Centroid Estimation Research Articles

Multi-instance learning in the presence of positive and unlabeled bags

Multi-instance learning is a classic algorithm within the weakly supervised learning framework. Most previous approaches to multi-instance learning have typically assumed that every bag comes with its own label. However, in real-world applications, obtaining fully-labeled bags can be a challenging and resource-intensive task, primarily due to the substantial time and labor required for labeling each instance. Fortunately, collecting bags with only positive and unlabeled instances is a more feasible option. In this paper, we aim to learn an efficient binary classifier using positive and unlabeled bags. To address the absence of negative bags, we adopt a novel strategy that combines label noise learning and multi-instance kernels. Our approach involves a comprehensive analysis of empirical risk minimization in the presence of label noise, allowing us to decompose the loss function for negative bags with false negative labels into two distinct parts. Importantly, only the second part of this loss function is affected by the presence of noisy labels. To mitigate the influence of noisy labels on the negative bags, we propose the Multi-Instance Kernel-based Centroid Estimation (MIKCE) technique. MIKCE is a versatile method that can be employed with various types of data, including linear and nonlinear cases. Additionally, we provide an upper bound on the generalization error, ensuring the convergence of the MIKCE algorithm. Finally, we conduct numerical experiments on 31 public datasets to empirically validate the effectiveness of the MIKCE approach.

Gap measurement method based on projection lines and convex analysis of 3D points cloud

Abstract Accurate measurement of the gap between the lower surface of the relay and the ground is critical for ensuring the quality of the finished product. Traditional gap measurement methods have some shortcomings, such as low accuracy, poor robustness, and loss of depth clues in obscured areas. In this study, a novel gap measurement method based on computer vision is proposed, which includes a projection line model based on guided filtering and a 3D surface point cloud model based on a three dimensional plane reference.- The relay gap was measured by calculating the projection lines of the upper and lower surfaces of the gap with an error of ±0.016 mm. A 3D point cloud model captures the key features of the underside of the relay through image processing techniques, and combines convex hull and centroid estimation to construct a three-dimensional reference plane for the gap, which could achieve high-precision, real-time measurement of the gap (with an error less than ±0.0087 mm). The experimental measurement results show that the proposed method is better than the SelfConvNet method, which has a high measurement accuracy and strong anti-interference ability, and an accuracy rate of up to 99.5% in factory relay quality inspection experiments.

K-Means NANI: An Improved Clustering Algorithm for Molecular Dynamics Simulations.

One of the key challenges of k-means clustering is the seed selection or the initial centroid estimation since the clustering result depends heavily on this choice. Alternatives such as k-means++ have mitigated this limitation by estimating the centroids using an empirical probability distribution. However, with high-dimensional and complex data sets such as those obtained from molecular simulation, k-means++ fails to partition the data in an optimal manner. Furthermore, stochastic elements in all flavors of k-means++ will lead to a lack of reproducibility. K-means N-Ary Natural Initiation (NANI) is presented as an alternative to tackle this challenge by using efficient n-ary comparisons to both identify high-density regions in the data and select a diverse set of initial conformations. Centroids generated from NANI are not only representative of the data and different from one another, helping k-means to partition the data accurately, but also deterministic, providing consistent cluster populations across replicates. From peptide and protein folding molecular simulations, NANI was able to create compact and well-separated clusters as well as accurately find the metastable states that agree with the literature. NANI can cluster diverse data sets and be used as a standalone tool or as part of our MDANCE clustering package.

Multi-line-of-sight Hartmann-Shack wavefront sensing based on image segmentation and K-means sorting

Multi-line-of-sight wavefront sensing, crucial for next-generation astronomy and laser applications, often increases system complexity by adding sensors. This research introduces, to the best of our knowledge, a novel method for multi-line-of-sight Hartmann-Shack wavefront sensing by using a single sensor, addressing challenges in centroid estimation and classification under atmospheric turbulence. This method contrasts with existing techniques that rely on multiple sensors, thereby reducing system complexity. Innovations include combining edge detection and peak extraction for precise centroid calculation, improved k-means clustering for robust centroid classification, and a centroid filling algorithm for subapertures with light loss. The method’s effectiveness was confirmed through simulations for a five-line-of-sight system and experimental setup for two-line and three-line-of-sight systems, demonstrating its potential in real atmospheric aberration correction conditions. Experimental findings indicate that, when implemented in a closed-loop configuration, the method significantly reduces wavefront residuals from 1 λ to 0.1 λ under authentic atmospheric turbulence conditions. Correspondingly, the quality of the far-field spot is enhanced by a factor of 2 to 4. These outcomes collectively highlight the method’s robust capability in enhancing optical system performance in environments characterized by genuine atmospheric turbulence.

