Projection Filter Research Articles

Target Fitting Method for Spherical Point Clouds Based on Projection Filtering and K-Means Clustered Voxelization.

Industrial computed tomography (CT) is widely used in the measurement field owing to its advantages such as non-contact and high precision. To obtain accurate size parameters, fitting parameters can be obtained rapidly by processing volume data in the form of point clouds. However, due to factors such as artifacts in the CT reconstruction process, many abnormal interference points exist in the point clouds obtained after segmentation. The classic least squares algorithm is easily affected by these points, resulting in significant deviation of the solution of linear equations from the normal value and poor robustness, while the random sample consensus (RANSAC) approach has insufficient fitting accuracy within a limited timeframe and the number of iterations. To address these shortcomings, we propose a spherical point cloud fitting algorithm based on projection filtering and K-Means clustering (PK-RANSAC), which strategically integrates and enhances these two methods to achieve excellent accuracy and robustness. The proposed method first uses RANSAC for rough parameter estimation, then corrects the deviation of the spherical center coordinates through two-dimensional projection, and finally obtains the spherical center point set by sampling and performing K-Means clustering. The largest cluster is weighted to obtain accurate fitting parameters. We conducted a comparative experiment using a three-dimensional ball-plate standard. The sphere center fitting deviation of PK-RANSAC was 1.91 μm, which is significantly better than RANSAC's value of 25.41 μm. The experimental results demonstrate that PK-RANSAC has higher accuracy and stronger robustness for fitting geometric parameters.

Diagnostic Value of Menstrual Blood Lipidomics in Endometriosis: A Pilot Study.

Endometriosis is a prevalent chronic inflammatory disease characterized by a considerable delay between initial symptoms and diagnosis through surgery. The pressing need for a timely, non-invasive diagnostic solution underscores the focus of current research efforts. This study examines the diagnostic potential of the menstrual blood lipidome. The lipid profile of 39 samples (23 women with endometriosis and 16 patients in a control group) was acquired using reverse-phase high-performance liquid chromatography-mass spectrometry with LipidMatch processing and identification. Profiles were normalized based on total ion counts. Significant differences in lipids were determined using the Mann-Whitney test. Lipids for the diagnostic model, based on logistic regression, were selected using a combination of variance importance projection filters and Akaike information criteria. Levels of ceramides, sphingomyelins, cardiolipins, triacylglycerols, acyl- and alkenyl-phosphatidylethanolamines, and alkenyl-phosphatidylcholines increased, while acyl- and alkyl-phosphatidylcholines decreased in cases of endometriosis. Plasmenylphosphatidylethanolamine PE P-16:0/18:1 and cardiolipin CL 16:0_18:0_22:5_22:6 serve as marker lipids in the diagnostic model, exhibiting a sensitivity of 81% and specificity of 85%. The diagnostic approach based on dried spots of menstrual blood holds promise as an alternative to traditional non-invasive methods for endometriosis screening.

Neural Projection Filter: Learning Unknown Dynamics Driven by Noisy Observations.

In this article, we propose the novel neural stochastic differential equations (SDEs) driven by noisy sequential observations called neural projection filter (NPF) under the continuous state-space models (SSMs) framework. The contributions of this work are both theoretical and algorithmic. On the one hand, we investigate the approximation capacity of the NPF, i.e., the universal approximation theorem for NPF. More explicitly, under some natural assumptions, we prove that the solution of the SDE driven by the semimartingale can be well approximated by the solution of the NPF. In particular, the explicit estimation bound is given. On the other hand, as an important application of this result, we develop a novel data-driven filter based on NPF. Also, under certain condition, we prove the algorithm convergence; i.e., the dynamics of NPF converges to the target dynamics. At last, we systematically compare the NPF with the existing filters. We verify the convergence theorem in linear case and experimentally demonstrate that the NPF outperforms existing filters in nonlinear case with robustness and efficiency. Furthermore, NPF could handle high-dimensional systems in real-time manner, even for the 100-D cubic sensor, while the state-of-the-art (SOTA) filter fails to do it.

