Least-square Ellipse Fitting Research Articles

Comparison of a conventional image processing approach with an artificial neural network approach to three‐dimensionally trace multiple particles in dynamic x‐ray microtomography experiments under laboratory conditions

AbstractThis paper compares a classic digital image processing approach to trace particles in laboratory x‐ray micro‐computed tomography (µCT), which is based on a combination of random sample consensus (RANSAC) algorithm and least squares ellipse fitting (LSF), with an approach based on artificial neural networks (ANNs). In order to be able to perform the comparison, dynamic experiments were carried out in a laboratory microtomography facility. During active scans with a duration of 30–75 s several sedimentation experiments have been carried out with an exposure time of 0.13 s/projection. Through the movement of the particles during the scan curved motion artefacts in the reconstructed data occur, where the vertex marks the coordinate of the particle. It could be shown that both approaches enable the tracing of particles in laboratory x‐ray µCT with deviations from a manually evaluated result of exemplarily 1.25% for the conventional digital image processing (CDIP) and 0.48% for the ANN. It was found that ANNs are able to identify particle positions in non‐symmetrical motion artefacts, appearing around the first and last position of the particles in the scan, allowing an extension of the motion range of the particles that can be evaluated. Both methods have their advantages and disadvantages. Due to the high complexity and size as well as partly black box structures of neural networks, they are not 100% comprehensible whereas conventional image processing is 100% transparent and understandable. But because of the complexity of the tracing of particles, the CDIP code offers many parameters that can be set, which is why the application is therefore slightly more complex.

A Method for Automatic Three-Dimensional Particle Tracing Under Laboratory Conditions Using Dynamic X-Ray Computed Microtomography

AbstractThis paper presents a method for particle tracing in laboratory X-ray micro-computed tomography (µCT) using an adjusted Random Sample Consensus (RANSAC) algorithm combined with least squares ellipse fitting (LSF). For method testing, a setup for the investigation of deep bed filtration (DBF) has been used as an example of a complex process that can be elucidated with such a method. Particle tracking with tomography systems requires high-temporal resolution which can only be achieved with synchrotron radiation computer tomography. Therefore, in this work, it has been demonstrated that instead of particle tracking, particle tracing in opaque systems such as DBF can be performed in laboratory µCT systems. To achieve particle tracing, dynamic µCT scans with a duration between 30 and 110 s combined with an exposure time of 0.13 s/projection were executed and during the scan time the filtration was performed, causing parabola shaped motion artefacts. The developed method exploits the motion artefacts created by the particle motion during the scan. It could be shown that it is possible to trace particles in complex structures within only one 30 s scan. Furthermore, through trace length and time, it is possible to determine the average velocity. Whereby, the accuracy and limits depend on the particle size, particle velocity/data rate and the X-ray attenuation of particle and medium.

High-Precision Measuring System for Internal Deformation Monitoring Pipeline of Rockfill Dams: Design and Validation

The monitoring of internal deformation in rockfill dams using pre-buried flexible pipelines is a promising technique; however, achieving precise measurements over a long-range pipeline is crucial and challenging. In this paper, we present a high-precision pipeline measuring system for monitoring internal deformation in rockfill dams, which can simultaneously measure the pipeline centerline and cross-section geometry. The system leverages the inertial measurement principle to perform positioning by fusing an inertial measurement unit (IMU) with odometers. It utilizes a Kalman filter and Rauch-Tung-Striebel (RTS) smoothing to estimate the optimal 3D curves of the pipeline. The pipeline’s inner diameter is measured using three wheel swing arms and a set of load-bearing wheels, and the pipeline cross-section geometry is fitted using a direct least-square ellipse fitting approach. Finally, we validated the measuring system through both model and on-site experiments and compared the measurements with the Leica AT-960LR absolute tracker and hydraulic overflow settlement gauge. The results indicate that the measuring system has excellent accuracy for measuring pipeline curves and deformation, and the settlement trend is consistent with the hydraulic overflow settlement gauge. We also assessed the cross-section deformation of the deformation monitoring pipeline in the Lianghekou dam for six months, and the results showed that if deployed in strict accordance with the design requirements, the monitoring pipeline buried inside the rockfill dam would not deform significantly. These findings provide a tremendous incentive for the continued development of rockfill dam internal deformation monitoring.

