Curvature Measurements Research Articles

Neural dissociation between computational and perceived measures of curvature

There is substantial evidence to suggest that preference for visual curvature is a reliable phenomenon. Yet, little is known about the ways in which the encoding of curvature in the brain contributes to hedonic evaluation while participants are actively engaged in making choices about objects varying in curvature. To address this question, we reanalyzed fMRI data collected while participants made aesthetic judgments (beautiful vs. not beautiful) and approach-avoidance decisions (enter vs. exit) in relation to measures of (a) computational curvature, (b) perceived curvature, (c) perceived angularity, and (d) aesthetic pleasure in the domain of architecture. Our results show that a region in early visual cortex (BA 17) encompassing largely areas V2-V3 is sensitive to variation in computational curvature across both beauty judgments and approach-avoidance decisions, whereas a region encompassing the fusiform gyrus (BA 37) exhibits sensitivity to perceived curvature only when participants made beauty judgments. These results contribute to our understanding of the neurobiological basis of curvature preference by demonstrating that the sensitivity of the visual cortex to computational curvature is context invariant, whereas the sensitivity of the fusiform gyrus to perceived curvature varies by context.

Method for Extracting Optical Element Information Using Optical Coherence Tomography

This study examines the measurement of film thickness, curvature, and defects on the surface or inside of an optical element using a highly accurate and efficient method. This is essential to ensure their quality and performance. Existing methods are unable to simultaneously extract the three types of information: thickness, curvature, and defects. Spectral-domain optical coherence tomography (SD-OCT), a non-invasive imaging technique with imaging depths down to the millimeter scale, provides the possibility of detecting the optical element components’ parameters. In this paper, we propose an error correction model for compensating delay differences in A-scan, field curvature, and aberration to improve the accuracy of system fitting measurements using SD-OCT. During data processing, we use the histogram-equalized gray stretching (IAH-GS) method to deal with strong reflections in the thin film layers inside the optics using individual A-scan averages. In addition, we propose a window threshold cutoff algorithm to accurately identify defects and boundaries in OCT images. Finally, the system is capable of rapidly detecting the thickness and curvature of film layers in optical elements with a maximum measurement depth of 4.508 mm, a diameter of 15 × 15 mm, a resolution of 5.69 microns, and a sampling rate of 70 kHz. Measurements were performed on different standard optical elements to verify the accuracy and reliability of the proposed method. To the best of our knowledge, this is the first time that thickness, curvature, and defects of an optical film have been measured simultaneously, with a thickness measurement accuracy of 1.924 µm, and with a difference between the calibrated and nominal curvature measurements consistently within 1%. We believe that this research will greatly advance the use of OCT technology in the testing of optical thin films, thereby improving productivity and product quality.

Large Range Curvature Measurement Using FBGs in Two-Core Fiber with Protective Coating

In this work, we propose a fiber Bragg grating (FBG)-based sensor for curvature measurements. Two gratings are inscribed through the protective coating in a specialty optical fiber using focused femtosecond laser pulses and point-by-point direct writing technology. One grating is inscribed on the central core adjacent to an air channel, while the other is inscribed on the eccentric core. The bending characteristics of the two-core fiber strongly depend on the bending direction due to the asymmetry of the fiber cores. A bending sensitivity of 58 pm/m−1 is achieved by the FBG in the eccentric fiber core over the curvature range of 0–50 m−1 . Temperature and humidity cross-sensitivity could be significantly reduced by analyzing the differences in peak shifts between the two gratings. The sensor features a large sensing range and good robustness due to the presence of its protective buffer coating, which makes it a good candidate for curvature sensing in engineering fields.

