Comparing Reliability Between 3D Imaging And 2D Photography For External Nasal Anthropometry

Background: This study investigates and compare the reliability and reproducibility of two facial anthropometric methods about external nasal angles, 3D imaging and conventional 2D photography. Methods: 2D photograph images and 3D images about external nose of 30 volunteers were taken using digital camera and Morpheus 3D scanner. To evaluate intra-rater reliability, each images were taken over two different days for each subject by the same researcher. To evaluate inter-rater reliability, another researcher took each images for each subject on the first day. The reliability of each method for measuring 4 external nasal angle is obtained using intraclass correlation coefficient (ICC) and compared.Results: Inter-rater and intra-rater reliability of both 3D imaging and 2D photography had excellent agreement in all 4 nasal angles. In the nasofacial angular parameter, Inter-rater ICC, 2D photography was significantly higher than 3D imaging. Result of intra-rater ICC also showed both 3D imaging and 2D photography had good reliability in all 4 nasal angles. Similar to those of inter-rater ICC, nasofacial angular parameter showed statistically significant differences between 3D imaging and 2D photography.Conclusion: In terms of reliability, both 2D and 3D showed appropriate anthropometric results and considering its own advantage, each methods can be used complementarily.

SIS-BAM Algorithm for Angular Parameter Estimation of 2-D Incoherently Distributed Sources

For two-dimensional (2-D) incoherently distributed sources, this paper presents an effective angular parameter estimation method based on shift invariant structure (SIS) of the beamspace array manifold (BAM), named as SIS-BAM algorithm. In the proposed method, a shift invariance structure (SIS) of the observed vectors is firstly established utilizing a generalized array manifold of an uniform linear orthogonal array (ULOA). Secondly, based on Fourier basis vectors and the SIS, a beamspace transformation matrix can be performed. It projects received signals into the corresponding beamspace, so as to carry out dimension reduction of observed signals in beamspace domain. Finally, according to the SIS of beamspace observed vectors, the closed form solutions of the nominal azimuth and elevation are derived. Compared with the previous works, the presented SIS-BAM method provides better estimation performance, for example: 1) the computational complexity is reduced due to dealing with low-dimension beamspace signals and avoiding spectral search; 2) it can not only improve the angular parameter estimation accuracy but also have excellent robustness to the change of signal-to-noise ratio (SNR) and snapshot number. The theoretical analysis and simulation results confirm the effectiveness of the proposed method.

EXTERNAL ROLLING OF A POLYGON ON CLOSED CURVILINEAR PROFILE

The rolling of a flat figure in the form of an equilateral polygon on a curvilinear profile is considered. The profile is periodic. It is formed by a series connection of an arc of a symmetrical curve. The ends of the arc rely on a circle of a given radius. The equation of the curve, from which the curvilinear profile is constructed, is found. This is done provided that the centre of the polygon, when it rolls in profile, must also move in a circle. Rolling occurs in the absence of sliding. Therefore, the length of the arc of the curve is equal to the length of the side of the polygon. To find the equations of the curve of the profile, a first-order differential equation is constructed. Its analytical solution is obtained. The parametric equations of the curve are obtained in the polar coordinate system. The limits of the change of an angular parameter for the construction of a profile element are found. It is a part of the arc of the curve. According to the obtained equations, curvilinear profiles with different numbers of their elements are constructed.

Predictability of ANB, Beta, and YEN Angles as Anteroposterior Dysplasia Indicators in Gulbarga Population

In orthodontics, various methods of assessing sagittal jaw base relationship are formulated. Earlier, skeletal pattern was analyzed only clinically; however, after the introduction of cephalometrics by Broadbent and Hofrath in 1931, ANB and Beta angles are being used to describe skeletal discrepancies between the maxilla and mandible. YEN angle has also been used as a sagittal dysplasia indicator after its introduction in 2009. The aim of our study is to assess the predictability of ANB, Beta, and YEN angles as anteroposterior dysplasia indicators in skeletal class II malocclusion in Gulbarga population. This study is an attempt to check the variation as well as correlation existing between these 3 parameters, so that a more presumable and least variable parameter can be obtained. Total of 70 lateral cephalograms of skeletal class II patients were selected based on Down’s facial angle and tracing was carried out manually to measure ANB, Beta, and YEN angles. Statistical analysis was carried out to assess the coefficient of variation and the Pearson coefficient. Our study concluded that YEN angle is highly predictable and a homogenously distributed angular parameter used to assess sagittal discrepancy in class II patients compared to ANB and Beta angles.

Quasinormal modes of Dirac field in the Einstein–Dilaton–Gauss–Bonnet and Einstein–Weyl gravities

Quasinormal modes of Dirac field in the background of a non-Schwarzschild black holes in theories with higher curvature corrections are investigated in this paper. With the help of the semi-analytic WKB approximation and further using of Padé approximants as prescribed in Matyjasek and Opala (Phys Rev D 96(2):024011. arXiv:1704.00361 [gr-qc], 2017) we consider quasinormal modes of a test massless Dirac field in the Einstein–Dilaton–Gauss–Bonnet (EdGB) and Einstein–Weyl (EW) theories. Even though the effective potential for one of the chiralities has a negative gap we show that the Dirac field is stable in both theories. We find the dependence of the modes on the new dimensionless parameter p (related to the coupling constant in each theory) for different values of the angular parameter $$\ell $$ℓ and show that the frequencies tend to linear dependence on p. The allowed deviations of qausinormal modes from their Schwarzschild limit are one order larger for the Einstein–Weyl theory than for the Einstein–Dilaton–Gauss–Bonnet one, achieving the order of tens of percents. In addition, we test the Hod conjecture which suggests the upper bound for the imaginary part of the frequency of the longest lived quasinormal modes by the Hawking temperature multiplied by a factor. We show that in both non-Schwarzschild metrics the Dirac field obeys the above conjecture for the whole range of black-hole parameters.