Ellipse Fitting Research Articles

A novel methodology for water-sensitive papers analysis focusing on the segmentation of overlapping droplets to better characterize deposition pattern

Water-sensitive papers (WSPs), as an artificial target, have been generally used to evaluate spray quality in pesticide applications. Though many tools were available to analyze WSPs, they were not effective in processing the presented overlapping droplets, which prevented accurate quantification of spray quality. Here, a novel methodology was proposed to analyze WSPs, focusing on the segmentation of overlapping droplets based on concave point detection and ellipse fitting. Up to 553 WSPs obtained from field trials in apple trees were used to validate this methodology. A high overall segmentation accuracy of 77.8% was achieved for the WSPs with coverage below 25%, which allowed to precisely characterize the corresponding deposition pattern. A universal linear relationship was observed between the droplet density and coverage, independent of the sprayer and canopy characteristics. In addition, the droplet size distributions for all spray applications showed a similar trend. As the proposed methodology was not effective to segment the complex overlapping spots on the WSP with high coverage (>25%), simulated WSPs were generated to estimate the deposition pattern of high coverage based on the droplet size distribution deposited on the WSPs with low coverage. A linear relationship with a much higher slope was observed between droplet density and coverage for the high deposition, which enabled an approximate estimation of the corresponding droplet density. In general, the proposed approaches allowed to obtain more accurate spray quality indicators from the WSP collectors and could be widely used for spray application evaluation to promote precision spraying.

In situ stress field detection of stress-induced strong anisotropy media based on Mohr circle theory

The prediction and evaluation of in situ stress field plays an important role in many engineering fields. How to accurately obtain in situ stress field information of a large area becomes a focus in geophysics. Wide-azimuth seismic data establish a bridge between in situ stress and rock anisotropy, making it possible to predict the large-scale in situ stress field. Ellipse fitting (EF) is a common method to predict in situ stress according to the characteristics of seismic attribute change with azimuth, but there are some problems such as 90° ambiguity in orientation prediction and the unclear stress-related physical meaning of the fitting parameters. Moreover, the variation of azimuthal seismic attribute in strongly anisotropic media does not meet ellipse hypothesis, which also limits the application of EF method. Through mathematical simulation experiment, the mechanism of seismic response characteristics under orthotropic stress situation is explored. Focusing on the property of strong anisotropy induced by in situ stress in subsurface media, a new stress circle fitting (SCF) method for in situ stress prediction is established by combining the azimuthal variation characteristics of reflection coefficient with the Mohr circle theory. The fitting results have clear physical significance related to in situ stress. In addition, through analysis of fitting parameters, the influence of 90° ambiguity problem can be eliminated. EF and SCF methods are applied to actual wide-azimuth seismic data. Comparison indicates that the SCF result is more suitable for azimuth seismic data in strongly anisotropic media. Compared to EF, in situ stress field distribution predicted by SCF method is more reasonable. The actual imaging logging results also prove the accuracy of SCF method.

High Precision and Stabilization PGC Demodulation Scheme for Fiber Optic Interferometric Sensors

Ellipse fitting algorithm (EFA) has attracted tremendous interest in phase demodulation schemes to eliminate nonlinear errors, however, there is an inherent drawback that the EFA fails to work when the desired phase signal is small. A high precision and stabilization phase generated carrier (PGC) demodulation scheme using hyper least squares (LS) fitting of ellipse is proposed for the first time, to our best knowledge. The contaminated quadrature signals obtained after mixing and low pass filtering are processed by a hyper LS based EFA to eliminate nonlinear errors. Hyper LS relies on algebraic distance minimization with a carefully chosen scale normalization and statistical bias is eliminated up to second order noise terms, which is far superior to the traditional LS. The temporary stability of the fitting result is used to resolve the drawback of the EFA. A module for judging the ellipse arc of quadrature signals is developed. The EFA is executed when the Lissajous figure is larger than 1/4 ellipse arc, otherwise the fitting result of the previous executed EFA is used to correct the ellipse. Experimental results show that the proposed scheme is highly precise and stable regardless of the desired signal amplitude. It has a high response linearity of 99.997%, a minimum detectable phase of 3.16 μrad and a large dynamic range of 123.52 dB @1 kHz & 1% THD.