Interventricular abnormal septum displacement as contributory mechanism for impaired peak oxygen consumption and exercise cardiac output response in heart failure

Abstract Background In Heart failure (HF), the role of septum position and abnormal right ventricular (RV) geometry in determining exercise performance is unknown. Especially an abnormal interventricular septal (IVS) position is a well-known sign of RV pressure overload which affects left ventricular filling and output due to interdependence. Aim We postulated that an abnormal septum displacement during exercise and RV geometry alteration would affect peak exercise oxygen consumption (VO2) and cardiac output (CO) increase. Methods 17 HF patients with reduced ejection fraction (HFrEF) (mean age 71±12) underwent a cardiopulmonary exercise testing imaging (iCPET) with RV 3D-imaging analysis and were compared with a control population (mean age 67±14). 3D imaging of the RV chamber was examined off-line using the 4D RV TomTec software and obtained 3D mesh of the RV model using custom software to obtain the mean curvature value of IVS in 4 regions of: inflow tract (RVIT), outflow tract (RVOT), apical and body.We acquired measurements of curvature during end-diastole (ED) and at end systole (ES) phases and obtained a parametric curvature map. Results HF patients typically exhibited an abnormal of septal curve, with a more leftward configuration either at rest and under exercise (rest =−0.01±0.004 at ED, and −0.01±0.006 at ES; peak exercise= −0.01±0.004 at ED, and −0.01±0.004 at ES, Figure) compared to controls (rest=−0.02±0.003 at ED, and −0.02±0.005 at ES; peak exercise −0.02±0.008 at ED, and −0.03±0.006 at ES, Figure). Notably, the degree of the IVS curvature was found to linearly correlate with an impaired gas exchange performance as lower peak VO2 and a limited CO in HF (respectively r=0.62, p<0.001 and r=0.5, p<0.001 at ED during exercise; r=0.34, p<0.001 at ES during exercise, Figure). Conclusions In HF, the RV geometrical alterations reflected by an abnormal IVS displacement appear as novel contributory factors to a reduced exercise performance, impaired oxygen uptake and decreased CO.

New four-point bending test protocol for the strength grading of timber: relationship between local and global modulus of elasticity (MOE) of maritime pine

ABSTRACT This study focuses on the characterisation of maritime pine according to standards EN408 and EN384 required for timber grading. A comparison of the EN408 bending test setup is performed with a new four-point bending protocol, reducing as much as possible, the effects of the shear force in the span where the deflection is measured. The study highlights difficulties to estimate accurately, the elasticity modulus of wood by using EN408 bending test setup. This is probably due to inaccuracies in the measurements of small curvatures and due to the local heterogeneities of wood. An original four-point bending test is proposed with 75% of the span of the wood beams in pure bending. This configuration clearly exhibits the convergence of measurements, in comparison to EN408 setup. The deformations generated by this new loading protocol allow a better evaluation of the bending modulus E 0. Moreover, the study reveals that the proposed setup supplies an increase of elasticity modulus close to 20%. In addition, dynamic tests are also performed to characterise the Young’s modulus. The experimental results reveal a better agreement between static test, using the new four-point bending configuration and dynamic method, than considering EN408 as a reference.

Comparison of four light-response models using relative curvature measures of nonlinearity

Photosynthetic light response curves serve as powerful mathematical tools for quantitatively describing the rate of photosynthesis of plants in response to changes in irradiance. However, in practical applications, the daunting task of selecting an appropriate nonlinear model to accurately fit these curves persists as a significant challenge. Thus, there arises a need for a method to systematically evaluate the efficacy of such models. In the present study, four distinct nonlinear models, namely Exponential Model (EM), Rectangular Hyperbola Model (RHM), Nonrectangular Hyperbola Model (NHM), and Modified Rectangular Hyperbola Model (MRHM), were used to fit the relationship between light intensity and the rate of photosynthesis across 42 empirical datasets. The goodness of fit for each model was assessed using the root-mean-square error, and relative curvature measures of nonlinearity were employed to assess the nonlinear behavior of the models. In terms of goodness of fit, pairwise difference tests of the root-mean-square error revealed that there was little to choose among the four models, although RHM gave a marginally poorer fit. However, in terms of nonlinear behavior, EM not only provided the most favorable linear approximation performance at the global level, but also exhibited the best close-to-linear behavior at the individual parameter level among the four models across the 42 datasets. Consequently, the results strongly advocate for EM as the most suitable mathematical framework for fitting photosynthetic light response curves. These findings provide insights into the model assessment for nonlinear regression in describing the relationship between the photosynthetic rate and light intensity.

