second step experiment, we use a CNN classifier to test the emotion classification accuracy, making a comparison of the proposed illumination removal algorithm and the state-of-the-art illumination removal algorithm as face image preprocessing methods. The experimental results show that our algorithm works best for facial expression classification at about 5 to 7 percent accuracy higher than other algorithms. Therefore, our algorithm is proven to provide effective lighting processing technical support for the complex face classification problems which require a high degree of preservation of facial texture. The contribution of this paper is, first, that this paper proposes an enhanced TV model with an L0 boundary constraint for illumination estimation. Second, the boundary response is formulated with the Gaussian difference, which strongly responds to illumination boundaries. Third, this paper emphasizes the necessity of reserving details for preprocessing face images. Full article

In ultrasound B-mode imaging, the axial resolution (AR) is commonly determined by the duration or bandwidth of an excitation signal. A shorter-duration pulse will produce better resolution compared to a longer one but with compromised penetration depth. Instead of relying on the pulse duration or bandwidth to improve the AR, an alternative method termed filtered multiply and sum (FMAS) has been introduced in our previous work. For spatial-compounding, FMAS uses the autocorrelation technique as used in filtered-delay multiply and sum (FDMAS), instead of conventional averaging. FMAS enables a higher frame rate and less computational complexity than conventional plane-wave compound imaging beamformed with delay and sum (DAS) and FDMAS. Moreover, it can provide an improved contrast ratio and AR. In previous work, no explanation was given on how FMAS was able to improve the AR. Thus, in this work, we discuss in detail the theory behind the proposed FMAS algorithm and how it is able to improve the spatial resolution mainly in the axial direction. Simulations, experimental phantom measurements and in vivo studies were conducted to benchmark the performance of the proposed method. We also demonstrate how the suggested new algorithm may be used in a practical biomedical imaging application. The balloon snake active contour segmentation technique was applied to the ultrasound B-mode image of a common carotid artery produced with FMAS. The suggested method is capable of reducing the number of iterations for the snake to settle on the region-of-interest contour, accelerating the segmentation process. Full article

Objectives: Low-field MRI at 0.55 Tesla (T) with deep learning image reconstruction has recently become commercially available. The objective of this study was to evaluate the image quality and diagnostic reliability of knee MRI performed at 0.55T compared with 1.5T. Methods: A total of 20 volunteers (9 female, 11 male; mean age = 42 years) underwent knee MRI on a 0.55T system (MAGNETOM Free.Max, Siemens Healthcare, Erlangen, Germany; 12-channel Contour M Coil) and a 1.5T scanner (MAGNETOM Sola, Siemens Healthcare, Erlangen, Germany; 18-channel transmit/receive knee coil). Standard two-dimensional (2D) turbo spin echo (TSE), fat-suppressed (fs) proton density-weighted (PDw), T1w TSE, and T2w TSE sequences were acquired in approximately 15 min. In total, 2 radiologists blinded to the field strength subjectively assessed all MRI sequences (overall image quality, image noise, and diagnostic quality) using a 5-point Likert scale (1–5; 5 = best). Additionally, both radiologists evaluated the possible pathologies of menisci, ligaments, and cartilage. Contrast ratios (CRs) of different tissues (bone, cartilage, and menisci) were determined on coronal PDw fs TSE images. The statistical analysis included Cohen’s kappa and the Wilcoxon rank sum test. Results: The overall image quality of the 0.55T T2w, T1w, and PDw fs TSE sequences was diagnostic and rated similar for T1w (p > 0.05), but lower for PDw fs TSE and T2w TSE compared with 1.5T (p < 0.05). The diagnostic accordance of meniscal and cartilage pathologies at 0.55T was similar to 1.5T. The CRs of the tissues were not significantly different between 1.5T and 0.55T (p > 0.05). The inter-observer agreement of the subjective image quality was generally fair between both readers and almost perfect for the pathologies. Conclusions: Deep learning-reconstructed TSE imaging at 0.55T yielded diagnostic image quality for knee MRI compared with standard 1.5T MRI. The diagnostic performance of meniscal and cartilage pathologies was equal for 0.55T and 1.5T without a significant loss of diagnostic information. Full article

Fibre optic sensors using tilted fibre Bragg grating (TFBG) have high sensitivity for refractive index measurements. In order to achieve good metrological parameters of the measurement, an appropriate method of spectrum demodulation must be used. The method proposed in the article is an improvement of the spectral length algorithm. The spectral length parameter is treated as the sum of the derivative filter responses. In the original version, the first difference of spectrum elements was used, while this article proposes to use the wavelet transform to calculate the numerical derivative approximation. The advantage of this solution is an easy way to select the level of smoothing filtration by changing the scale parameter. The derivation is appropriate even for a relatively low signal-to-noise level. The approximation of the spectral length by the derivative calculated using the wavelet transform eliminates the high-frequency noise of the optical signal. The absolute value of determined spectral derivatives after significant smoothing can be used to estimate the wavelength of the decay of modes. After analyzing experimental data and performing calculations, it turns out that this is a linear method with better resolution than the contour length algorithm. Full article

Using a contour integral method, the de Montmort-Prudnikov sum is extended to derive a new series representation involving the incomplete gamma function. The series is uniformly convergent and completely analytical, which can be evaluated for general complex ranges of the parameters involved. Applications and evaluations of this formula are discussed. Full article

This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the Riemann Zeta function and fundamental mathematical constants, including Catalan’s constant. This representation of Catalan’s constant suggests it could be rational. Full article

The image of expressway asphalt pavement crack disease obtained by a three-dimensional line scan laser is easily affected by external factors such as uneven illumination distribution, environmental noise, occlusion shadow, and foreign bodies on the pavement. To locate and extract cracks accurately and efficiently, this article proposes a three-stage asphalt pavement crack location and segmentation method based on traditional digital image processing technology and deep learning methods. In the first stage of this method, the guided filtering and Retinex methods are used to preprocess the asphalt pavement crack image. The processed image removes redundant noise information and improves the brightness. At the information entropy level, it is 63% higher than the unpreprocessed image. In the second stage, the newly proposed YOLO-SAMT target detection model is used to locate the crack diseases in asphalt pavement. The model is 5.42 percentage points higher than the original YOLOv7 model on mAP@0.5, which enhances the recognition and location ability of crack diseases and reduces the calculation amount for the extraction of crack contour in the next stage. In the third stage, the improved k-means clustering algorithm is used to extract cracks. Compared with the traditional k-means clustering algorithm, this method improves the accuracy by 7.34 percentage points, the true rate by 6.57 percentage points, and the false positive rate by 18.32 percentage points to better extract the crack contour. To sum up, the method proposed in this article improves the quality of the pavement disease image, enhances the ability to identify and locate cracks, reduces the amount of calculation, improves the accuracy of crack contour extraction, and provides a new solution for highway crack inspection. Full article