Three-dimensional shape measurement technique for hot and shiny forging

For hot and shiny forging, rapid optical three-dimensional (3D) shape measurement can find the defects in time, improve manufacturing efficiency and reduce manufacturing cost. Optical 3D measurement of hot and shiny forging faces following three challenges. (a) Influence of blackbody radiation on the red band of visible light leads to saturation of captured fringe pattern. (b) Infrared band of blackbody radiation causes the camera to heat up. (c) Specular reflection of shiny forging leads to local saturation of captured fringe pattern. To address the above issues, we propose an effective optical 3D measurement scheme for hot and shiny forging in this paper. Firstly, the experiments demonstrate that the influence of blackbody radiation on visible light is concentrated in red light band and has no crosstalk in the blue light band, so we adopt blue light projection and blue light band-pass filter (BBF) to capture clear fringe pattern. Secondly, since the BBF cannot block the near-infrared component, we use an infrared light cutoff filter (ICF) to reduce the thermal effect of blackbody radiation. Finally, we analyze the Fourier transform (FT) spectrum of saturated fringe pattern caused by specular reflection, and propose an efficient Butterworth low-pass filtering (BLPF) method that does not require additional hardware, algorithm processing, and image assistance. The experimental results verify the effectiveness of the proposed scheme.

Gaussian-Based Parametric Bijections for Automatic Projection Filters

Gaussian-Based Parametric Bijections for Automatic Projection Filters

A short wave radar beam sharpening method based on generalised oblique projection operator with flexible parameter

AbstractBeamforming is an effective way of resolving target direction and anti‐jamming in short wave (SW) radar systems. In conventional beamforming (CBF) at a certain frequency, to get high resolution, the array aperture should be increased, and this is often not allowed in practical applications. A new narrow beam forming (NBF) method for beam sharpening based on the generalised oblique projection (GOP) filter with a flexible parameter is proposed. This method uses a GOP filter bank to form deep nulls in the undesired azimuth range on the pattern and utilises the logic product process to synthesise the GOP filters’ outputs and thus obtains a narrow beam. Compared to traditional beamforming methods, the result of NBF has the characteristics of narrower beam width and bigger side lobe suppression ratio (SLSR). Especially, a narrower beam can be obtained in the case of a small array aperture, which is valuable for practical applications. Experimental results of the range‐Doppler spectrum of short wave radar show that this narrow beam forming method can achieve super resolution of targets within a wide beam and greatly suppress clutter. Therefore, NBF can improve the azimuth resolution and achieve interference suppression in a conventional beam.

Efficient projection filter algorithm for stochastic dynamical systems with correlated noises and state-dependent measurement covariance

This paper focuses on deriving the projection filter equation for a class of stochastic differential equations that incorporate correlated state and measurement noises, where the measurement process covariances depend on the state. To effectively implement the projection filter algorithm for exponential families, it is crucial to compute not only the expectation and variance of the natural statistics but also higher-dimensional statistics. However, computing these high-dimensional statistics can be computationally intensive and potentially compromise the numerical stability of the projection filter. To tackle this challenge, this study proposes a method for the careful selection of natural statistics. We shows that, subject to specific technical conditions, it is feasible to compute all the required statistics by utilizing only partial differentiation of an approximated cumulant-generating function. Notably, this approach eliminates the need to increase the parameter dimension, which was previously required in Emzir et al. (2023).

Topology optimization of labyrinth seals using interface identification techniques

Labyrinth seals are mechanical devices that reduce the leakage between moving components of rotating machines. They are crucial for determining the performance of these machines and essential for reducing greenhouse gas emissions. Therefore, mathematical optimization algorithms for labyrinth seals are of high interest. This work concerns the topology optimization of labyrinth seals, which is a challenging task because the optimizer must distribute solids at different velocities to properly model the flow in the cavity of the labyrinth seal. Also, the model must not allow the optimizer to close the fluid channel or to leave free-floating islands of solid elements in the final design. Therefore, the interface identification method based on a series of erosion-dilate projection filters is used to model the fluid channel as the interface between the rotor and stator, allowing the representation of different velocities and avoiding the channel closure. The virtual temperature method is employed as a connectivity constraint to avoid free-floating islands of solid material. Still, thin structural members appear in the optimized designs, so geometric constraints are used to impose the minimum length scale on rotor and stator components. The final topology optimization results are labyrinth seals with contorted channels constricted to the minimum allowed gap size (as expected for low Reynolds flows), showing the success of the proposed formulation. The staggered and stepped labyrinth seal configurations are optimized to show the generality of the method.