Repeatability and agreement of two swept-source optical coherence tomographers and scheimpflug imaging for measurements of corneal curvature

PurposeTo evaluate the repeatability and agreement of two swept-source optical coherence tomographers and Scheimpflug imaging for corneal curvature in healthy subjects to obtain data on the clinical application of a new device.MethodsThis prospective study was conducted in January and February 2021 with 100 healthy subjects at the Eye Hospital of Wenzhou Medical University. Simulated keratometry (Sim-K), posterior keratometry (Kp), total corneal power (TCP), and total corneal astigmatism (TCA) were measured with CASIA2, Anterion, and Pentacam. Within-subject standard deviation (Sw), repeatability coefficient (RC), coefficient of variation (CoV), and intraclass correlation coefficient (ICC) were used to assess inter-device repeatability. Bland–Altman analysis was performed to determine inter-device agreement.ResultsThe three devices showed good repeatability for Sim-K, Kp, and TCP with all ICC > 0.980. Pentacam showed the highest repeatability (ICC ≥ 0.993; ICC ≥ 0.993) while the CASIA2 demonstrated the lowest repeatability (ICC: ≥ 0.986; ICC: ≥ 0.985) for Sim-K and TCP. Anterion and CASIA2 revealed better repeatability (ICC ≥ 0.998; ICC ≥ 0.981) for Kp than Pentacam (ICC ≥ 0.980). Pentacam and Anterion showed good repeatability for TCA (ICC: 0.935 and 0.916), whereas the CASIA2 showed moderate repeatability (ICC: 0.836). Three instruments demonstrated good agreement with the maximum absolute 95% Limits of agreement (LoA) of 1.00 D for Sim-K, Kp, and TCP. Wide LoA were found for TCA with the maximum absolute 95% LoA ≥ 0.66 D between the three devices.ConclusionsIn healthy subjects, the three devices (Pentacam, Anterion and CASIA2) displayed comparable repeatability and accuracy for SimK, Kp, and TCP, and could be used interchangeably for these parameters. However, TCA measured by the three devices was not interchangeable.Trial registrationChinese Clinical Trial Registry Center (10/10/2020, ChiCTR2000038959).

Energy barriers govern catheter herniation during endovascular procedures: a 2.5D vascular flow model analysis.

Endovascular procedures rely on navigating guidewires, catheters and other devices through tortuous vasculature to treat disease. A critical challenge in these procedures is catheter herniation, in which the device deviates from its intended path, often irrecoverably. To elucidate the mechanics of herniation, we developed a physical flow model of the aortic arch that enables direct measurement of device curvature during experimentally simulated neuroendovascular procedures conducted from an upper arterial access. Combined with measurements of initial, unstressed device shapes and flexural rigidities, the method enables the experimental estimation of the device bending energies during these simulated procedures. Characteristic energy profiles revealed distinct stages in both herniation and successful navigation, governed by the interplay between device properties and vascular anatomy. A deterministic progression from successful navigation to herniation was identified, with catheter systems following paths determined by measurable energy barriers. Increasing guidewire stiffness or decreasing catheter stiffness reduced the energy barrier for successful navigation while increasing that for herniation. This framework enables the prediction of endovascular herniation risk and offers unique insight into improved device design and clinical decision-making.

Regional-scale, high-resolution measurements of hilltop curvature reveal tectonic, climatic, and lithologic controls on hillslope morphology

