Circle Fitting Method Research Articles

A robust circle fitting method for component fiducialization

The fiducialization for the round component is an indispensable step in the alignment. The traditional geometric and algebraic fitting algorithms are prone to be contaminated by outliers and the accuracy of existing robust algorithms can be further improved. In this study, we present a robust weighted Hyper method that combines the strengths of both the M-estimator and the Hyper method. Through Black-Rangarajan duality, outliers are assigned minimal or even zero weights, effectively enhancing robustness. We tested the proposed algorithm with several benchmarking algorithms using Monte Carlo data. In the presence of outliers, our method demonstrates the lowest root mean squared errors (RMSE). Specifically, when fitting points observed by the laser tracker in Dalian Advanced Light Source (DALS), our method outperforms existing algorithms in terms of repeat accuracy, yielding standard errors (STD) of 11.7 μm and 14.31 μm for the center and radius respectively. The robust weighted Hyper algorithm enhances fiducialization precision without requiring additional instruments and provides valuable guidance in the alignment.

A Transit Tilt and Offset Errors Calibration Method for Improving Laser Tracker Measurement Accuracy Based on the Telecentric Measurement System

Laser trackers are instruments used to measure the three-dimensional coordinates of objects with high precision. It is necessary to study calibration methods to identify geometric errors of laser trackers so as to compensate for errors and improve measurement accuracy. Among the offsets, tilts, and eccentricity errors in the system, the transit tilt and offset errors play important roles and have an essential effect on the measurement accuracy, which need to be calibrated and compensated for. Current methods for detecting geometric errors between the transit and standing axes are complex and time-consuming. In this paper, a fast and novel calibration method is proposed, which can be easily operated with high precision. Two test rods are coaxially mounted on the ends of the transit axis to extend the hidden transit axis. Then, a telecentric measurement system is used to record the projection images of the test rods and identify the position of the transit axis. The transit offset and tilt errors were thus obtained by comparing the central axis positions of the two test rods before and after the standing axis rotated 180 degrees. Moreover, a numerical analysis method was proposed based on the least square circle fitting method to calibrate the installation eccentricity errors of the test rods. Experimental results verify that the measurement accuracy of the laser tracker can be improved after error compensation using the calibrated transit offset and tilt errors. The measurement error of the laser tracker can be reduced from 161 µm to about 73 µm after compensation at a distance of 5 m, while the error can be decreased from 143 µm to about 108 µm at a distance of 10 m.

Lightweight Meter Pointer Recognition Method Based on Improved YOLOv5.

In substation lightning rod meter reading data taking, the classical object detection model is not suitable for deployment in substation monitoring hardware devices due to its large size, large number of parameters, and slow detection speed, while is difficult to balance detection accuracy and real-time requirements with the existing lightweight object detection model. To address this problem, this paper constructs a lightweight object detection algorithm, YOLOv5-Meter Reading Lighting (YOLOv5-MRL), based on the improved YOLOv5 model's speed while maintaining accuracy. Then, the YOLOv5s are pruned based on the convolutional kernel channel soft pruning algorithm, which greatly reduces the number of parameters in the YOLOv5-MRL model while maintaining a certain accuracy loss. Finally, in order to facilitate the dial reading, the dial external circle fitting method is proposed to calculate the dial reading using the circular angle algorithm. The experimental results on the self-built dataset show that the YOLOv5-MRL object detection model achieves a mean average precision of 96.9%, a detection speed of 5 ms/frame, and a model weight size of 5.5 MB, making it better than other advanced dial reading models.

Non-Contact Measurement of Cardiopulmonary Activity Using Software Defined Radios.

Vital signs are important indicators to evaluate the health status of patients. Channel state information (CSI) can sense the displacement of the chest wall caused by cardiorespiratory activity in a non-contact manner. Due to the influence of clutter, DC components, and respiratory harmonics, it is difficult to detect reliable heartbeat signals. To address this problem, this paper proposes a robust and novel method for simultaneously extracting breath and heartbeat signals using software defined radios (SDR). Specifically, we model and analyze the signal and propose singular value decomposition (SVD)-based clutter suppression method to enhance the vital sign signals. The DC is estimated and compensated by the circle fitting method. Then, the heartbeat signal and respiratory signal are obtained by the modified variational modal decomposition (VMD). The experimental results demonstrate that the proposed method can accurately separate the respiratory signal and the heartbeat signal from the filtered signal. The Bland-Altman analysis shows that the proposed system is in good agreement with the medical sensors. In addition, the proposed system can accurately measure the heart rate variability (HRV) within 0.5m. In summary, our system can be used as a preferred contactless alternative to traditional contact medical sensors, which can provide advanced patient-centered healthcare solutions.