Estimating Per-Class Statistics for Label Noise Learning.

Real-world data may contain a considerable amount of noisily labeled examples, which usually mislead the training algorithm and result in degraded classification performance on test data. Therefore, Label Noise Learning (LNL) was proposed, of which one popular research trend focused on estimating the critical statistics (e.g., sample mean and sample covariance), to recover the clean data distribution. However, existing methods may suffer from the unreliable sample selection process or can hardly be applied to multi-class cases. Inspired by the centroid estimation theory, we propose Per-Class Statistic Estimation (PCSE), which establishes the quantitative relationship between the clean (first-order and second-order) statistics and the corresponding noisy statistics for every class. This relationship is further utilized to induce a generative classifier for model inference. Unlike existing methods, our approach does not require sample selection from the instance level. Moreover, our PCSE can serve as a general post-processing strategy applicable to various popular networks pre-trained on the noisy dataset for boosting their classification performance. Theoretically, we prove that the estimated statistics converge to their ground-truth values as the sample size increases, even if the label transition matrix is biased. Empirically, we conducted intensive experiments on various binary and multi-class datasets, and the results demonstrate that PCSE achieves more precise statistic estimation as well as higher classification accuracy when compared with state-of-the-art methods in LNL.

Fast eye centre localization using combined unsupervised technics

Eye movements offer precious information about persons? state. Video surveillance, marketing, driver fatigue as well as medical diagnosis assistance applications manage eye behavior. We propose a new method for efficiently detecting eye movement. In this paper, we combine circle eye model with eye feature method to improve the accuracy. A set of detectors estimate the eyes centers to increase the localization rate. As a pre-processing stage, the mean of the edges yields the center of the two eye regions. Image treatment operations reduce the ROI. A Circle Hough Transform (CHT) algorithm is adopted in a modified version as a detector to find the circle eye in the image; the circle center found represents the eye's pupil estimation. We introduced the Maximally Stable Extremal Region (MSER) as a second detector, which has never been used for eye localization. Invariant to continuous geometric transformations and affine intensity changes and detected at several scales, MSERs efficiently detect regions of interest, in our case eye regions, and precisely, their centers. Ellipses fit MSERs, and their centroid estimation match eyes center. We demonstrate that the true eye centers can be found by combining these methods. The validation of the proposed method is performed on a very challenging BioID base. The proposed approach compares well with existing state-of-the-art techniques and achieves an accuracy of 82.53% on the BioID database when the normalized error is less than 0.05, without prior knowledge or any learning model.

Multi-task label noise learning for classification

Multi-task classification improves generalization performance via exploiting the correlations between tasks. However, most multi-task learning methods fail to recognize and filter noisy labels for the classification problems with label noises. To address this issue, this paper proposes a novel multi-task label noise learning method based on loss correction, called MTLNL. MTLNL introduces the class-wise denoising (CWD) method for loss decomposition and centroid estimation of the loss function in multi-task learning, and eliminates the impact of label noise by using label flipping rate. It also extends to the multi-task positive-unlabeled (PU) learning domain, which offers better flexibility and generalization performance. Moreover, Nesterov’s method is applied to accelerate the solution of the model. MTLNL is compared with other algorithms on five benchmark datasets, five image datasets, and a multi-task PU dataset to demonstrate its effectiveness.

A robust and precise centroid positioning method for the weak beacon spot in long-distance inter-satellite optical wireless communications.

The centroid estimation of the beacon spot is crucial to the pointing, acquisition, and tracking subsystem in inter-satellite optical wireless communication (IsOWC), especially for the received very weak beacon caused by a long link distance. In this work, we propose an accurate centroid positioning method to calculate the centroid of such a weak beacon with a low peak signal-to-noise ratio. The proposed method is based on the idea that uses the normalized amplitude of the gray gradient to enhance the weights near the center of the beacon spot. Both comparative numerical simulation and experimental verification are implemented, which demonstrate the effectiveness and feasibility of the proposed method. Compared to the gray centroid method, interpolation-based method, Hough transform method, and Gaussian fitting method, the proposed method has stronger robustness and higher accuracy, which could be helpful to applications in IsOWC as well as beacon-based pointing and tracking systems.