Climate, tectonics, lithology, and biology are encoded within the morphology of landforms. Hillslopes record uplift and erosion rate through hilltop curvature, in which sharper, more convex hilltops correspond with more rapid erosion rates. However, past hilltop curvature studies that map uplift and erosion rates have been limited to small spatial scales largely due to relatively slow speeds of curvature measurement techniques. This lack of regional-scale observations has made deconvolving the relative contributions of tectonics, climate, and lithology to hillslope morphology a challenge. Here, we used high performance computing and continuous wavelet transforms of topography to rapidly map hilltop curvature in the steep and dissected Oregon Coast Range (OCR) and the adjacent gentler Cascadia Forearc Lowland (CFL) in western Oregon, amounting to ∼43,000 km2 of 1-meter lidar data. We additionally compared mapped hilltop curvature to published erosion rates derived from cosmogenic 10Be, including 11 newly sampled watersheds. We observed that hilltops are systematically sharper in the OCR than in the CFL, and we noted a linear relationship between catchment-averaged erosion rate and hilltop curvature, consistent with previous observations and theory that erosion rate scales linearly with hilltop curvature in soil-mantled landscapes. The boundary between the OCR and CFL, as demarcated by hilltop curvature, is often abrupt and occurs across mapped structures that separate disparate baselevels but where lithology and mean annual precipitation remain constant. Thus, while we observed significant variability in hilltop curvature that results from secondary lithologic and climatic controls, our results demonstrate that hillslope morphology in western Oregon is set primarily by uplift via tectonically-controlled baselevel lowering rates. These regional interpretations additionally highlight the computational advantages of the wavelet transform for rapidly quantifying hilltop curvature.

Dissociated urethral plate Onlay and standard Onlay urethroplasty for mid-distal hypospadias: A comparative study

BackgroundUrethral plate(UP) reserved Onlay urethroplasty currently had been widely used in mid-distal hypospadias. However, for children with 15-30° bending after degloving, only dorsal tunica albuginea plication was performed to correct penile ventral curvature(VC), and long-term follow-up showed a high recurrence rate of penile curvature. We developed a modified Onlay urethroplasty which dissociated the UP and completely removed the tissue beneath UP to fully correct penile curvature, and compared it with the standard Onlay urethroplasty to explore its rationality and feasibility. MethodsWe prospectively collected clinical data from 68 children with hypospadias who underwent standard or modified Onlay urethroplasty between September 2019 and June 2021, and evaluated interim outcomes to identify the complications between two groups. And we conducted histological examination of the tissue beneath the UP. ResultsA total of thirty-two patients underwent modified Onlay urethroplasty. Intraoperative curvature measurements showed that 37.5% (12/32) of patients had completely straightened their penis after dissecting UP and removing fibrous tissue beneath it. A total of thirty-six patients underwent standard Onlay urethroplasty. Totally five fistulas were reported in the first and second groups, respecitively as well as the complication rates were 15.6% and 13.9%, respectively (P > 0.05). The histological results showed that the tissue below the UP contains a large amount of collagen, mainly type I collagen. ConclusionThe dissociated UP Onlay urethroplasty can maximally remove factors limiting penis growth and completely correct penile curvature, without increasing the incidence of postoperative complications.Therefore, we recommend the application of improved Onlay urethroplasty in children with mid-distal hypospadias.

A Simultaneous Measurement Sensor for Temperature and Curvature Based on Congruent Quasi-Helical Long-Period Fiber Grating.

This article presents a long-period fiber-grating sensor based on a congruent quasi-helical structure (CQH-LPFG) with the two-parameter measurement of both temperature and curvature. The CQH-LPFG sensor was manufactured using a high-frequency CO2 laser, and an innovative quasi-helical structure was introduced into the two-parameter measurement of the temperature and curvature of the optical fiber sensor with excellent results. The experiment and analysis demonstrate that the curvature sensitivities of the three resonance peaks in the 1440 nm to 1540 nm transmission spectrum were 11.88 nm/m-1, 8.05 nm/m-1, and 11.11 nm/m-1, and the curvature varied ranging from 0.156 m-1 to 0.494 m-1. The three resonance peaks showed temperature responsivities of 29.87 pm/°C, 24.65 pm/°C, and 36.85 pm/°C, respectively, and the linear fit was of excellent quality. In the case of measuring both curvature and temperature changes simultaneously, the resonant peak wavelength of the CQH-LPFG sensor was demodulated through matrix analysis, with dip A and dip C providing superior simultaneous measurements. These features make it a promising candidate for applications such as engineering machinery and the health inspection of buildings.

Structural Magnetic Resonance Imaging-Based Surface Morphometry Analysis of Pediatric Down Syndrome.