Algorithm improvement for the surface morphology diagnostics based on the Gram-Schmidt orthonormalization and the least square ellipse fitting under the EAST-like vibrational environments

To realize in situ surface morphology diagnosis of Plasma-Facing Materials (PFMs) in the Experimental Advanced Superconducting Tokamak (EAST), a diagnostic system which is called DUT-SIEP (Speckle Interferometry Experiment Platform in Dalian University of Technology) is in development. Mimicking the actual vibrational conditions in EAST, Dual-wavelength Phase-Shifting Interferometry (DPSI) should be sensitive to vibrational environment and would reduce accuracy in the morphology measurements. Therefore, an approach combining the Gram–Schmidt orthonormalization and the Least-Square Ellipse Fitting (GS-LSEF) was proposed to replace the conventional phase extraction process to improve the measurement accuracy in the EAST-like vibration conditions. The new approach only requires two interferograms at each wavelength while the conventional method needs three at least for each wavelength. This significantly reduces the phase errors in the acquisition processes. The Gram–Schmidt orthonormalization is performed to correct the phase shift errors and determine the elliptic coefficients. In the Least-Square Ellipse Fitting, the elliptic coefficients are used to compensate the phase errors from the disturbed background intensity. The approach can significantly improve the measurement efficiency and avoid the infinite loops caused by the numeric divergent. The method was verified by laser ablation on tungsten (W) material for simulating erosion-processes in EAST. Results show that the proposed approach has significantly improved in accuracy by approximately twofold comparing with those by the convenient Four-step phase-shifting approaches due to reducing the noise superposition problems in the EAST-like vibrational conditions.

Efficient fetal ultrasound image segmentation for automatic head circumference measurement using a lightweight deep convolutional neural network.

Fetal head circumference (HC) is an important biometric parameter that can be used to assess fetal development in obstetric clinical practice. Most of the existing methods use deep neural network to accomplish the task of automatic fetal HC measurement from two-dimensional ultrasound images, and some of them achieved relatively high prediction accuracy. However, few of these methods focused on optimizing model efficiency performance. Our purpose is to develop a more efficient approach for this task, which could help doctors measure HC faster and would be more suitable for deployment on devices with scarce computing resources. In this paper, we present a very lightweight deep convolutional neural network to achieve automatic fetal head segmentation from ultrasound images. By using sequential prediction network architecture, the proposed model could perform much faster inference while maintaining a high prediction accuracy. In addition, we used depthwise separable convolution to replace part of the standard convolution in the network and shrunk the input image to further improve model efficiency. After getting fetal head segmentation results, post-processing, including morphological processing and least-squares ellipse fitting, was applied to obtain the fetal HC. All experiments in this work were performed on a public dataset, HC18, with 999 fetal ultrasound images for training and 335 for testing. The dataset is publicly available on https://hc18.grand-challenge.org/ and the code for our method is also publicly available on https://github.com/ApeMocker/CSM-for-fetal-HC-measurement. Our model has only 0.13 million [M] parameters and can achieve an inference speed of 28 [ms] per frame on a CPU and 0.194 [ms] per frame on a GPU, which far exceeds all existing deep learning-based models as far as we know. Experimental results showed that the method achieved a mean absolute difference of 1.97( ± 1.89) [mm] and a Dice similarity coefficient of 97.61( ± 1.72) [%] on HC18 test set, which were comparable to the state of the art. We presented a very lightweight deep learning-based model to realize fast and accurate fetal head segmentation from two-dimensional ultrasound image, which is then used for calculating the fetal HC. The proposed method could help obstetricians measure the fetal HC more efficiently with high accuracy, and has the potential to be applied to the situations where computing resources are relatively scarce.