Decentralized fault tolerant source localization without sensor parameters in wireless sensor networks

In this paper, we study the source (event) localization problem in decentralized wireless sensor networks (WSNs) under faulty sensor nodes without knowledge of the sensor parameters. Source localization has many applications, such as localizing WiFi hotspots and mobile users. Some works in the literature localize the source by utilizing the knowledge or estimates of the fault probability of each sensor node or the region of influence of the source. However, this paper proposes two approaches: the hitting set and feature selection for estimating the source location without any knowledge of the sensor parameters under faulty sensor nodes in WSN. The proposed approaches provide better or comparable source localization performances. For the hitting set approach, we also derive a lower bound on the required number of samples. In addition, we extend the proposed methods for localizing multiple sources. Finally, we provide extensive simulations to illustrate the performances of the proposed methods against the centroid, maximum likelihood (ML), fault-tolerant ML (FTML), and subtract on negative add on positive (SNAP) estimators. The proposed approaches significantly outperform the centroid and maximum likelihood estimators for faulty sensor nodes while providing comparable or better performance to FTML or SNAP algorithm. In addition, we use real-world WiFi data set to localize the source in comparison to the support vector machine based estimator in the literature, where the proposed methods outperformed the estimator.

Integrated Approach for Cobb Angle Estimation in X-Ray C-Curve Scoliosis Using Image Processing and Inverse Cosine Law

Cobb angle is the angle subtended by the most tilted vertebrae. It represents the degree of the spinal curvature and has been used to diagnose scoliosis. The severity of the scoliosis based on the cobb angle will determine the guide treatment and surgical planning. Manual measurement of Cobb angle using protractor or semi-manual using ONIS software is quite time consuming, and it is subjected to variations in interobserver and intraobserver measurements. This research proposed an algorithm to determine the Cobb angle using image processing and inverse cosine methods. The raw samples of X-ray images were obtained from Pusat Kesihatan Universiti (PKU), UTHM. Several interviews were conducted with radiologist at Pantai Hospital for verification purpose. Gaussian blur and unsharp mask were initially applied for noise removal in the preprocessing step. Three points were marked at the vertebrae image to assist for centroid estimation using Haar Cascade. The Cobb angle was estimated by applying the triangle formula derived from the inverse cosine law. In comparison to semi-manual method (Onis Software), the proposed technique has an error of less than 5 % and computes the Cobb angle 3.28 times quicker. In the future, it is suggested to explore other techniques such as deep learning for alternative data analysis for Cobb angle estimation.

An Object SLAM Framework for Association, Mapping, and High-Level Tasks

Object SLAM is considered increasingly significant for robot high-level perception and decision-making. Existing studies fall short in terms of data association, object representation, and semantic mapping and frequently rely on additional assumptions, limiting their performance. In this paper, we present a comprehensive object SLAM framework that focuses on object-based perception and object-oriented robot tasks. First, we propose an ensemble data association approach for associating objects in complicated conditions by incorporating parametric and nonparametric statistic testing. In addition, we suggest an outlier-robust centroid and scale estimation algorithm for modeling objects based on the iForest and line alignment. Then a lightweight and object-oriented map is represented by estimated general object models. Taking into consideration the semantic invariance of objects, we convert the object map to a topological map to provide semantic descriptors to enable multi-map matching. Finally, we suggest an object-driven active exploration strategy to achieve autonomous mapping in the grasping scenario. A range of public datasets and real-world results in mapping, augmented reality, scene matching, relocalization, and robotic manipulation have been used to evaluate the proposed object SLAM framework for its efficient performance.

Order Statistic Estimation With Application to Tracking in Autonomous Driving

In this work, we study the order statistic estimation and provide a simple solution to lidar bounding box (BB) centroid estimation for an autonomous vehicle (AV). The estimated BB centroid and its uncertainty will be used in object tracking as measurement and measurement noise variance; the latter is commonly not available from the sensor manufacturer, and is needed for data association and target state estimation. The detected and clustered sensor observations for a single target, on one axis, are assumed to have i) a triangular density, or ii) a uniform (rectangular) density. These densities constitute the likelihood function (LF) of the corresponding support (the interval where they are nonzero) boundaries. Estimators are proposed for the LF support boundary parameter estimation and the centroid coordinates are given by the centers of the boundaries. Experiments using real data are carried out to show the performance of the proposed methods for autonomous driving applications. A comparison with the Max-Min average approach shows the superiority of the proposed algorithm.