Data-Driven Attack Detection and Identification for Cyber-Physical Systems Under Sparse Sensor Attacks

This paper studies the issues of data-driven attack detection and identification for cyber-physical systems under sparse sensor attacks. First, based on the available input and output data sets, a data-driven monitor is formulated with two objectives: attack detection and attack identification. Then, with the subspace approach, a data-driven attack detection policy is presented, wherein the attack detector is designed directly by the process data. A subspace projection-based attack identification scheme is proposed via designing a bank of projection filters to determine the locations of attacked sensors. Moreover, the sparse recovery technique is adopted to decrease the combinatorial complexity of the subspace projection based identification method. The attack identification is recast into a block-sparse recovery problem. Finally, the proposed methods are verified by the simulations on a flight vehicle system.

Optimal projection filters with information geometry

We review the introduction of several types of projection filters. Projection structures coming from information geometry are used to obtain a finite dimensional filter in the form of a stochastic differential equation (SDE), starting from the exact infinite-dimensional stochastic partial differential equation (SPDE) for the optimal filter. We start with the Stratonovich projection filters based on the Hellinger distance as introduced and developed in Brigo et al. (IEEE Trans Autom Control 43(2):247–252, 1998, Bernoulli 5(3):495–534, 1999), where the SPDE is put in Stratonovich form before projection, hence the term “Stratonovich projection”. The correction step of the filtering algorithm can be made exact by choosing a suitable exponential family as manifold, there is equivalence with assumed density filters and numerical examples have been studied. Other authors further developed these projection filters and we present a brief literature review. A second type of Stratonovich projection filters was introduced in Armstrong and Brigo (Math Control Signals Syst 28(1):1–33, 2016) where a direct L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document} metric is used for projection. Projecting on mixtures of densities as a manifold coincides with Galerkin methods. All the above projection filters lack optimality, as the single vector fields of the Stratonovich SPDE are projected optimally but the SPDE solution as a whole is not approximated optimally by the projected SDE solution according to a clear criterion. This led to the optimal projection filters in Armstrong et al. (Proc Lond Math Soc 119(1):176–213, 2019, Projection of SDEs onto submanifolds. “Information Geometry”, 2023 special issue on half a century of information geometry, 2018), based on the Ito vector and Ito jet projections, where several types of mean square distances between the optimal filter SPDE solution and the sought finite dimensional SDE approximations are minimized, with numerical examples. After reviewing the above developments, we conclude with the remaining challenges.

Self-paced principal component analysis

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as ℓ1-norm and ℓ2,p-norm, can deal with noise or outliers to some extent. However, real-world data may display structures that can not be fully captured by these simple functions. In addition, existing methods treat complex and simple samples equally. By contrast, a learning pattern typically adopted by human beings is to learn from simple to complex and less to more. Based on this principle, we propose a novel method called Self-paced PCA (SPCA) to further reduce the effect of noise and outliers. Notably, the complexity of each sample is calculated at the beginning of each iteration in order to integrate samples from simple to more complex into training. Based on an alternating optimization, SPCA finds an optimal projection matrix and filters out outliers iteratively. Theoretical analysis is presented to show the rationality of SPCA. Extensive experiments on popular data sets demonstrate that the proposed method can improve the state-of-the-art results considerably.

Robust Mainlobe Interference Suppression Based on Joint Oblique Projection for Dual Polarization Conformal Array

In this paper, a robust mainlobe interference suppression algorithm is proposed in a space-polarization joint domain based on a dual-polarized conformal array. An oblique projection filter can eliminate the interference while retaining the desired signal information. However, little deviation in signal parameters will lead to significant performance degradation. To solve such problems, the joint steering vector of the desired signal is corrected by solving the quadratic convex optimization problem. Parameters of interferences are first estimated by using multiple signal classification (MUSIC) joint spectrum, and then, the interference covariance matrix can be reconstructed individually to further estimate the interference steering vector. After that, the joint oblique projection operator can be established by the estimated steering vectors. Consequently, an antijamming beamformer can be obtained by the joint oblique projection filter to achieve robustness on the interference parameter estimation deviation and desired signal mismatch. Simulation experiments verify the effectiveness of the proposed method.

Surgical Treatment of Facial Abscesses and Jaw Osteomyelitis of Dental Origin Using Extraoral Tooth Extraction in the Domestic Rabbit: A Case Series.