On the Structure and Kinematics of an Algerian Eddy in the Southwestern Mediterranean Sea

An Algerian Eddy, anticyclonic vortex generated by the instability of the Algerian Current in the southwestern Mediterranean Sea, is studied using data provided by drifters (surface currents), Argo floats (temperature and salinity profiles), environmental satellites (absolute dynamic topography maps and ocean color images) and operational oceanography products. The eddy was generated in May 2018 and lasted as an isolated vortex until November 2018. Its morphology and kinematics are described in June–July 2018 when drifters were trapped in its core. During that period, the eddy was slowly moving to the NE (~2 km/day), with an overall diameter of about 200 km (slowly growing with time) and maximal surface swirl velocity of ~50 cm/s at a radius of ~50 km. Geostrophic currents derived from satellite altimetry data compare well with low-pass filtered drifter velocities, with only a slight overestimation, which is expected as its maximum vorticity corresponds to a small Rossby number of ~0.6. Satellite ocean color images and some drifters show that the eddy has an elliptical spiral structure. The looping tracks of the drifters trapped in the eddy were analyzed using two statistical methods: least-squares ellipse fitting and wavelet ridge analysis, revealing a typical eccentricity of about 0.5, a wide range of inclination and a rotation period between 3 and 10 days. Clusters of drifters on the northeastern limb of the eddy were also considered to estimate divergence and vorticity. The results indicate convergence (divergence) and downwelling (upwelling) at scales of 20–50 km near the northeastern (northwestern) edge of the eddy, in agreement with the quasi-geostrophic theory. Vertically, the eddy extends mostly down to 250 m depth, with a warm, low-salinity and low-density signature and with geostrophic currents near 50 cm/s in the top layer (down to ~80 m) reducing to less than 10 cm/s near 250 m. Near the surface, colder water is advected into it.

Direct least squares fitting of ellipses segmentation and prioritized rules classification for curve-shaped chart patterns

In financial markets, appearances of chart patterns in time series are commonly considered as potential signals for imminent change in the direction of price movement. To identify chart patterns, time series data is usually segmented before it can be processed by different classification methods. However, existing segmentation methods are less effective in classifying 16 curve-shaped chart patterns from financial time series. In this paper, we propose three novel segmentation methods for classification of curve-shaped chart patterns based on direct least squares fitting of ellipses. These methods are implemented based on the principles of sliding windows, turning points, and bottom-up piece wise linear approximation. To further enhance the efficiency of classifying chart patterns from real-time streaming data, we propose a novel algorithm called Accelerating Classification with Prioritized Rules (ACPR). Experiments based on real datasets from financial markets reveal that the proposed approaches are effective in classifying curve-shaped patterns from time series. Experiment results reveal that the proposed segmentation methods with ACPR can significantly reduce the total execution time.

Monitoring driver attention distraction with binocular vision

Driver attention distraction (DAD) is a typical artificial factor traffic accident, and DAD monitoring can improve driving security. In this study, a method was developed for accurate DAD monitoring based on binocular vision. A binocular vision system was built, and camera parameters of the system were calibrated based on Open CV. In the method, the driver’s facial image is obtained by using active infrared imaging technology and preprocessed to locate the eye positions. The connected component labeling algorithm for binary images is used to pinpoint the eye locations. The characteristic information of the eye pupils is extracted with the least-squares ellipse fitting algorithm, and the characteristic information of the Purkinje image is obtained with the Harris corner detection algorithm. A DAD warning model based on the binocular vision system was established to evaluate the attention state of the driver.

Vision-based detection of container lock holes using a modified local sliding window method

Container yards have been facing the increase of freight volume. In order to improve the efficiency of container handling, automatic stations have been established in many terminals. However, current container handling still needs a manual operation to locate container lock holes. Hence, it is inefficient and potential to risk workers’ health under long working hours. This paper presented a hybrid machine vision method to automatically recognize and locate container lock holes. The proposed method extracted the top area of the container from the multiple container areas, and then presented a new modified local sliding window to detect the keyhole region. The algorithm learned the histograms of oriented gradients (HOG) features using a multi-class support vector machine (SVM). Finally, the holes were located using direct least square fitting of ellipses. We carried an experiment under various weather and light conditions including nights and rainy days. The results showed that both the recognition and location accuracy outperformed the state-of-the-art results.