Robust Centroid Estimation Method with the Rough and Refined Estimation for Interplanetary Optical Navigation

As the interest in probing deep space increases, it is necessary to enhance the autonomous navigation capabilities of the spacecraft. Since traditional navigation methods rely on ground-based radiometric tracking, the vehicle has a significant communication delay resulting in no ability to handle unexpected situations on time. Image-based optical navigation allows interplanetary spacecraft to determine their orbits autonomously. This paper explores how to accurately extract optical observations from the original images to perform autonomous navigation. First, we introduce a simple and efficient idea to locate valuable contours of the celestial body based on gradient variations. Then, we establish a rough estimation with RANSAC to remove the outliers around the edges. Next, we propose a refined estimation based on the hybrid genetic algorithm to precisely estimate the navigation observations. Lastly, numerous experiments have confirmed that our method achieves outstanding accuracy and robustness.

FPGA Implementation of Shack–Hartmann Wavefront Sensing Using Stream-Based Center of Gravity Method for Centroid Estimation

We present a fast and reconfigurable architecture for Shack–Hartmann wavefront sensing implemented on FPGA devices using a stream-based center of gravity to measure the spot displacements. By calculating the center of gravity around each incoming pixel with an optimal window matching the spot size, the common trade-off between noise and bias errors and dynamic range due to window size existing in conventional center of gravity methods is avoided. In addition, the accuracy of centroid estimation is not compromised when the spot moves to or even crosses the sub-aperture boundary, leading to an increased dynamic range. The calculation of the centroid begins while the pixel values are read from an image sensor and further computation such as slope and partial wavefront reconstruction follows immediately as the sub-aperture centroids are ready. The result is a real-time wavefront sensing system with very low latency and high measurement accuracy feasible for targeting on low-cost FPGA devices. This architecture provides a promising solution which can cope with multiple target objects and work in moderate scintillation.

Impact of SAR Azimuth Ambiguities on Doppler Velocity Estimation Performance: Modeling and Analysis

Doppler Centroid Analysis (DCA) technique is one of the major techniques that do permit a direct retrieval of ocean surface velocity from synthetic aperture radar (SAR) data. However, azimuth ambiguities in the SAR images severely restrict the capability of DCA technique to obtain accurate ocean surface Doppler velocities. Therefore, it is necessary to investigate how the azimuth ambiguities impact the Doppler velocity estimation performance and to evaluate how significant the impact is. In this paper, a model for ocean surface Doppler velocity estimation affected by azimuth ambiguities is developed resorting to jointly circular Gaussian processes, and its statistic is derived. The impact of azimuth ambiguities on Doppler velocity estimation performance in terms of Doppler centroid estimation bias and the standard deviation of Doppler centroid estimates is analyzed. The theoretical results are validated through simulation and Doppler velocities retrieved from Chinese Gaofen-3 (GF-3) SAR Doppler centroid estimates affected by azimuth ambiguities. This study will help researchers better understand the impact of azimuth ambiguities on Doppler velocity estimation, and will provide a theoretical reference for subsequent research on how to reduce the impact of azimuth ambiguities more effectively.

Improved Analytical Formula for the SAR Doppler Centroid Estimation Standard Deviation for a Dynamic Sea Surface

The existing formulas for the synthetic aperture radar (SAR) Doppler centroid estimation standard deviation (STD) suffer from various limitations, especially for a dynamic sea surface. In this study, we derive an improved version of these formulas through three steps. First, by considering the ocean wavenumber spectrum information, a new strategy for determining the number of independent samples of the sea wave velocity field is adopted in the new formula. This is contrary to the method used in the existing formulas, where the number of SAR geometric resolution cells is taken as the number of samples assuming that adjacent SAR resolution cells are statistically uncorrelated. Second, the pulse repetition frequency and Doppler bandwidth are decoupled in the new formula, unlike in the existing formulas where they are unchangeably related to each other. Third, the effects of thermal noise and Doppler aliasing are jointly quantified in a mathematically exact manner instead of being treated separately, as in the existing formulas. Comprehensive SAR raw data simulations for the ocean surface show that the new formula has a better performance in predicting the Doppler centroid estimation STD than the existing formulas.