Kilometer-precise (UII) Umbriel physical properties from the multichord stellar occultation on 2020 September 21

ABSTRACT We report the results of the stellar occultation by (UII) Umbriel on 2020 September 21. The shadow crossed the USA and Canada, and 19 positive chords were obtained. A limb parameter accounted for putative topographic features in the limb fittings. Ellipse fittings were not robust – only upper limits were derived for the true size/shape of a putative Umbriel ellipsoid. The adopted spherical solution gives radius = 582.4 ± 0.8 km, smaller/close to 584.7 ± 2.8 km from Voyager II. The apparent ellipse fit results in a true semi-major axis of 584.9 ± 3.8 km, semi-minor axis of 582.3 ± 0.6 km, and true oblateness of 0.004 ± 0.008 for a putative ellipsoid. The geometric albedo was pV = 0.26 ± 0.01. The density was ρ = 1.54 ± 0.04 g cm−3. The surface gravity was 0.251 ± 0.006 m s−2 and the escape velocity was 0.541 ± 0.006 km s−1. Upper limits of 13 and 72 nbar (at 1σ and 3σ levels, respectively) were obtained for the surface pressure of a putative isothermal CO2 atmosphere at T = 70 K. A milliarcsecond precision position was derived: α = 02h30m28${_{.}^{\rm s}}$84556 ± 0.1 mas, δ = 14o19′36″.5836 ± 0.2 mas. A large limb parameter of 4.2 km was obtained, in striking agreement with opposite Southern hemisphere measurements by Voyager II in 1986. Occultation and Voyager results indicate that the same strong topography variation in the surface of Umbriel is present on both hemispheres.

Research on desktop object grasping based on ellipse fitting

The grasping operation task in service scenes faces several problems including too many kinds of objects and a large amount of training data. This paper focuses on the grasping strategy and pose detection in desktop object grasping tasks. A grasping strategy is given based on the combination of desktop normal vector detection, object category detection, and grasping pose detection. The grasping pose is calculated by ellipse fitting on the depth map. An optimal function is designed to evaluate the possibility of the object sliding along the ellipse axis and the stability of the grasping height. The most reliable grasping pose is selected. Finally, experiments were carried out with a six-degree-of-freedom manipulator, and the proposed grasping method achieved effective grasping of desktop objects without prior knowledge of the object.

Trial frame for evaluating eye movements.

Eye movement research is an established methodology and widely used in fundamental research fields such as psychology or neuroscience. Most research is performed in controlled environments with screen-based eye trackers, but demand for a wearable requirement is on the rise. Yet, a state of the art wearable eye tracking system thus far has not been feasible for subjects with refractive errors; therefore, a trial frame is proposed for researching the eye movement of people with or without refractive errors. Two iris cameras and several infrared radiation LEDs were fixed behind the frame for recording eye images. The images were sent to a host computer using 2.4G wireless, which was also fixed on the frame. The entire electronic system in the trial frame was driven using a battery. Eye position in the images was recognized and segmented by a model that was trained through machine learning. Then the pupil and blinks were detected from the segmented eye area using ellipse fitting and the eye aspect ratio. Experiments showed that the correct rate of pupil and blink detections were 97.24% and 96.14%, respectively.