Hybrid algorithm based on radial symmetry and weighted least-square ellipse fitting for three-dimensional nanometer particle localization

Choosing the localization algorithm in superresolution microscopy is an important factor in determining the resolution in such a modality. The point spread function (PSF) in defocused images has ring structures that can be used to localize the three-dimensional (3-D) position of single particles by calculating the ring center (x and y) and radius (z). As there is no well-developed mathematical model for a defocused PSF, it is difficult to perform a fitting-based algorithm in such images. A particle localization algorithm based on radial symmetry and ellipse fitting is developed to localize the centers and radii of defocused PSFs. Our method can localize the 3-D position of a fluorophore within 20-nm precision in three-dimensions in a range of 40 μm in z-dimension from defocused two-dimensional (2-D) images.

Three dimensional least-squares fitting of ellipsoids and hyperboloids

Spatial continuity can be described as a variogram model that has an ellipsoid anisotropy. In previous research, two-dimensional least-square ellipse fitting method by Fitzgibbon, Pilu and Fisher has been applied to the analysis of spatial continuity for coal deposits. However, it is not easy to generalize their method to three-dimensional least-square ellipsoid fitting. In this research, we obtain a three-dimensional least-square fitting for ellipsoids and hyperboloids by generalizing two-dimensional least-square ellipse fitting method introduced by Gander, Golub and Strebel.

McMC-based AVAZ direct inversion for fracture weaknesses

Considering that wide-azimuth seismic data contains abundant azimuthal amplitude information about the fractured reservoir with obvious characteristics of amplitude variation with incident angle and azimuth (AVAZ), azimuthal seismic data can be used for the inversion of anisotropic parameters in fractured reservoir. Fractured reservoir with a single set of vertically aligned fractures embedded in a purely isotropic background medium may be considered as a long-wavelength effective transversely isotropic medium with a horizontal symmetry axis (HTI). The normal and tangential fracture weaknesses are two key parameters to the evaluation of fracture properties in HTI media, thus the inversion of fracture weaknesses may be used for characterizing the anisotropy in fractured reservoir. The elastic properties of background isotropic media without fractures, however, do not cause azimuthal changes in AVAZ data compared to the fracture anisotropic properties, therefore simultaneous inversion for the background elastic parameters and fracture anisotropic parameters may be not stable. Thus we propose a method of azimuth-difference-based AVAZ direct inversion for fracture weaknesses. First, we extract the fracture symmetry axis azimuth based on the least square ellipse fitting (LSEF) method to obtain a linear AVAZ approximation. Then we build a fractured anisotropic rock-physics model for the estimation of anisotropic well-log information, building the initial background low-frequency trend of fracture weaknesses. Finally, an AVAZ direct inversion method of normal and tangential fracture weaknesses is proposed with the nonlinear Markov chain Monte Carlo (McMC) strategy. So we can eliminate the influence of isotropic background elastic properties on the fracture weakness properties and obtain the normal and tangential fracture weaknesses more stably. Tests on both 2D over-thrust model and real data demonstrate that the normal and tangential fracture weaknesses may be estimated more stably, and it turns out that fracture-developed zones can be identified using the estimated fracture weaknesses.

Size distribution measurement of packed tower drift based on hydrophobic materials

Droplet size distribution of packed tower drift is of great significance in selecting drift eliminators. A sizing procedure based on hydrophobic material sampling and image processing is presented. Hydrophobic materials with great adhesiveness whose contact angle is 129.5° and rolling angle is greater than 90°, are prepared by liquid-phase oxidation based on an aluminum alloy. The drop shape and diameter are figured out by the process of hydrophobic materials sampling, imaging and least square fitting of ellipses. The experiment demonstrates that the error of diameter is less than 3%, in which the drop diameters are 0–3850 µm. Size distribution of packed tower drift is carried out, the results show that packed tower drift have a distribution of 0–1000 µm and packed tower with inertia drift eliminators can get rid of droplets bigger than 200 µm.

