Ellipse Approximation Research Articles

EFFICIENT AREA CALCULATION OF JACKFRUIT LEAVES: LEVERAGING GREEN'S THEOREM AND LEAST SQUARES FUNCTION

Leaves are an important part of a plant. As a place for photosynthetic organs, leaves can be used as indicators to assess a plant's growth and physiological performance. Leaf measurement is carried out as an important effort to collect leaf area data which is useful in analyzing a leaf's growth. This study aims to apply the green theorem to calculate leaf area and compare leaf area with the least square approximation, Simpson 1/3, the elliptic approach, and the millimeter block method, with the research object used being Jackfruit leaves. From this research, we obtain the results as follows leaf area by applying the green theorem by least square approximation is 5946.75 mm2, the leaf area with Simpson 1/3 method is 5938.25 mm2, the leaf area with ellipse approximation is 6850.23 mm2, and leaf area with millimeter block method is 5387.5 mm2. From the several approximation methods used in this study, it was found that by using the Least Square Quadratic approximation and the Simpson 1/3 method, effective results were obtained for the observed object because the functions of the Least Square Quadratic approximation and the Simpson 1/3 method are almost close to the actual function so that the results obtained are close to accurate with an area the original of the observed object is jackfruit leaves.

Measurement of the Macular Hole Diameter by En Face Slab Optical Coherence Tomography Reflectance Imaging.

PurposeTo evaluate the repeatability of macular hole (MH) diameter measurement on en face slab optical coherence tomography (OCT) reflectance images and assess its potential to predict visual acuity (VA).MethodsWe enrolled 27 eyes with full-thickness MHs in this study. Preoperative en face slab OCT reflectance images were obtained. Image binarization, ellipse approximation, and uncorrected measurement of minimum diameter, min(ef_uc), and maximum diameter, max(ef_uc), were performed using ImageJ. In addition, magnification-corrected diameters were calculated as min(ef) and max(ef) using the Littman and modified Bennett formulas. Spectral-domain OCT horizontal images were used as the conventional method for the analysis: min(conv) and max(conv). The inter-rater reliability of the method was evaluated by calculating the intraclass correlation coefficient (ICC). The following relationships were analyzed: (1) between logMAR VA and min(ef_uc), min(ef), and min(conv); and (2) between logMAR VA and max(ef_uc), max(ef), and max(conv).ResultsThe min(ef) and max(ef) values were 439.4 ± 240.5 µm and 720.7 ± 346.1 µm, respectively. The ICC values were 0.985 and 0.999 for min(ef) and max(ef), and 0.885 and 0.909 for min(conv) and max(conv), respectively. Multivariate analysis suggested that min(ef), but not min(ef_uc) or min(conv), was associated with pre- and postoperative logMAR VA. Furthermore, max(ef), but not max(ef_uc) or max(conv), was also closely correlated with pre- and postoperative logMAR VA.ConclusionsThe MH diameter measured by our method is highly reproducible and closely associated with VA compared to that measured by the conventional method.Translational RelevanceThe MH diameter measured by this modality might serve as an accurate biomarker to predict visual function in eyes with MH.

Effects of Recrystallization on Tensile Anisotropic Properties for IN738LC Fabricated by Laser Powder Bed Fusion

This study demonstrates the effects of recrystallization on tensile properties and the anisotropy of IN738LC, a typical γ’ precipitation-strengthened alloy, at both room and high temperatures via the laser powder bed fusion process. The nonrecrystallized columnar microstructure, subjected to standard IN738LC heat treatment up to 1120 °C, and the almost fully recrystallized microstructure, heat-treated at 1204 °C, were compared. The tensile properties strongly depend on whether recrystallization was completed as well as the tensile direction. This can be explained by microstructure characterization, featuring the Taylor factor in the tensile direction, average grain size estimated by ellipse approximation, and the relationship between the grain shape and tensile direction. The shape of the recrystallized grains and the distribution of coarse MC carbides inside the recrystallized grains were determined by the microstructure in an as-built state. In high-temperature tensile tests conducted in the horizontal direction, the separation of the columnar grains caused a brittle fracture. In contrast, dimples were observed at the fracture surface after recrystallization, indicating scope for further improvement in ductility.