Down syndrome (DS) is a genetic disorder characterized by intellectual disability whose etiology includes an additional partial or full copy of chromosome 21. Brain surface morphometry analyses can potentially assist in providing a better understanding of structural brain differences, and may help characterize DS-specific neurodevelopment. We performed a retrospective surface morphometry study of 73 magnetic resonance imaging (MRI) examinations of DS patients (aged 1 day to 22 years) and compared them to a large cohort of 993 brain MRI examinations of neurotypical participants, aged 1 day to 32 years. Surface curvature measurements, absolute surface area measurements, and surface areas as a percentage of total brain surface area (%TBSA) were extracted from each brain region in each examination. Results demonstrate broad reductions in surface area and abnormalities of surface curvature measurements across the brain in DS. After adjusting our regional surface area measurements as %TBSA, abnormally increased presentation in DS relative to neurotypical controls was observed in the left precentral, bilateral entorhinal, left parahippocampal, and bilateral perirhinal cortices, as well as Brodmann's area 44 (left), and the right temporal pole. Findings suggest the presence of developmental abnormalities of regional %TBSA in DS that can be characterized from clinical MRI examinations.

In-Fiber Hybrid Structure Sensor Based on the Vernier Effect for Vector Curvature and Temperature Measurement

A vector curvature and temperature sensor based on an in-fiber hybrid microstructure is proposed and experimentally demonstrated. The proposed scheme enables the dimensions of the Fabry–Perot and Mach–Zehnder hybrid interferometer to be adjusted for the formation of the Vernier effect by simply changing the length of a single optical fiber. The sensor is fabricated using a fiber Bragg grating (FBG), multimode fiber (MMF), and a single-hole dual-core fiber (SHDCF). The sensor exhibits different curvature sensitivities in four vertical directions, enabling two-dimensional curvature sensing. The temperature and curvature sensitivities of the sensor were enhanced to 100 pm/°C and −25.55 nm/m−1, respectively, and the temperature crosstalk was minimal at −3.9 × 10−3 m−1/°C. This hybrid microstructure sensor technology can be applied to high-sensitivity two-dimensional vector curvature and temperature detection for structural health monitoring of buildings, bridge engineering, and other related fields.

Large measurement range curvature sensor based on all-fiber Mach-Zehnder interferometer using triple-ring-core few-mode fiber

This study experimentally demonstrates a large measurement range curvature sensor based on a Mach-Zehnder interferometer (MZI) in a triple-ring-core fiber (TRCF). The sensor is fabricated by fusion splicing a segment of TRCF between two pieces of single-mode fiber (SMF), forming the SMF-TRCF-SMF sandwich structure. Since the TRCF can support the propagation of a few guided modes, the fundamental mode interferes with high-order modes in the sensing part to produce a periodic interference spectrum. Bending causes the effective refractive index of the mode to change, which shifts the interference spectrum. The bending measurement is achieved by monitoring the wavelength variation of interference dips. The proposed sensors can realize curvature measurements up to 100 m-1, with a bending sensitivity of -225.9 pm/m-1. It is believed that the proposed MZI sensor may have potential applications in robot hand gesture recognition and control.

Fully Automated Measurement of Cobb Angles in Coronal Plane Spine Radiographs.

Background/Objectives: scoliosis is a three-dimensional structural deformity characterized by lateral and rotational curvature of the spine. The current gold-standard method to assess scoliosis is the measurement of lateral curvature of the spine using the Cobb angle in coronal plane radiographs. The interrater variability for Cobb angle measurements reaches up to 10°. The purpose of this study was to describe and assess the performance of a fully automated method for measuring Cobb angles using a commercially available artificial intelligence (AI) model trained on over 17,000 images, and investigate its interrater/intrarater agreement with a reference standard. Methods: in total, 196 AP/PA full-spine radiographs were included in this study. A reference standard was established by four radiologists, defined as the median of their Cobb angle measurements. Independently, an AI-based software, IB Lab SQUIRREL (version 1.0), also performed Cobb angle measurements on the same radiographs. Results: after comparing the readers' Cobb angle end vertebrae selection to the AI's outputs, 194 curvatures were considered valid for performance assessment, displaying an accuracy of 88.58% in end vertebrae selection. The AI's performance showed very low absolute bias, with a mean difference and standard deviation of differences from the reference standard of 0.16° ± 0.35° in the Cobb angle measurements. The ICC comparing the reference standard and the AI's measurements was 0.97. Conclusions: the AI model demonstrated good results in the determination of end vertebrae and excellent results in automated Cobb angle measurements compared to radiologists and could serve as a reliable tool in clinical practice and research.