Parameters estimation-based calibration method for rotational axis of line-structured light 3D reconstruction.

Rotation is a critical component in 3D reconstruction systems, where accurate calibration of rotation axis parameters is essential for 3D stitching. In this study, what we believe to be a novel parameters estimation-based method for calibrating rotation axis parameters using 2D planar targets is proposed. Compared to traditional circle fitting methods, this method takes both orientation and position information into account, resulting in better precision performance. By leveraging the transmission of spatial pose relationships, the parameters estimation-based calibration method also effectively mitigates the impact of noise for more accurate calibration of rotation axis parameters. Error validation and 3D reconstruction experiments proved the superior performance of the proposed method. The experiment results demonstrate the effectiveness and applicability of the approach in enhancing the calibration of rotation axis parameters for 3D reconstruction systems.

Research on the measurement method of crankshaft coaxiality error based on three-dimensional point cloud

Aiming at the demand of rapid detection for coaxiality of crankshaft journal, a method of visual measurement of coaxiality error based on 3D point cloud is proposed. In this research, a laser scanner is utilized to obtain a 3D point cloud model of the part to be measured, and a circular method of rotary cutting is put forward to obtain equally spaced optimal slices of the journal. The center of the slice is then obtained using the Pratt circle fitting method optimized in this paper. After that, the center of the slice is used to obtain the common reference axis using the least squares method, which finally realizes the measurement of the coaxiality error. The experimental results show that the proposed method of getting the slices is more accurate, the maximum absolute error of the circle fitting method compared with the results of the coordinate measuring machine (CMM) is no more than 4.2 μm, and the maximum absolute error of the coaxiality detection results and the results of the CMM is 5.5 μm, which can satisfy the practical needs of fast and efficient measurement of the coaxiality error of crankshafts.

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.

Sequential calibration of transmission ratios for joints of 6-DOF serial industrial robots based on laser tracker

PurposeIn traditional calibration methods of kinematics parameters of industrial robots, dozens of model parameters are identified together based on an optimization procedure. Due to different contributions of model parameter errors to the tool center point positioning error of industrial robots, obtaining good results for all model parameters is very difficult. Therefore, the purpose of this paper is to propose a sequential calibration method specifically for transmission ratio parameters, which includes reduction ratios and coupling ratios of industrial robot joints.Design/methodology/approachThe ABB IRB 1410 industrial robot is considered as an example in this study. The transmission ratios for each joint of the robot are identified using the spatial circle fitting method based on spatial vectors, which fit the center and radius of joint rotation with the least squares optimization algorithm. In addition, a method based on the Rodrigues’ formula is designed and presented for identifying the actual coupling ratio of the robot. Subsequently, an experiment is carried out to verify the proposed sequential calibration method of transmission ratios.FindingsIn this experiment, the actual positions of the linkages before and after joint rotations are measured by a laser tracker. Accurate results of the reduction ratios and the coupling ratios are calculated, and the results are verified experimentally. The results show that by calibrating the reduction ratios and coupling ratios of the ABB robot, the rotation angle errors of the robot joints can be reduced.Originality/valueThe authors propose a sequential calibration method for transmission ratio parameters, including reduction ratios and coupling ratios of industrial robot joints. An experiment is carried out to verify this proposed sequential calibration method. This study may be beneficial for calibrating the kinematic parameters of industrial robots and improving their positioning accuracy.

Automatic Recognition Reading Method of Pointer Meter Based on YOLOv5-MR Model.