The treatment of facial abscesses of dental origin is difficult as jaw osteomyelitis in rabbits is mainly associated with a thick caseous pus that is particularly difficult to drain. Precise identification of the teeth involved in the infected site with the use of cone beam computed tomography (CBCT) was expected to ensure a favorable surgical treatment plan without a long-term local antibiotic strategy or local marsupialization. The first part of the study compared multi-planar reconstruction (MPR) and 3D reconstruction complemented by a maximum intensity projection filter (MIP). The surgical part of the study included rabbits with documentation of the treatment outcome for a period greater than one month after surgery and having had at least one post-operative CBCT demonstrating the achievement of surgical extraction. MPR is significantly more efficient than MIP techniques for alveolar bone (P < 10-7), spongious bone (P < 10-10) and apical elongation (P < 10-5) parameters. Nineteen of 20 surgical sites gave radiological confirmation of the success of the surgical plan. Eighteen of 20 of the abscess sites were clinically healed within one month. Seven out of 20 of the abscess sites presented evidence of one dental structure regrowth following the CBCT recheck. Two out of these seven cases presented with a concomitant persistent chronic facial fistula. Both cases healed after second-stage surgery to extract the tooth structure. The mean number of teeth extracted was 2.85, and seven of the 20 procedures included one incisor.

Constraining Continuous Topology Optimizations to Discrete Solutions for Photonic Applications.

Photonic topology optimization is a technique used to find the permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common versions are used: continuous density-based optimizations that optimize a gray scale permittivity defined over a grid, and discrete level-set optimizations that optimize the shape of the material boundary of a device. In this work we present a method for constraining a continuous optimization such that it is guaranteed to converge to a discrete solution. This is done by inserting a constrained suboptimization with low computational overhead cost at each iteration of an overall gradient-based optimization. The technique adds only one hyperparameter with straightforward behavior to control the aggressiveness of binarization. Computational examples are provided to analyze the hyperparameter behavior, show this technique can be used in conjunction with projection filters, show the benefits of using this technique to provide a nearly discrete starting point for subsequent level-set optimization, and show that an additional hyperparameter can be introduced to control the overall material/void fraction. This method excels for problems where the electromagnetic figure-of-merit is majorly affected by the binarization requirement and situations where identifying suitable hyperparameter values becomes challenging with existing methods.

Exact Solution and Projection Filters for Open Quantum Systems Subject to Imperfect Measurements

In this letter, we consider an open quantum system undergoing imperfect and indirect measurement. For quantum non-demolition (QND) measurement, we show that the system evolves on an appropriately chosen manifold and we express the exact solution of the quantum filter equation in terms of the solution of a lower dimensional stochastic differential equation. In order to further reduce the dimension of the system under study, we consider the projection on the lower dimensional manifold originally introduced in Gao et al. (2019) for the case of perfect measurements. An error analysis is performed to evaluate the precision of this approximate quantum filter, focusing on the case of QND measurement. Simulations suggest the efficiency of the proposed quantum projection filter, even in presence of a stabilizing feedback control which depends on the projection filter.

Vital Signs Detection With Difference Beamforming and Orthogonal Projection Filter Based on SIMO-FMCW Radar

Noncontact vital signs detection based on radar has attracted a lot of interest in recent years. Many efforts have been made to make this technology more complete. However, there still exist some challenges, such as vital signs detection of two closely positioned subjects and heart rate estimation with the interference of the high-order respiration harmonics. This article designs a single-input multiple-output (SIMO) frequency-modulated continuous-wave (FMCW) radar. Based on this system, difference beamforming and orthogonal projection filter (OPF) have been proposed to solve the two challenges. Difference beamforming is able to separate the vital signs of the two subjects even if the angular difference between the two subjects is smaller than the angular resolution of the array antenna. OPF can remove the high-order respiration harmonics without complex parameter adjustment operations and tedious calculations. The experimental results show that the proposed algorithm can successfully separate the vital signs of two closely positioned subjects and estimate the heart rate accurately with the interference of high-order respiration harmonics. The results also verify that the designed SIMO FMCW radar can separate the vital signs of subjects at different distances.

A Method for the Automatic Extraction of Support Devices in an Overhead Catenary System Based on MLS Point Clouds