Investigation into the impact of charging rates on the stress development within silicon composite electrodes.

Silicon, renowned for its remarkable energy density, has emerged as a focal point in the pursuit of high-energy storage solutions for the next generation. Nevertheless, silicon electrodes are known to undergo significant volume expansion during the insertion of lithium ions, leading to structural deformation and the development of internal stresses, and causing a rapid decline in battery capacity and overall lifespan. To gain deeper insights into the intricacies of charge rate effects, this study employs a combination of in situ measurements and computational modeling to elucidate the cyclic performance of composite silicon electrodes. The findings derived from the established model and curvature measurement system unveil the substantial alterations in stress and deformation as a consequence of varying charge rates. Notably, the active layer experiences compressive forces that diminish as the charge rate decreases. At a charge rate of 0.2, the active layer endures a maximum stress of 89.145 MPa, providing a comprehensive explanation for the observed deterioration in cycling performance at higher charge rates. This study not only establishes a fundamental basis for subsequent stress analyses of silicon electrodes but also lays a solid foundation for further exploration of the impact of charge rates on composite silicon electrodes.

Comparison of egg-shape equations using relative curvature measures of nonlinearity

A 2-dimensional (2D) egg-shape equation can be used to construct a 3D egg geometry based on the hypothesis that an egg is a solid of revolution, which helps to calculate egg volume and surface area. The parameters in the 2D egg-shape equation are potentially valuable for providing a clue to the ecology and evolution of avian eggs. In this study, the 5-parameter Preston equation (PE), the 4-parameter Troscianko equation (TE), and another 2 egg-shape equations, were compared in describing real 2D egg-shape data of 300 Gallus gallus domesticus eggs and additional 50 eggs that represented the variation in avian egg geometries. Adjusted root-mean-square error was used to quantify each equation's prediction error. Given that the 4 equations are nonlinear, relative curvature measures of nonlinearity were used to assess the extent of nonlinearity in each equation. PE was found to be the best among the 4 equations in terms of adjusted root-mean-square error and minimizing nonlinearity. The empirically determined egg volumes using a graduated cylinder were compared with the predicted egg volumes using the formula for a solid of revolution based on 2D predictions from the 4 egg-shape equations. There were negligible differences in the predicted egg volumes and surface areas among the 4 equations, indicating that these equations are all valid in calculating egg volume and surface area. In addition, we proposed a 5-parameter TE and found that it outperformed the above 4 equations in describing the 2D egg shape of G. gallus, but was less general than PE for other egg shapes. This work provides statistical evidence to show which equation is the best for describing the geometry of avian eggs and nondestructively calculating their volume and surface area, helping to classify poultry eggs into different grades according to the morphological characteristics of the eggs.

Concatenated Bragg grating fiber-optic sensors for simultaneous measurement of curvature, temperature, and axial pressure

Abstract. This paper presents the development and evaluation of four sensors based on multiple fiber Bragg grating (FBG) constellations embedded in a silicon dioxide single-mode fiber (SMF) for simultaneous measurement of pressure, temperature, and bending curvature. We applied dimension and material variations – including core, cladding, and coating dimensions; coating material; and the number and arrangement of the FBGs – to optimize the reflected signal response and increase information density. A bootstrap-aggregated ensemble of decision trees was used to evaluate the sensor signal. The results show that adjusting the cladding-to-coating ratio led to significant improvements in pressure and bending prediction performance. Additionally, two combined FBGs were fabricated to form a fiber Bragg grating Fabry–Pérot interferometer, which enabled the detection of curvature with a root-mean-square error (RMSE) of 0.0034 L mm−1 (R2=1), axial pressure with an RMSE of 0.0564 bar (R2=0.99), and temperature with an RMSE of 0.0265 °C (R2=1). At the time of writing, there is no commercially available instrument that can perform these measurements simultaneously.