Meter reading is an important part of intelligent inspection, and the current meter reading method based on target detection has problems of low accuracy and large error. In order to improve the accuracy of automatic meter reading, this paper proposes an automatic reading method for pointer-type meters based on the YOLOv5-Meter Reading (YOLOv5-MR) model. Firstly, in order to improve the detection performance of small targets in YOLOv5 framework, a multi-scale target detection layer is added to the YOLOv5 framework, and a set of Anchors is designed based on the lightning rod dial data set; secondly, the loss function and up-sampling method are improved to enhance the model training convergence speed and obtain the optimal up-sampling parameters; Finally, a new external circle fitting method of the dial is proposed, and the dial reading is calculated by the center angle algorithm. The experimental results on the self-built dataset show that the Mean Average Precision (mAP) of the YOLOv5-MR target detection model reaches 79%, which is 3% better than the YOLOv5 model, and outperforms other advanced pointer-type meter reading models.

A novel method to calibrate the rotation axis of a line-structured light 3-dimensional measurement system

Rotation axis calibration is the key to line-structured light 3-dimensional (3D) measurement. The traditional calibration method based on circle fitting only uses the position information of the calibration target and ignores the orientation information, which is easily affected by noise. This paper proposes a new calibration method combining the orientation and position information to improve the calibration accuracy. Compared with the circle fitting method, the added orientation information makes the description of rotation more complete. On this basis, an improved extrinsic parameters estimation method is proposed to obtain more accurate position and orientation information of the target, which further improves the calibration accuracy. The experiment results show that, the radius error is reduced by about 90% and the standard deviation of radius error is reduced by about 40% compared with the traditional circle fitting method.

Iron Ore Pellet Size Analysis: A Machine Learning-Based Image Processing Approach

In this article, an ensembled convolutional neural network (CNN)-based algorithm is proposed for iron ore pellet size analysis. A new customized CNN is ensembled along with VGG16, MobileNet, and ResNet50. The algorithm uses images captured from the inside area of a pelletizer disk to directly estimate the pellet size class instead of employing a circle fitting method. An image data set is created for different size classes (VERY SMALL, SMALL, GOOD, BIG, and VERY BIG) by using a novel cropping and resizing method, where the mean sizes are 7–19 mm, at a step of 3 mm. Actual industrial images captured using an industrial camera during pellet production are used as the seed images for the data set creation and training, validation, and testing of the proposed model. Through extensive experimentation, it is shown that the proposed classification algorithm can achieve about 96%–99% accuracy, whereas if the custom-designed CNN is not used, the accuracy obtained is about 77%–95% for different classes. In addition to this, the proposed trained network is validated with pellet images of an intermediate mean size to show that the trained model is not overfitted.

A high-accuracy circular hole measurement method based on multi-camera system

Industrial parts often contain a large number of circular holes that are often used as assembly datums. Measuring circular holes with high accuracy is very challenging due to the low signal-to-noise ratio of the edges on the image. This problem is further complicated when chamfers and nonuniform reflections are present. In this paper, a high-accuracy method for measuring circular holes is proposed to realize on-line inspection under a multi-camera system. In the image processing stage, an ellipse detector is designed based on a high-confidence edge detection algorithm and state-of-the-art ellipse fitting technology to significantly eliminate the ellipse fitting bias caused by blurred edges. In the ellipse matching and validation stage, the ambiguous objects are reconstructed first using ambiguous ellipse pairs matched by the epipolar geometry. Then, the similarity between the reprojected ellipse and the detected ellipse is assessed by calculating the Euclidean distance to significantly eliminate mismatched candidates and select the best matching ones. Subsequently, the discrete 3-D points are calculated by spatial intersection after obtaining the homologous points on the corresponding ellipses. Furthermore, a robust spatial circle fitting method is developed to adapt to discrete 3-D points that are not strictly located on a plane. Finally, extensive experiments on both real-world datasets and simulation datasets demonstrate that the proposed algorithm is beneficial for improving the measurement accuracy compared with the state-of-the-art algorithms and demonstrate great potential for industrial applications.

An Algorithm to Extract the Boundary and Center of EUV Solar Image Based on Sobel Operator and FLICM

An algorithm to extract the disk boundary and center of EUV solar image using the Sobel operator, Fuzzy Local Information C-Means Clustering algorithm (FLICM), and the least square circle fitting method is proposed in this paper. The Sobel operator can determine the solar disk boundary preliminarily, and then the image is processed further using the FLICM algorithm. After the background is removed based on the clustered image and the boundary points can be highlighted, these points are fitted using the least square circle fitting method as the final boundary circle. The solar data used in this paper was from the observation of the Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA) instrument. The 2523 19.3 nm solar images covering solar minimum, moderate solar activity, and more active suns were calculated using the proposed algorithm to analyze the accuracy statistically. The statistical comparison results demonstrate that the method is accurate and effective. This method can support the processing of solar EUV images and serve the operational system of a space weather forecast.