Cell Behavior in Flow Passing Through Micromachined Gap

Abstract A microgap was created in the flow channel, and the behavior (deformation, rotation) of each cell when passing through the gap was investigated. A gap with a rectangular cross section (7 μm high, 0.4 mm wide, and 0.1 mm long) was manufactured in the middle part of the flow path by photolithography technique. Myoblasts (C2C12: mouse myoblast cell line) sparsely suspended in the medium were used for the test. Deformation of each cell passing through the microgap was observed with an inverted phase contrast microscope. From the contour of the image of each cell passing through the gap, several parameters were analyzed: the two-dimensional projected area, the degree of deformation by ellipse approximation, and the alignment of the major axis of the deformed cell. The experimental results show that the alignment of each cell tends to deviate from the flow direction as the larger projected two-dimensional area pressed in the gap.

High Accuracy Motion Detection Algorithm via ISM Band FMCW Radar

The conventional frequency modulated continuous wave (FMCW) radar accuracy range detection algorithm is based on the frequency estimation and additional phase evaluation which contains Fourier transform and frequency refining analysis in each chirp, so it has the disadvantages of being computationally expensive, and not being suitable for real-time motion measurement. In addition, if there are other objects near the target, the spectra of the clutter and the target will be adjacent and affect each other, making it more challenging to estimate the frequency of the target. In this paper, the analytical expression of the Fourier transform of the beat signal is presented and it can be seen that spectrum leakage makes the phase of Fourier transform no longer consistent with the real phase of signal. The change regularities of real and imaginary parts of Fourier transform are studied, and the corrected phase of ellipse approximation is given in the industrial, scientific, and medical (ISM) band. Accurate displacement can be obtained by accurate phase. The algorithm can filter the direct current (DC) offset which is mainly caused by stationary objects. The performance of the algorithm is evaluated by a radar system whose center frequency is 24.075 GHz and the bandwidth is 0.15 GHz; the measurement accuracy of displacement is 0.087 mm and the accuracy of distance is 0.043 m.

Sweeping Effects Modify Taylor’s Frozen Turbulence Hypothesis for Scalars in the Roughness Sublayer

AbstractTaylor’s frozen turbulence hypothesis (FTH) is investigated in the roughness sublayer of a sloped vineyard canopy using a spatial array of fine‐wire thermocouples and ultrasonic anemometers. The Ellipse Approximation (EA) method is applied to the measured space‐time temperature correlation function to delineate sweeping effects from advection velocity. Sweeping effects are explained primarily by the turbulence kinetic energy. Upon the removal of sweeping effects, the advection velocity is found to be commensurate with the mean velocity.

Distance between the center of the FAZ measured automatically and the highest foveal bulge using OCT-angiography in elderly healthy eyes

The center of the fovea, termed the foveola, is the area of highest visual acuity, has the highest density of cone photoreceptors. We investigated the distance between the automatically-determined center of the foveal avascular zone (FAZ) and the manually-determined highest foveal bulge (FB) point using single swept-source optical coherence tomography angiography (OCTA) instrument. This cross-sectional study included 49 eyes of 49 individuals (34 women and 15 men; median age: 68 years) with no history of ocular disorders. The FAZ in the superficial capillary plexus was automatically determined using the Kanno–Saitama macro method, and the center of the FAZ was automatically determined using ellipse approximation. Another candidate foveal center, the highest FB point, was determined manually on the serial cross-sectional B-scan images. As a result, the foveal center was manually identified as the highest FB point on B-scan OCTA images. The center of the FAZ was more likely to be located inferior to the highest FB point (p = 0.031). In participants with a total (linear) distance of more than 50 μm between the center of the FAZ and the highest FB point, the displacement was significantly more in the horizontal direction than in the vertical direction (p = 0.017). These results can be applicable to further studies regarding the spatial relationships between the center of the FAZ and the highest FB point in various macular diseases or previously-treated eyes.