A binocular vision method for precise hole recognition in satellite assembly systems

The prevalent manual assembly process for satellites is marked by inefficiencies and a heightened risk of collision, thus limiting its scalability and potential for integration. To address these limitations, the adoption of industrial robots for an intelligent assembly mode has emerged as a promising alternative. Nonetheless, the implementation of an industrial robot satellite assembly system brings its own challenges, including low accuracy of the robot, large manufacturing errors of the satellite products and accumulated errors in the picking and placing process. As the main positioning feature, the detection of holes plays an important role in solving these problems. This paper introduces a novel binocular vision hole recognition system, coupled with an associated hole recognition algorithm, aiming at enhancing the detection accuracy of characteristic holes of satellite products. The proposed methodology includes the development of a confidence-based indicator to assess the quality of two-dimensional hole detection, and an iterative optimization of the fitting ellipse. Furthermore, a confidence-based neighborhood denoising two-stage fitting method is designed for accurate hole positioning. Experimental results validate the proposed methodology, showcasing a recognition accuracy of 0.060 mm and an assembly accuracy within 0.2 mm, thereby fulfilling the requirements of the industrial robot satellite assembly system.

Design and implementation of a real-time compensation algorithm for nonlinear error based on ellipse fitting.

To improve the measurement accuracy of interferometer displacement measurement systems, this study analyzes the characteristics of the interference signal to identify sources of nonlinear errors and develops compensation strategies. Specifically, a model is established for the nonlinear errors of the interferometer, which can be attributed to a laser and polarizing beam splitter (PBS). Following that, the dual orthogonal lock-in amplification algorithm is used to separate and compensate for the frequency uncertainty and amplitude errors. Additionally, a real-time compensation algorithm based on ellipse fitting is proposed to compensate for errors caused by the PBS and the uncertainty of amplitude caused by the light source. Experimental results demonstrate that the peak-to-peak value of the compensated nonlinear error is reduced from 11.62 nm to 5.37 nm.

Efficacy of differential phase extraction methods in dual atom interferometers under correlated noise conditions

Atom interferometry-based sensors have demonstrated remarkable precision, making them attractive for diverse applications compared to traditional sensors. However, practical experiments inevitably encounter noise, which limits precision. We investigate the performance of two commonly used methods, ellipse fitting (EF) and fringe fitting (FF), for differential phase estimation in a dual atom interferometer under various noise conditions. We comprehensively analyze the efficacy of these methods for each type of Gaussian noise, including phase noise, amplitude noise, and offset noise. Using a colored noise model, we investigate the Allan deviation results. Our investigations will offer valuable insights for future quantum sensing based on dual interferometers.

Improving concave point detection to better segment overlapped objects in images

This study presents a method to improve state-of-the-art concave point detection methods as the first step towards effectively segmenting overlapping objects in images. The approach relies on analysing the curvature of the object contour. This method comprises three main steps. First, the original image is preprocessed to obtain the curvature value at each contour point. Second, the regions with higher curvatures are selected and a recursive algorithm is applied to refine previously selected regions. Finally, a concave point is obtained for each region by analysing the relative position of their neighbourhood. Furthermore, the experimental results indicate that improving the detection of concave points leads to better division of clusters. To evaluate the quality of the concave point detection algorithm, a synthetic dataset was constructed to simulate the presence of overlapping objects. This dataset includes the precise location of concave points, which serve as the ground truth for evaluation. As a case study, the performance of a well-known application, such as the splitting of overlapping cells in images of peripheral blood smears samples from patients with sickle cell anaemia, was evaluated. We used the proposed method to detect concave points in cell clusters and then separated these clusters by ellipse fitting.

Two-stage automated diagnosis framework for urogenital schistosomiasis in microscopy images from low-resource settings.