Tree position estimation from TLS data using hough transform and robust least-squares circle fitting

Forest management and planning require information regarding the current state of the forest. Remote sensing techniques allow to obtain geospatial data, also for the forestry sector. As one of the remote-sensed technologies datasets, Terrestrial Laser Scanning data is widely used to derive detailed information about tree and forest stand parameters. This article presents the combination of circular Hough transform, denoising procedure, and robust least-square circle fitting method to extract stem positions from Terrestrial Laser Scanning data. In the proposed approach, initial tree stems position was detected with circular Hough transform. Then, obtained results were denoised to exclude most non-tree trunk points and analyze three-dimensional data from laser scanning to find exact circular tree stems with a robust least-square circle fitting method. The developed algorithm is effective in obtaining the trees’ geodetic positions from laser scanning data. The results generated in this study can be used as basics for further automatic determination of tree characteristics, such as tree species, height, or crown range. In this study, 94.8% tree stems delineation was generated with a mean accuracy of 87.2%, 1.64 cm of root mean square error for stem position, and 1.15 cm for tree radius measured at ground level. The process conducted in this research can be used to detect other circle-shaped objects, such as lamps or power towers, for which obtaining dense Terrestrial Laser Scanning data is available. The detected positions of these objects can power the geographic information systems or thematic industry systems, where it is necessary to determine the geodetic object position results from legal regulations.

Tiny hole inspection of aircraft engine nacelle in 3D point cloud via robust statistical fitting

In the aircraft manufacturing industry, drilling hole inspection is a vital task for the noise reduction ability and the aircraft structure stability. Due to the complexity of the inner surface of the engine nacelle, inspecting drilling holes of a small size and a large number is fairly challenging. In this paper, we propose a framework for automatic hole inspection on composite flat parts. The raw data of traditional 3D laser scanning usually contain considerable noise and outliers, which has a great influence on tiny hole inspection. First, to perform measurement efficiently and to get raw data of good quality, we design a measurement platform to perform automatic measurement on a preset path. Instead of applying common boundary detection methods, we design a method to detect boundary points by evaluating the boundary possibility of each point, which is more likely to detect the points on a real hole boundary than noise. Based on the characteristics of laser scanning data, we then combine an effective algebraic circle fitting method with an iterative fitting strategy and develop a robust circle fitting method. The improved circle fitting method is capable of estimating a circle closest to the ground truth. Experiments demonstrate that our fitting method performs better than other common fitting methods for comparison under both synthetic and real scanning data.

Estimating tree Diameter at Breast Height (DBH) using an iPad Pro LiDAR sensor

ABSTRACT Diameter at Breast Height (DBH) plays an important role in forest management. New technologies such as airborne and terrestrial Light Detection and Ranging (LiDAR) are expensive and time-consuming. We explored the iPad LiDAR sensor to measure DBH considering affordability and availability. The study was carried out at a research forest plantation near Thunder Bay, Ontario, Canada. Five plots were selected for differences in stem spacing, average DBH and species, and made 360° scans separately. A manual circle fitting method was used to produce circular features for the estimation of DBH. The coefficient of determination (R 2) between estimated DBH and field measurements was 0.52, indicating a moderate accuracy. The Root Mean Square Error (RMSE) of DBH estimation ranged from 2.82 cm to 8.24 cm. The accuracy of smaller red pine trees was found to be relatively higher than that of larger red pine and white spruce trees. These accuracies did not change with the distance from the scanning location to trees. Therefore, results showed the potential use of an iPad LiDAR Scanner for DBH estimation. We recommend developing an application combining the iPad’s location and LiDAR sensors and incorporating a precise positioning method for fieldwork, and further broad field testing.