Optimized geometry of the carotid artery cross-section: Comparison between circular and elliptical approximations in B-mode ultrasound images

Cross-sectional area (CSA) measurement obtained from transverse ultrasound images is the general method used for carotid artery stenosis calculation which assumes a circular CS, however, atherosclerotic stenosis may change the CSA geometry and lead to miscalculation. This study aims to determine the accuracy of circular or elliptical approximation of the normal and stenosed carotid artery CSA. Sixty transverse B-mode ultrasound images (30 from healthy and 30 from stenosed carotid arteries) were recorded. Contours of the internal lumen of the arteries were segmented and the encompassed lumen area was calculated. Based on the fitting accuracy and computational cost effectiveness, pattern search (PS) optimization algorithm was selected by which the parameterized equations of the circular and elliptical geometries were fitted to the segmented point clouds. Goodness of fit analysis of two geometries was carried out using root mean square error (RMSE) and the relative deviation of the approximated CSA. Results of this study showed that elliptical approximation better fits to the artery CS of carotid arteries, with the average RMSE of [Formula: see text] and [Formula: see text] pixels in healthy and [Formula: see text] and [Formula: see text] pixels in stenosed carotid arteries, respectively, for circle and ellipse approximation. Mean values of the relative deviation of the approximated CSA by circle and ellipse geometries were 5.14%[Formula: see text]±[Formula: see text]4.53% and 3.89%[Formula: see text]±[Formula: see text]4.19% in normal arteries; and 12.18%[Formula: see text]±[Formula: see text]10.94% and 4.59%[Formula: see text]±[Formula: see text]3.75% in stenosed arteries, respectively. This study represented that elliptical approximation provides increased accuracy for carotid artery CSA for both normal and stenosed carotid arteries.

Calculation of Nonlinear Stiffness of Rubber Pad under Different Temperatures and Prepressures

The static stiffness of rubber springs is affected by temperature and prepressure. In this thesis, the relationship between Young’s modulus and temperature of rubber was studied, and the quantitative relationship between them was determined. The approximate formula for calculating the static stiffness of rubber pads was further modified, and the ellipse approximation method and convexity coefficient correction method were proposed. In addition, the influence of temperature on geometric nonlinearity was considered. The formula for calculating nonlinear stiffness includes two variables: temperature and prepressure. The results of tests and theoretical calculations demonstrate that the nonlinear formula can be a good approximation and that it can meet the requirements of engineering applications.

Novel semi-automated algorithm for high-throughput quantification of adipocyte size in breast adipose tissue, with applications for breast cancer microenvironment

ABSTRACT The size distribution of adipocytes in fat tissue provides important information about metabolic status and overall health of patients. Histological measurements of biopsied adipose tissue can reveal cardiovascular and/or cancer risks, to complement typical prognosis parameters such as body mass index, hypertension or diabetes. Yet, current methods for adipocyte quantification are problematic and insufficient. Methods such as hand-tracing are tedious and time-consuming, ellipse approximation lacks precision, and fully automated methods have not proven reliable. A semi-automated method fills the gap in goal-directed computational algorithms, specifically for high-throughput adipocyte quantification. Here, we design and develop a tool, AdipoCyze, which incorporates a novel semi-automated tracing algorithm, along with benchmark methods, and use breast histological images from the Komen for the Cure Foundation to assess utility. Speed and precision of the new approach are superior to conventional methods and accuracy is comparable, suggesting a viable option to quantify adipocytes, while increasing user flexibility. This platform is the first to provide multiple methods of quantification in a single tool. Widespread laboratory and clinical use of this program may enhance productivity and performance, and yield insight into patient metabolism, which may help evaluate risks for breast cancer progression in patients with comorbidities of obesity. ABBREVIATIONS: BMI: body mass index.

Multi-parameter diagnostics for high-resolution in-situ measurements of single coal particle combustion

To study volatile combustion processes of single coal particles non-intrusive simultaneous multi-parameter measurements were performed. The experiment was carried out in a fully premixed flat flame burner with well-defined boundary conditions. For flame visualization high-speed luminescence imaging was combined with high-resolution high-speed OH-PLIF. To address particle size and shape a stereoscopic high-resolution backlight-illumination system was set up. Due to simultaneous recording of individual particle events the volatile combustion duration related to particle size, shape and velocity was measured. A comparison of luminescence imaging and OH-PLIF for flame visualization was investigated to define their application areas in coal combustion. The stereoscopic backlight-illumination setup was benchmarked to a well characterized bituminous coal. With a pixel resolution of ∼2.5 µm fine particle contours were resolved. The particle diameter and eccentricity were evaluated by an ellipse approximation. The experimental setup can be used to investigate different coal ranks and biomass in N2/O2 and CO2/O2 atmospheres in future.