Automated diagnosis of urogenital schistosomiasis using digital microscopy images of urine slides is an essential step toward the elimination of schistosomiasis as a disease of public health concern in Sub-Saharan African countries. We create a robust image dataset of urine samples obtained from field settings and develop a two-stage diagnosis framework for urogenital schistosomiasis. Urine samples obtained from field settings were captured using the Schistoscope device, and S. haematobium eggs present in the images were manually annotated by experts to create the SH dataset. Next, we develop a two-stage diagnosis framework, which consists of semantic segmentation of S. haematobium eggs using the DeepLabv3-MobileNetV3 deep convolutional neural network and a refined segmentation step using ellipse fitting approach to approximate the eggs with an automatically determined number of ellipses. We defined two linear inequality constraints as a function of the overlap coefficient and area of a fitted ellipses. False positive diagnosis resulting from over-segmentation was further minimized using these constraints. We evaluated the performance of our framework on 7605 images from 65 independent urine samples collected from field settings in Nigeria, by deploying our algorithm on an Edge AI system consisting of Raspberry Pi + Coral USB accelerator. The SH dataset contains 12,051 images from 103 independent urine samples and the developed urogenital schistosomiasis diagnosis framework achieved clinical sensitivity, specificity, and precision of 93.8%, 93.9%, and 93.8%, respectively, using results from an experienced microscopist as reference. Our detection framework is a promising tool for the diagnosis of urogenital schistosomiasis as our results meet the World Health Organization target product profile requirements for monitoring and evaluation of schistosomiasis control programs.

Assessment of body shape variation using Elliptic Fourier descriptors and ellipse fitting estimators and their genetic estimates in the flatfish Senegalese sole

Body shape is an important morphological trait in aquaculture. This study investigates the use of Elliptic Fourier descriptors (EFDs) analysis and ellipse fitting estimators to assess shape variation in Senegalese sole and their genetic variance components. A total of 2271 fish were individually photographed and body contours reconstructed using 20 Elliptic Fourier harmonics. Principal component analysis identified four symmetric components that explained the 68.6% of the total variation. They were mainly related to the adjustment of the body to an ellipse (PC1s and PC3s) and caudal fin morphological features (PC2s, PC3s, PC4s). Moreover, four asymmetric components related to caudal fin (PC1a, PC2a, PC3a) and head orientation (PC4a) that explained 24.5% of the total variation were also found. In addition to EFDs, body perimeter and five ellipse fitting estimators including the maximum body height to caudal peduncle height ratio (MBH/CPH), body aspect ratio (AR), ellipticity (ELL), AR from theoretical ellipse (ARe) and solidity (SOL) were calculated. PC1s was strongly correlated with ARe, AR and ELL (≥0.75), PC2s with SOL (−0.79) and PC3s with AR and ELL (0.48–0.49). Males appeared more elliptic than females as revealed by all ellipse descriptors with a tendency to caudal fins with obtuse angles (PC3a) and heads orientated toward the abdominal cavity (PC4a). Overall, heritabilities for symmetric components were higher than for asymmetric. Heritabilities for body ellipse fitting estimators including PC1s were high or very high with the highest values for AR (0.80) and ARe (0.78) for body and whole-body, respectively. Heritability for MBH/CPH was high (0.51) with low genetic correlation with other morphological traits. Heritabilities for symmetrical and asymmetrical features of caudal fin were moderate or low and indirect selection using other highly correlated traits such as PC2s through SOL and PC3a through PC4a or PC1s would facilitate progress in the selection. Perimeter showed a moderate heritability and it was more genetically correlated with growth than shape-related traits. The data provided represent a valuable tool to assess body shape in sole and in the design of genetic breeding programs in Senegalese sole.

Determination of the major axis direction and macroseismic epicenter of the assessed intensity map based on relocated aftershock sequences