Measuring avian bill size: comparing and evaluating 3D surface scanning with traditional size estimates in Australian birds

Unidimensional measurements for estimating bill size, like length and width, are commonly used in ecology and evolution, but can be criticised due to issues with repeatability and accuracy. Furthermore, formula‐based estimates of bill surface area tend to assume uniform bill shapes across species, which is rarely the case. 3D surface scanning can potentially help overcome some such issues by collecting detailed external morphology and direct measurements of surface area, rather than composite estimates of size. Here, we evaluate the use of 3D surface scanners on avian museum specimens to test the repeatability of 3D‐based measurements and compare these to traditional formula‐based methods of estimating bill size from unidimensional measurements. Using 28 Australian bird species, we investigate inter‐observer repeatability of surface area measurements from 3D surface scans. We then compare 3D‐based size estimates to formula‐based size estimates to infer the accuracy and precision of formula‐based measurements of bill surface area. We find that morphometric measurements from 3D surface scans are highly repeatable between observers, without the need for extensive training, demonstrating an advantage over unidimensional measuring methods, like callipers. When comparing 3D‐based measurements to formula‐based estimates of bill surface area, most formulae for estimating size consistently underestimate surface area, and with considerable variation between species. Where 3D scanning is not possible, we find that a commonly used cone formula for estimating bill size is most precise across diverse bill shapes, therefore supporting its use in interspecific contexts. However, we find that incorporating an additional unidimensional measure of bill curvature into formulae improves the accuracy of the calculated area. Our results reveal the high potential for 3D surface scanners in avian morphometric research, especially for studies necessitating large sample sizes collected by multiple observers, and gives suggestions for formula‐based approaches to estimate bill size.

Quantitative analysis of sagittal curvatures of the tibial plafond by computed tomography.

Although the talar morphology has been well understood, studies on the corresponding tibial plafond are still lacking. Based on computed tomography (CT) data, this quantitative study divided the tibial plafond into anterior and posterior regions on five sagittal sections. The objectives of this study were (I) to determine whether the sagittal curvatures of the tibial plafond can be quantitatively and accurately described using the double-diameter method; (II) to compare the difference between the anterior and posterior diameters on five sagittal sections. In this study, CT data were collected from 100 adult ankles, and the three-dimensional (3D) ankle joint model was reconstructed using CT images. An anatomical coordinate system of the 3D ankle joint model was created to establish the standard coronal and sagittal planes. The measurement outcomes of sagittal curvatures included: the anterior and posterior diameters, the distal tibial arc length (TiAL) and the distal tibial mortise depth (TMD) on five sagittal sections (the most medial, medial 1/4, middle, lateral 1/4 and the most lateral section). Subgroup analysis was performed to compare the differences between males and females. Analysis of the sagittal curvatures showed that the anterior diameter of tibial plafond was significantly smaller than the posterior diameter on five sagittal sections with a mean difference ranging from 3.9 to 6.8 mm (P<0.001). For the anterior diameters, the anteromedial curve had the smallest diameter (35.3±5.3 mm), and the anterolateral curve had the largest diameter (38.0±5.8 mm). For the posterior diameter, the posteromedial curve had the smallest diameter (39.2±6.4 mm), and the posterolateral 1/4 curve had the largest diameter (43.5±6.9 mm). One-way analysis of variance (ANOVA) revealed significant differences in the anterior and posterior diameters among five groups (P<0.012). Subgroup analysis showed that gender partly affected the results of sagittal curvature measurements. The sagittal curvatures of the tibial plafond can be described quantitatively and accurately using anterior and posterior diameters. Our study showed that there were significant differences between the anterior and posterior diameters, and gender was an important factor influencing the sagittal curvatures of the tibial plafond.