一种圆形禁令交通标志快速提取和识别方法

随着社会的发展，智能交通系统的开发受到广泛的关注，交通标志识别系统作为智能交通的一部分，如何对其快速的提取并识别开始被越来越多的人关注和研究。本文提出一种基于RGB空间的圆形禁令交通标志的提取与识别算法，该方法根据标志的颜色特征和形状特征，通过RGB空间阈值分割和最小二乘椭圆拟合过滤的方法对交通标志进行检测，最后利用BP人工神经网络构建最佳识别网络，达到自动识别圆形禁令交通标志的目的。实验结果表明，该方法具有较好的提取和识别能力。 With the development of the society, the intelligent transportation system has been widely focused on. More and more people are paying attention to traffic sign recognition system, which as a part of the entire intelligent transportation system. This paper put forward a method, which based on RGB space, to detect and to recognize circular ban traffic signs. This method uses threshold segmentation in RGB space and the least-squares ellipse fitting to filter and detect traffic signs, due to their color features and shape features. At last, the method uses BP artificial neural network to build the best recognition network to automatically recognize circular ban traffic signs. The experimental results show that the method has good detect and recognize ability.

Robust Ellipse Fitting via Half-Quadratic and Semidefinite Relaxation Optimization.

Ellipse fitting is widely applied in the fields of computer vision and automatic manufacture. However, the introduced edge point errors (especially outliers) from image edge detection will cause severe performance degradation of the subsequent ellipse fitting procedure. To alleviate the influence of outliers, we develop a robust ellipse fitting method in this paper. The main contributions of this paper are as follows. First, to be robust against the outliers, we introduce the maximum correntropy criterion into the constrained least-square (CLS) ellipse fitting method, and apply the half-quadratic optimization algorithm to solve the nonlinear and nonconvex problem in an alternate manner. Second, to ensure that the obtained solution is related to an ellipse, we introduce a special quadratic equality constraint into the aforementioned CLS model, which results in the nonconvex quadratically constrained quadratic programming problem. Finally, we derive the semidefinite relaxation version of the aforementioned problem in terms of the trace operator and thus determine the ellipse parameters using semidefinite programming. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.

The high precision positioning algorithm of circular landmark center in visual measurement

For vision measurement in the center circle landmark location problem, an improved center of the ellipse based on Zernike moments sub-pixel positioning algorithm was proposed. First, using Sobel operator edge of the image pixel level positioning and then use the constructed Zernike moments to solve the model, combined with Zernike orthogonal polynomials and completeness and plural moment magnitude rotational invariance calculated edge sub-pixel position; followed by analysis of the principle deviation generated by the moments template and ideals model, a correction formula was proposed to compensate and improved edge criterion used to image sub-pixel edge positioning; finally, using the least-squares ellipse fitting algorithm fitting circle center, reverse edge point, filtered residuals larger point, and then precise positioning of the ellipse center. The experimental results show that this method has good stability and high positioning accuracy can be efficiently used in many applications.

Automatic diagnosis of malaria based on complete circle–ellipse fitting search algorithm

Diagnosis of malaria parasitemia from blood smears is a subjective and time-consuming task for pathologists. The automatic diagnostic process will reduce the diagnostic time. Also, it can be worked as a second opinion for pathologists and may be useful in malaria screening. This study presents an automatic method for malaria diagnosis from thin blood smears. According to this fact that malaria life cycle is started by forming a ring around the parasite nucleus, the proposed approach is mainly based on curve fitting to detect parasite ring in the blood smear. The method is composed of six main phases: stain object extraction step, which extracts candidate objects that may be infected by malaria parasites. This phase includes stained pixel extraction step based on intensity and colour, and stained object segmentation by defining stained circle matching. Second step is preprocessing phase which makes use of nonlinear diffusion filtering. The process continues with detection of parasite nucleus from resulted image of previous step according to image intensity. Fourth step introduces a complete search process in which the circle search step identifies the direction and initial points for direct least-square ellipse fitting algorithm. Furthermore in the ellipse searching process, although parasite shape is completed undesired regions with high error value are removed and ellipse parameters are modified. Features are extracted from the parasite candidate region instead of whole candidate object in the fifth step. By employing this special feature extraction way, which is provided by special searching process, the necessity of employing clump splitting methods is removed. Also, defining stained circle matching process in the first step speeds up the whole procedure. Finally, a series of decision rules are applied on the extracted features to decide on the positivity or negativity of malaria parasite presence. The algorithm is applied on 26 digital images which are provided from thin blood smear films. The images are contained 1274 objects which may be infected by parasite or healthy. Applying the automatic identification of malaria on provided database showed a sensitivity of 82.28% and specificity of 98.02%.