The rapid assessment of an intensity map following a strong earthquake forms the foundation for risk assessment and emergency response in Chinese mainland. The determination of the major axis direction in the assessed intensity map depends on various factors, including nearby active faults, instrumental intensities, and the distribution of aftershocks. To evaluate the effectiveness of promptly determining the major axis direction based on early aftershock distribution, we relocated and analyzed aftershock sequences occurring within 2 h of eighteen aftershock-rich earthquakes with a magnitude of Ms ≥ 6.0 in Chinese mainland from 2012 to 2021. HypoDD was used for relocation, and the standard deviational ellipse fitting technique was employed for analysis. Comparing the aftershock ellipses resulting from our analysis with the macroseismic intensity maps obtained from field surveys reveals a high level of agreement, with an average difference of approximately 9° in the major axis directions of the aftershock ellipses and the meizoseismal zones. For the majority of earthquakes, regardless of focal mechanisms, the lengths of the major axes of the aftershock ellipses closely correspond to the intensity VIII scale. Additionally, the spatial distribution of aftershocks aids in distinguishing the seismogenic fault from the two fault planes with distinctly different dips as indicated by the focal mechanism solution. Moreover, the distance between the aftershock center and the macroseismic epicenter systematically increases as the dip decreases. These findings hold significant scientific value as they contribute to the prompt determination of assessed intensity maps and provide effective guidance for earthquake emergency response.

Direct nonlinear parameter estimation method for a phase generated carrier position sensor.

Phase generated carrier (PGC) is widely applied in interferometric phase estimation for distance, vibration and velocity measurements. However, traditional PGC methods suffer from nonlinear effects, causing limitations to demodulation of signal. Modified PGC methods, such as ellipse fitting algorithm (EFA), resolves these issues, but usually requires additional phase shift. With our proposed method in this paper, only one period of signal and one test point is required to attain accurate depth of phase modulation and phase. We use a photodiode to calibrate light intensity in data acquisition, and develop a Levenburg-Marquadt algorithm to estimate values of PGC parameters. An improved algorithm is also proposed to avoid local optimization based on prior information to ensure measurement stability. Less than 5 × 10-3 rad phase measurement uncertainty and over 55 dB Signal to Noise and Distortion Ratio (SINAD) is obtained in experiment.

Aerial hyperspectral remote sensing detection for maritime search and surveillance of floating small objects

Over the past decades, maritime accidents have been increasing due to the rise in maritime transportation and ship traffic. While detecting accident-prone vessels is crucial, it is equally important to identify individuals in distress and small floating objects. Real-time monitoring and wide-area high-resolution observations enabled by aerial remote sensing have proven effective in maritime detection. In this study, we developed a technology for detecting small objects by conducting two aerial experiments targeting various objects, including ships, mannequins (human-shaped objects), and maritime safety equipment floating in coastal areas, thereby acquiring hyperspectral image data. By utilizing the hyperspectral data, we detected the pixels corresponding to the edges of ships and employed an ellipse fitting approach to identify the vessels, achieving a length error of 0.44 m. Additionally, we detected small floating objects based on a spectral database using spectral matching. The N-finder algorithm (N-FINDR) spectral unmixing technique was applied to detect lifebuoys, buoyant apparatus, and mannequins, resulting in relatively small length errors ranging from 0.08 to 0.17 m. As satellite hyperspectral sensors continue to advance significantly, it is expected that this study will contribute to future research in the field of detecting small objects and maritime surveillance.

Accurate and fast extraction of adhesive cells based on concave points detection and matching

AbstractPrecise image segmentation of adhesive cells is a challenge during the cell detection process for biomedical image analyses. In this article, a new segmentation and extraction method for adhesive cells based on concave points detection and matching is proposed. First, image preprocessing is used to reduce interference information, which mainly includes sequential gray scale transformation, binarization, hole filling, adhesive cells recognition, and median filtering process. Second, an improved concave detection algorithm is presented which can reduce the interfering feature points and detect the concave points on the adhesive cells accurately. Third, precise extraction of adhesive cell contour is realized by concave matching based on ellipse fitting. Experiments of blood cell sample detection show that the average accuracy is 97.18% with a costing time of 3.36 s. The proposed method can effectively reduce the interference of multiple concave points and extract the cell contour from adhesive regions with higher accuracy and less time, which shows great application potential in the field of biological image detection and analyses.