Scaling analysis and SE simulation of the tilted cylinder-interface capillary interaction

The capillary interaction induced by a tilted cylinder and interface is the basic configuration of many complex systems, such as micro-pillar arrays clustering, super-hydrophobicity of hairy surface, water-walking insects, and fiber aggregation. We systematically analyzed the scaling laws of tilt angle, contact angle, and cylinder radius on the contact line shape by SE simulation and experiment. The following in-depth analysis of the characteristic parameters (shift, stretch and distortion) of the deformed contact lines reveals the self-similar shape of contact line. Then a general capillary force scaling law is proposed to incredibly grasp all the simulated and experimental data by a quite straightforward ellipse approximation approach.

Sequence of Gn LN polynomial curves approximating circular arcs

In this paper we derive a sequence of linear normal (LN) curves b 2 n of degree 2 n which are G n endpoint interpolations of a circular arc and have approximation order 2 n + 2 . This is an extension of the circle approximation method by LN Bézier curves given in Ahn and Hoffmann (2014) to all even degrees. We also extend the circle approximation to an ellipse approximation by G n LN curves of degree 2 n . An upper bound of the Hausdorff distance between the ellipse and its LN approximation is obtained. We illustrate our results through an LN approximation of convolution curves of ellipses and a spline curve.

3-D modelling and statistical properties of surface pits of corroded wire based on image processing technique

A method based on image processing was proposed in this study to visualize and model surface pits of high-strength steel wire. Surface measurement based on infinite focus was employed to measure the pit depth all over the cylindrical surface. Corrosion pits were visually identified by a binary image with a greyscale threshold clustered by the optimal entropy threshold method. Ellipse approximation was simulated to precisely characterize individual corrosion pits, and the geometric and morphological parameters of the corrosion pits were calculated and statistically analysed. The proposed method provides an effective approach for 3D corrosion pit modelling.

An integrative modeling approach for the efficient estimation of cross sectional tibial stresses during locomotion

The purpose of this research was to utilize a series of models to estimate the stress in a cross section of the tibia, located 62% from the proximal end, during walking. Twenty-eight male, active duty soldiers walked on an instrumented treadmill while external force data and kinematics were recorded. A rigid body model was used to estimate joint moments and reaction forces. A musculoskeletal model was used to gather muscle length, muscle velocity, moment arm and orientation information. Optimization procedures were used to estimate muscle forces and finally internal bone forces and moments were applied to an inhomogeneous, subject specific bone model obtained from CT scans to estimate stress in the bone cross section. Validity was assessed by comparison to stresses calculated from strain gage data in the literature and sensitivity was investigated using two simplified versions of the bone model-a homogeneous model and an ellipse approximation. Peak compressive stress occurred on the posterior aspect of the cross section (−47.5±14.9MPa). Peak tensile stress occurred on the anterior aspect (27.0±11.7MPa) while the location of peak shear was variable between subjects (7.2±2.4MPa). Peak compressive, tensile and shear stresses were within 0.52MPa, 0.36MPa and 3.02MPa respectively of those calculated from the converted strain gage data. Peak values from a inhomogeneous model of the bone correlated well with homogeneous model (normal: 0.99; shear: 0.94) as did the normal ellipse model (r=0.89–0.96). However, the relationship between shear stress in the inhomogeneous model and ellipse model was less accurate (r=0.64). The procedures detailed in this paper provide a non-invasive and relatively quick method of estimating cross sectional stress that holds promise for assessing injury and osteogenic stimulus in bone during normal physical activity.

Novel image processing approach for solving the overlapping problem in agriculture

A general problem in computer vision is the detection of objects when they are partially occluded. This problem also extends to the identification of horticultural/agricultural products (e.g., plants and crops), where recognition can be very cumbersome due to the heavy overlapping situations that one can find. This paper presents a novel approach to solve the recognition of plantlets under such conditions. The methodology consists of two major steps: (1) The simplification of the complexity of leaf shapes by using ellipse approximation. (2) The clustering of the leaves (ellipses) found into plantlets using active shape models. Shape models of experimental plants with 2, 3 and 4 leaves were tested to analyse the ability of the method to overcome the overlapping problem. The results indicate that the presented technique is able to perform identification of individual plantlets under overlapping situations, by first decreasing the complexity of their form and then using these simplified characteristics in a statistical shape model.