A mobile laser scanning (MLS) system can acquire railway scene information quickly and provide a data foundation for regular railway inspections. The location of the catenary support device in an electrified railway system has a direct impact on the regular operation of the power supply system. However, multi-type support device data accounts for a tiny proportion of the whole railway scene, resulting in its poor characteristic expression in the scene. Therefore, using traditional point cloud filtering or point cloud segmentation methods alone makes it difficult to achieve an effective segmentation and extraction of the support device. As a result, this paper proposes an automatic extraction algorithm for complex railway support devices based on MLS point clouds. First, the algorithm obtains hierarchies of the pillar point clouds and the support device point clouds in the railway scene through high stratification and then realizes the noise that was point-cloud-filtered in the scene. Then, the center point of the pillar device is retrieved from the pillar corridor by a neighborhood search, and then the locating and initial extracting of the support device are realized based on the relatively stable spatial topological relationship between the pillar and the support device. Finally, a post-processing optimization method integrating the pillar filter and the voxelized projection filter is designed to achieve the accurate and efficient extraction of the support device based on the feature differences between the support device and other devices in the initial extraction results. Furthermore, in the experimental part, we evaluate the treatment effect of the algorithm in six types of support devices, three types of support device distribution scenes, and two types of railway units. The experimental results show that the average extraction IoU of the multi-type support device, support device distribution scenes, and railway unit were 97.20%, 94.29%, and 96.11%, respectively. In general, the proposed algorithm can achieve the accurate and efficient extraction of various support devices in different scenes, and the influence of the algorithm parameters on the extraction accuracy and efficiency is elaborated in the discussion section.

Multidimensional projection filters via automatic differentiation and sparse-grid integration

The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner–Stratonovich stochastic partial differential equation that governs the propagation of the optimal filtering density is projected to a manifold of parametric densities, resulting in a finite-dimensional stochastic differential equation. Despite the fact that projection filters are capable of representing complicated probability densities, their current implementations are limited to Gaussian family or unidimensional filtering applications. This work considers a combination of numerical integration and automatic differentiation to construct projection filter algorithms for more generic problems. Specifically, we provide a detailed exposition of this combination for the manifold of the exponential family, and show how to apply the projection filter to multidimensional cases. We demonstrate numerically that based on comparison to a finite-difference solution to the Kushner–Stratonovich equation and a bootstrap particle filter with systematic resampling, the proposed algorithm retains an accurate approximation of the filtering density while requiring a comparatively low number of quadrature points. Due to the sparse-grid integration and automatic differentiation used to calculate the expected values of the natural statistics and the Fisher metric, the proposed filtering algorithms are highly scalable. They therefore are suitable to many applications in which the number of dimensions exceeds the practical limit of particle filters, but where the Gaussian-approximations are deemed unsatisfactory.

Trainable segmentation for transmission electron microscope images of inorganic nanoparticles.

We present a trainable segmentation method implemented within the python package ParticleSpy. The method takes user labelled pixels, which are used to train a classifier and segment images of inorganic nanoparticles from transmission electron microscope images. This implementation is based on the trainable Waikato Environment for Knowledge Analysis (WEKA) segmentation, but is written in python, allowing a large degree of flexibility and meaning it can be easily expanded using other python packages. We find that trainable segmentation offers better accuracy than global or local thresholding methods and requires as few as 100 user-labelled pixels to produce an accurate segmentation. Trainable segmentation presents a balance of accuracy and training time between global/local thresholding and neural networks, when used on transmission electron microscope images of nanoparticles. We also quantitatively investigate the effectiveness of the components of trainable segmentation, its filter kernels and classifiers, in order to demonstrate the use cases for the different filter kernels in ParticleSpy and the most accurate classifiers for different data types. A set of filter kernels is identified that are effective in distinguishing particles from background but that retain dissimilar features. In terms of classifiers, we find that different classifiers perform optimally for different image contrast; specifically, a random forest classifier performs best for high-contrast ADF images, but that QDA and Gaussian Naïve Bayes classifiers perform better for low-contrast TEM images.

HoneyTop90: A 90-line MATLAB code for topology optimization using honeycomb tessellation

This paper provides a simple, compact and efficient 90-line pedagogical MATLAB code for topology optimization using hexagonal elements (honeycomb tessellation). Hexagonal elements provide nonsingular connectivity between two juxtaposed elements and, thus, subdue checkerboard patterns and point connections inherently from the optimized designs. A novel approach to generate honeycomb tessellation is proposed. The element connectivity matrix and corresponding nodal coordinates array are determined in 5 (7) and 4 (6) lines, respectively. Two additional lines for the meshgrid generation are required for an even number of elements in the vertical direction. The code takes a fraction of a second to generate meshgrid information for the millions of hexagonal elements. Wachspress shape functions are employed for the finite element analysis, and compliance minimization is performed using the optimality criteria method. The provided Matlab code and its extensions are explained in detail. Options to run the optimization with and without filtering techniques are provided. Steps to include different boundary conditions, multiple load cases, active and passive regions, and a Heaviside projection filter are also discussed. The code is provided in Appendix~A, and it can also be downloaded along with supplementary materials from \url{https://github.com/PrabhatIn/HoneyTop90}.