Estimation of the Repeat-Pass ALOS PALSAR Interferometric Baseline Through Direct Least-Square Ellipse Fitting

The precise estimation of the baseline is a crucial procedure in repeat-pass interferometric synthetic aperture radar (InSAR) applications. Using the ephemeris of the satellite, a polynomial regression algorithm can fit the satellite orbit at the third or higher order with a main shortcoming that the mutual constraints among the three dimensions defining the orbit are missed. In this paper, a new approach is presented to fit the satellite orbit based on the assumption that the satellite orbit is a 3-D ellipse, which retains the relations among the three dimensions. Considering the complexity of 3-D ellipse parameters estimation, the 3-D orbit is first transformed into three 2-D ellipses. Then, the parameters of these 2-D ellipses are estimated with a direct least-square ellipse fitting method (DLS-EFM). These two orbit fitting algorithms are tested with ten sets of advanced land observation satellite phased array L-band SAR data, which were acquired in north Toronto, Ontario, Canada, from September, 2008 to January, 2009. Moreover, two of them acquired with an adjacent period were chosen to form a repeat-pass InSAR, and the corresponding baseline is calculated with the proposed method as an example. The experimental results show that the error of the satellite position using DLS-EFM is at a submetric level, which is less than one-tenth of that of the polynomial regression algorithm. Consequently, the proposed method is appropriate for the baseline estimation in spaceborne InSAR applications.

Circular grid pattern based surface strain measurement system for sheet metal forming

A surface strain measurement system (XJTUSM) for sheet metal forming is developed based on close range industry photogrammetry. A circular grid pattern is electrochemically etched onto the surface of flat sheet metal before forming. As the sheet metal is pressed into a desired shape, these circular grid nodes are deformed into approximate elliptical shapes. Original images are then recorded from different photo stations using a single camera. The three-dimensional (3D) coordinates of these ellipse centers are reconstructed according to image processing technologies, which include noise reduction, adaptive thresholding, sub-pixel edge detection, least-square ellipse fitting, camera calibration, fast matching and reconstruction of grid nodes. Subsequently, a 3D grid generation procedure is performed to build the topology of separate grid nodes and the deformation gradient tensor is calculated. Finally, the surface strains are derived from the deformation gradient tensor and the forming limit diagram (FLD) is thus obtained. To evaluate the accuracy of the novel system, a tensile experiment was carried out, and the high-accuracy surface strain measurement system XJTUDIC was employed for comparison. The surface strains measured by two systems agree well. The XJTUSM system can be used to diagnose production problems, identify critical areas and/or verify the accuracy of numerical modeling.

Estimation of cellular fabric in embryonic epithelia

Recent computational and analytical studies have shown that cellular fabric—as embodied by average cell size, aspect ratio and orientation—is a key indicator of the stresses acting in an embryonic epithelium. Cellular fabric in real embryonic tissues could not previously be measured automatically because the cell boundaries tend to be poorly defined, significant lighting and cell pigmentation differences occur and tissues contain a variety of cell geometries. To overcome these difficulties, four algorithms were developed: least squares ellipse fitting (LSEF), area moments (AM), correlation and axes search (CAS) and Gabor filters (GF). The AM method was found to be the most reliable of these methods, giving typical cell size, aspect ratio and orientation errors of 18%, 0.10 and 7.4°, respectively, when evaluated against manually segmented images. The power of the AM algorithm to provide new insights into the mechanics of morphogenesis is demonstrated through a brief investigation of gastrulation, where fabric data suggest that key gastrulation movements are driven by epidermal tensions circumferential to the blastopore.