Segmenting Individual Tree from TLS Point Clouds Using Improved DBSCAN

Terrestrial laser scanning (TLS) can provide accurate and detailed three-dimensional (3D) structure information of the forest understory. Segmenting individual trees from disordered, discrete, and high-density TLS point clouds is the premise for obtaining accurate individual tree structure parameters of forest understory, pest control and fine modeling. In this study, we propose a bottom-up method to segment individual trees from TLS forest data based on density-based spatial clustering of applications with noise (DBSCAN). In addition, we also improve the DBSCAN based on the distance distribution matrix (DDM) to automatically and adaptively determine the optimal cluster number and the corresponding input parameters. Firstly, the proposed method is based on the improved DBSCAN to detect the trunks and obtain the initial clustering results. Then, the Hough circle fitting method is used to modify the trunk detection results. Finally, individual tree segmentation is realized based on regional growth layer-by-layer clustering. In this paper, we use TLS multi-station scanning data from Chinese artificial forest and German mixed forest, and then evaluate the efficiency of the method from three aspects: overall segmentation, trunk detection and small tree segmentation. Furthermore, the proposed method is compared with three existing individual tree segmentation methods. The results show that the total recall, precision, and F1-score of the proposed method are 90.84%, 95.38% and 0.93, respectively. Compared with traditional DBSCAN, recall, accuracy and F1-score are increased by 6.96%, 4.14% and 0.06, respectively. The individual tree segmentation result of the proposed method is comparable to those of the existing methods, and the optimal parameters can be automatically extracted and the small trees under tall trees can be accurately segmented.

Detrending Technique for Denoising in CW Radar.

A detrending technique is proposed for continuous-wave (CW) radar to remove the effects of direct current (DC) offset, including DC drift, which is a very slow noise that appears near DC. DC drift is mainly caused by unwanted vibrations (generated by the radar itself, target objects, or surroundings) or characteristic changes in components in the radar owing to internal heating. It reduces the accuracy of the circle fitting method required for I/Q imbalance calibration and DC offset removal. The proposed technique effectively removes DC drift from the time-domain waveform of the baseband signals obtained for a certain time using polynomial fitting. The accuracy improvement in the circle fitting by the proposed technique using a 5.8 GHz CW radar decreases the error in the displacement measurement and increases the signal-to-noise ratio (SNR) in vital signal detection. The measurement results using a 5.8 GHz radar show that the proposed technique using a fifth-order polynomial fitting decreased the displacement error from 1.34 mm to 0.62 mm on average when the target was at a distance of 1 m. For a subject at a distance of 0.8 m, the measured SNR improved by 7.2 dB for respiration and 6.6 dB for heartbeat.

Dot Grid와 카메라 영상 오차 보정 알고리즘을 이용한 이차 전지 전극 Alignment 정밀 검사

Industrial cameras used in traditional machine vision are subject to errors because of the distortions induced in the images due to the camera lenses and various external factors. To calibrate these errors, a picture of the dot grid was taken and the center of the circle was calculated using the least squares circle-fitting method and the centroid method. In addition, an error map was generated using these methods, which can be used for generating a first-order equation with the least squares method. It is possible to calibrate the object point. In this work, an equation that can correct this error and perform an accurate measurement. It was applied to the stacking equipment of secondary batteries for automobiles to an algorithm that accurately measures the alignment of the cathode and the anode.

Accuracy Assessment of Total Stem Volume Using Close-Range Sensing: Advances in Precision Forestry

Accurate collection of dendrometric information is essential for improving decision confidence and supporting potential advances in forest management planning (FMP). Total stem volume is an important forest inventory parameter that requires high accuracy. Terrestrial laser scanning (TLS) has emerged as one of the most promising tools for automatically measuring total stem height and diameter at breast height (DBH) with very high detail. This study compares the accuracy of different methods for extracting the total stem height and DBH to estimate total stem volume from TLS data. Our results show that estimates of stem volume using the random sample consensus (RANSAC) and convex hull and HTSP methods are more accurate (bias = 0.004 for RANSAC and bias = 0.009 for convex hull and HTSP) than those using the circle fitting method (bias = 0.046). Furthermore, the RANSAC method had the best performance with the lowest bias and the highest percentage of accuracy (78.89%). The results of this study provide insight into the performance and accuracy of the tested methods for tree-level stem volume estimation, and allow for the further development of improved methods for point-cloud-based data collection with the goal of supporting potential advances in precision forestry.