Ego-motion-compensated object recognition using type-2 fuzzy set for a moving robot

This paper presents an efficient stereovision-based motion compensation method for moving robots. The vision system of a moving robot enables it to detect and localize known objects in the images obtained from the camera mounted in its head. However, ego-motion causes some errors that need to be eliminated. We therefore propose an ego-motion compensation method that eliminates the errors in environment recognition caused by the ego-motion of a moving robot, in addition to efficiently improving recognition accuracy. The proposed method uses the disparity map obtained from three-dimensional (3D) vision and can be divided into three modules: segmentation, feature extraction, and estimation. In the segmentation module, we propose the use of extended type-2 fuzzy information theory (ET2FIT) to extract the objects. The results of using ET2FIT are then compared and analyzed to those obtained using type-2 fuzzy set and normal type-1 fuzzy set. The conventional fuzzy information theory [11] can only be applied to the binary image case. Therefore, we need to modify the existing method.In the feature extraction module, features are extracted using wavelet level-set transform, and least-square ellipse approximation is used in the estimation module to calculate the displacement for the rotation and translation between image sequences. The results of experiments indicate that our proposed method is highly effective when applied to moving robots, especially humanoid robots walking and operating in the real world.

Limitation of average eshelby tensor and its application in analysis of ellipse approximation

By the aid of irreducible decomposition, the average Eshelby tensor can be expressed by two complex coefficients in 2D Eshelby problem. This paper proved the limitation of complex coefficients based on the span of elastic strain energy density. More discussions yielded the constraints on the sampling of module and phase difference of complex coefficients. Using this information, we obtained that the maximum relative error is 65.78% after an ellipse approximation. These results, as a supplement to our previous paper, further implied that Eshelby's solution for an ellipsoidal inclusion could not be applied to non-ellipsoidal inclusions without taking care.

SOLVING A TYPE OF FUZZY LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

In this study, a type of fuzzy linear systems of differential equations (FLSDE) is analyzed. The dynamics of the system is definite (crisp) but initial value is a fuzzy set the alpha-cuts of which are ellipsoids. Many practice problems are modeled with FLSDE naturally. For example, the motion equation of a satellite, a free-falling body or a charged particle is definite, but its initial position and velocity are usually uncertain. In the researches made up to now, FLSDE the initial value of which is given with a vector of fuzzy numbers is analyzed. It means that each component of the initial position vector has independent uncertainty. Such an assumption simplifies soft calculations, but it causes either serious data loss or excessive data handling in fuzzy model. For example, in two-dimensional case, approximation of a circle with the most appropriate square (or, in the more general case, approximation of an ellipse with the most appropriate rectangle) will leave out the regions that are necessary to examine or vice versa. The initial value given as a fuzzy ellipsoid makes solution of FLSDE significantly difficult and impossible to apply the methods proposed in the previous researches. In this study, a method of solution for such type of FLSDE is suggested. The method is based on the fact that a linear transformation maps an ellipsoid to another ellipsoid. At any time the system's solution constitutes a fuzzy set, alpha-cuts of which are nested ellipsoids. The suggested approach and method of solution were explained on different examples.

AN ANALYSIS OF OCCUPANCY AND VACANCY LENGTHS OF TENANTS IN OFFICE BUILDINGS IN TOKYO FIVE WARDS

In this article, we analyze the occupancy length and vacancy length of tenants located in 52 rental office buildings in main five wards of Tokyo by using survival analysis. Since the rental office market tends to change periodically, we model the phenomenon of the periodic change of 2-dimentional time-series data of tenant and vacancy rate by the ellipse approximation method.Average occupancy length is about 13 years. Attributes contributing to the increase of the occupancy length are building age and image of the rental room and etc. Average vacancy length is about 88 days. Attributes contributing to the decrease of vacancy length are good rental room image, high land price per floor-space ratio and the market condition such that its state is recovery or boom state, and etc.