Phase retrieval from single interferogram without carrier using Lissajous ellipse fitting technology

Phase extraction from single interferogram is of high significance and increasingly interest in optical metrology. In this contribute we propose an advanced Pixel-level Lissajous Ellipse Fitting (APLEF) method to extract the phase from single interferogram without carrier. At each pixel, a Lissajous figure is created by plotting N against D, where N and D are subtractions and additions of intensities of adjacent pixels in a small window. The so created Lissajous figure is already in phase quadrature because of the subtraction and addition process, and the Lissajous Figure is forced to be closed by taking the opposite values of N and D, i.e. –N and -D into account. The closed and in phase quadrature Lissajous Figure is the key point for APLEF to demodulate the single inteferogram without carrier in theoretically. The simulation shows its higher accuracy than existed SPT and Garbusi’s method and the experiments finally corroborate its effectiveness.

Ameliorated PGC demodulation scheme using Taubin least squares fitting of ellipse in fiber optic interferometric sensors

In this paper, we propose an ameliorated phase generated carrier (PGC) demodulation scheme using Taubin least squares (LS) fitting of ellipse to eliminate the nonlinear errors. Taubin LS has carefully chosen a normalization matrix and the ellipse fitting parameters are directly obtained by solving the generalized eigenvector problem, leading to a high accuracy result. Quadrature signals are extracted from the signal fundamental and the sidebands of the fundamental of the carrier, and then corrected by the ellipse fitting algorithm (EFA) based on Taubin LS. A combined internal modulation is used to ensure the proper operation of the EFA under small signals. And the desired phase signal is extracted from the corrected quadrature signals by the differential-cross-multiplying method and evaluated by the total harmonic distortion. Experimental results show that the proposed scheme is superior and highly stable, it has a phase resolution of 3.16 μrad/√Hz, a large dynamic range of 120 dB @ 1 KHz and a good linearity of better than 99.99%.

Precision vibration measurement using differential phase-modulated homodyne interferometry

A novel precision vibration measurement using differential phase-modulated homodyne interferometry is presented. The orthogonal linearly polarized phase-modulated single frequency laser source is constructed by using a distributed feedback (DFB) fiber laser and a fiber-coupled electro-optic phase modulator (EOM). An auxiliary monitoring signal is used to differentially compensate the optical path drift and common-mode noise of the fiber. By pre-scanning the wavelength of DFB laser to introduce enough phase changes, ellipse fitting can be realized without moving the object more than half a wavelength. Therefore, the periodic nonlinearity of the phase generated carrier (PGC) demodulation is compensated. Experimental setup was built and the real-time signal processing was realized based on field programmable gate array (FPGA). The experiments of pulse vibration, sinusoidal vibration and comparison with commercial laser vibrometer were performed to verify the feasibility of the proposed method. The experimental results show that the average deviation of vibration amplitude is about 0.97 nm in the frequency range of 0.5 kHz to 10.0 kHz, which indicates that the proposed method has significant application for precision vibration measurement.

A regressive encoder-decoder-based deep attention model for segmentation of fetal head in 2D-ultrasound images

Ultrasound imaging is the most commonly used imaging during pregnancy for tracking the fetus's growth and monitoring other biological parameters. The assessment of the development of the baby's growth requires imaging-based analysis in every trimester. The automatic computerized software and systems provide the platform for radiologists to more accurately access the fetus's head circumference as compared to manual estimation. The improvement of such computerized algorithms is always the key demand to improve accuracy and precision. This paper proposes an improved encoder-decoder model for the segmentation of the fetal head segmentation in 2D-ultrasound images. The proposed model uses regression in combination with attention to the encoder-decoder model to determine the fetus's head circumference. The model is further extended with the post-processing ellipse fitting to superimpose the segmentation region on ultrasound images for clear visualization of the fetus's head. Further, the proposed model performance is evaluated by using various statistical measures using segmented regions and available ground truth. The experimental results demonstrate a similarity score of 94.56%. The comparative result suggests that the proposed model is providing a more accurate fetus head segmentation region on 2D-ultrasound images as compared to other existing approaches.