Distributed Dual Averaging Based Data Clustering

Multiagent distributed clustering scheme is proposed herein to process data which are collected by dispersed sensors that are not under centralized control. Two methods based on distributed dual averaging (DDA) algorithm are proposed, which are able to incorporate network structure and do not require exchange of centroid estimates, which makes it appealing for security conscious applications. The first method provides the framework for distributed clustering using the DDA algorithm with predefined regularization parameter. The second method, called Adaptive DDA (ADDA), relaxes the condition concerning <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge about the centroids, assumed in the first method, without losing clustering performance. This is achieved by properly regularizing the problem where a data-driven approach is used to determine the regularization parameter. The proposed methods are further extended via the proposed Bin method to scenario where processing agents store unbalanced amount of data with non-IID class distribution. Experiments are conducted on both real-life and synthetic data. Numerical results show the efficacy of the proposed approaches compared to state-of-art centralized algorithm and other distributed approaches.

Achieving nanoscale precision using neuromorphic localization microscopy.

Neuromorphic cameras are a new class of dynamic-vision-inspired sensors that encode the rate of change of intensity as events. They can asynchronously record intensity changes as spikes, independent of the other pixels in the receptive field, resulting in sparse measurements. This recording of such sparse events makes them ideal for imaging dynamic processes, such as the stochastic emission of isolated single molecules. Here we show the application of neuromorphic detection to localize nanoscale fluorescent objects below the diffraction limit, with a precision below 20 nm. We demonstrate a combination of neuromorphic detection with segmentation and deep learning approaches to localize and track fluorescent particles below 50 nm with millisecond temporal resolution. Furthermore, we show that combining information from events resulting from the rate of change of intensities improves the classical limit of centroid estimation of single fluorescent objects by nearly a factor of two. Additionally, we validate that using post-processed data from the neuromorphic detector at defined windows of temporal integration allows a better evaluation of the fractalized diffusion of single particle trajectories. Our observations and analysis is useful for event sensing by nonlinear neuromorphic devices to ameliorate real-time particle localization approaches at the nanoscale.

On the Emergent Hypocycloidal and Epicycloidal Formations in a Swarm of Double Integrator Agents

In this letter, a multi-agent system with emergent hypocycloidal and epicycloidal behaviors is analyzed. Agents are assumed to be modeled as double integrators with an acceleration law designed so that the swarm exhibits cycloidal like trajectories. The resulting control protocol benefits from speeds and positions coupling among neighbors agents to let each agent perform hypocycloidal or epicycloidal curves according to the choice of the controller parameters and the agents initial conditions. As a first step, the model properties are obtained assuming that the communication topology of the multi-agent system is defined by a complete graph. As a further step, the model main features are extended by relaxing the complete connection assumption and replacing it with a more realistic one in which a connected graph is considered. This latter step is achieved by means of a consensus-based estimation of the swarm centroid, so that to virtualize the complete graph starting from a connected one. Simulations have been performed to show the properties of the obtained agents evolution.

Comparison of Doppler-Derived Sea Ice Radial Surface Velocity Measurement Methods From Sentinel-1A IW Data

The near-instantaneous radial velocity of a target can be obtained using the Doppler effect of SAR, which is widely used in ocean current retrieval. However, in sea ice drift velocity measurements, only a Doppler centroid estimation algorithm in frequency domain has been studied, so whether there is a better algorithm is worth exploring. In this study, based on Sentinel-1A IW data, three Doppler centroid estimation algorithms applied to ocean current retrieval are selected. Combined with the characteristics of the TOPS mode, made two applicability adjustments to each algorithm, and finally applied the three algorithms to sea ice radial surface velocity measurements. The first adjustment is to explore and determine the optimal parameters. The second adjustment is to use parallel computing to improve the efficiency, which is improved by an average of 43.55%. In addition, the deviation of Doppler centroid estimation bias correction is verified using rainforest data, and the deviation is controlled at approximately 3 Hz. Based on the three algorithms, five sets of experiments are carried out in this study. By analyzing and comparing the results of each algorithm, it is found that the results of the three algorithms are relatively consistent, among which the correlation Doppler estimation algorithm has the advantages of high efficiency and high precision and is the most suitable method for sea ice drift measurement among the three methods. However, for SAR images with abnormal speckles caused by human activities, the sign Doppler estimation algorithm can effectively remove abnormal speckles and ensure the smoothness of the image with better adaptability.