Regularized Level Set Research Articles

An h$h$‐principle for embeddings transverse to a contact structure

AbstractGiven a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general ‐principle. The flexibility follows from the ‐principles for isocontact and isosymplectic embeddings, it provides a framework for classical results, and we give two new applications. Our main result is that embeddings transverse to a contact structure satisfy a full ‐principle in two cases: if the complement of the embedding is overtwisted, or when the intersection of the image of the formal derivative with the contact structure is strictly contained in a proper symplectic subbundle. We illustrate the general framework on symplectic manifolds by studying the universality of Hamiltonian dynamics on regular level sets via a class of embeddings.

Infrared cluster target detection based on Facet kernel and adaptive distance regularization level set

The acquisition of high signal-to-noise ratio (SNR) detection results for targets in infrared images is of great significance for early warning detection and precision guidance. To address the issue of detecting cluster targets in complex backgrounds, a detection method combining the Facet kernel and adaptive distance regularization level set evolution (ADRLSE) is proposed. Firstly, local order-statistics and mean filters are applied to remove high-brightness noise and smooth the image. Subsequently, the Facet kernel filter is applied to enhance the target while suppress the background. Candidate target pixels are obtained through adaptive threshold segmentation. Additionally, based on the edge characteristics of cluster targets, a novel edge detection function is proposed that adaptively determines the parameters using the contour volume (CV) and peak signal-to-noise ratio (PSNR) as references. The enhanced mapping of the target region is obtained by extracting the cluster target contour using ADRLSE. The ADRLSE map is weighted using the target map obtained from the Facet kernel to further enhance the target, and the target is detected through thresholding operations. Finally, the separation result of a single target within a cluster is obtained through a novel adaptive k-means clustering algorithm. Simulation experiments demonstrate that our method has high detection accuracy for cluster targets and can accomplish detection tasks such as cluster contour extraction and single target division.

A Transformer Model for Coastline Prediction in Weitou Bay, China

The simulation and prediction of coastline changes are of great significance for the development and scientific management of coastal zones. Coastline changes are difficult to capture completely but appear significantly periodic over a long time series. In this paper, the transformer model is used to learn the changing trend of the coastline so as to deduce the position of the coastline in the coming year. First, we use the distance regularization level set evolution (DRLSE) model for instantaneous waterline extraction (IWE) from preprocessed Landsat time-series images from 2010–2020 in Weitou Bay, China. Then, tidal correction (TC) is performed on the extracted instantaneous waterline dataset to obtain coastlines projected to a single reference tidal datum. Finally, the coastline datasets from 2010–2019 are used for model training, and the coastline in 2020 is used for accuracy assessment. Three precision evaluation methods, including receiver operating characteristic curve matching, the mean offset, and the root mean square error, were used to verify the predicted coastline data. The receiver operating characteristic curve was specifically designed and improved to evaluate the accuracy of the obtained coastline. Compared with the support vector regression (SVR) and long–short-term memory (LSTM) methods, the results showed that the coastline predicted by the transformer model was the closest to the accurate extracted coastline. The accuracies of the correct values corresponding to SVR, LSTM, and transformer models were 88.27%, 94.08%, and 98.80%, respectively, which indicated the accuracy of the coastline extraction results. Additionally, the mean offset and root mean square error were 0.32 pixels and 0.57 pixels, respectively. In addition, the experimental results showed that tidal correction is important for coastline prediction. Moreover, through field investigations of coastlines, the predicted results obtained for natural coastlines were more accurate, while the predicted results were relatively poor for some artificial coastlines that were intensely influenced by human activities. This study shows that the transformer model can provide natural coastline changes for coastal management.

Active contour model based on hybrid signed pressure force function

AbstractTo segment noisy and multi‐target images, an active contour model based on a hybrid signed pressure force function that fuses global and local information of the image is proposed. Firstly, a local signed pressure force function is defined using the local area information of the image. Then, it is combined with the existing global grey density function to construct a new signed pressure force function. Finally, the selective binary and Gaussian filtering regularized level set are modified using the newly defined function. Extensive experiments and comparisons on both synthetic and real images demonstrate that the proposed method is robust to noise and can handle noisy and multi‐target images with high accuracy.

Quantifying emphysema in lung screening computed tomography with robust automated lobe segmentation.

Anatomy-based quantification of emphysema in a lung screening cohort has the potential to improve lung cancer risk stratification and risk communication. Segmenting lung lobes is an essential step in this analysis, but leading lobe segmentation algorithms have not been validated for lung screening computed tomography (CT). In this work, we develop an automated approach to lobar emphysema quantification and study its association with lung cancer incidence. We combine self-supervised training with level set regularization and finetuning with radiologist annotations on three datasets to develop a lobe segmentation algorithm that is robust for lung screening CT. Using this algorithm, we extract quantitative CT measures for a cohort () from the National Lung Screening Trial and analyze the multivariate association with lung cancer incidence. Our lobe segmentation approach achieved an external validation Dice of 0.93, significantly outperforming a leading algorithm at 0.90 (). The percentage of low attenuation volume in the right upper lobe was associated with increased lung cancer incidence (odds ratio: 1.97; 95% CI: [1.06, 3.66]) independent of risk factors and diagnosis of whole lung emphysema. Quantitative lobar emphysema improved the goodness-of-fit to lung cancer incidence (, ). We are the first to develop and validate an automated lobe segmentation algorithm that is robust to smoking-related pathology. We discover a quantitative risk factor, lending further evidence that regional emphysema is independently associated with increased lung cancer incidence. The algorithm is provided at https://github.com/MASILab/EmphysemaSeg.

Correction to: Obstructions to Integrability of Nearly Integrable Dynamical Systems Near Regular Level Sets

Correction to: Obstructions to Integrability of Nearly Integrable Dynamical Systems Near Regular Level Sets

Obstructions to Integrability of Nearly Integrable Dynamical Systems Near Regular Level Sets

Obstructions to Integrability of Nearly Integrable Dynamical Systems Near Regular Level Sets

Uniqueness of free boundary minimal hypersurfaces in rotational domains

In this work, we investigate the existence of compact free boundary minimal hypersurfaces immersed in several domains. Using an original integral identity for compact free boundary minimal hypersurfaces that are immersed in a domain whose boundary is a regular level set, we study the case where this domain is a quadric or, more generally, a rotational domain. This existence study is done without topological restrictions. We also obtain a new gap theorem for free boundary hypersurfaces immersed in an Euclidean ball and in a rotational ellipsoid.

Enhanced damage imaging in three-dimensional composite structures via electrical impedance tomography with mixed and level set regularization

Electrical impedance tomography (EIT) is a promising tool for nondestructive evaluation (NDE) of materials that exhibit stimulus-responsive electrical conductivity. To date, materials practitioners of EIT have used standard regularization methods such as smoothness-promoting operators to solve the ill-posed EIT inverse problem. However, more sophisticated and better performing regularization methods exist. It is essential that these other regularization methods be explored in order for EIT to see more widespread adoption in NDE. To that end, we present two novel regularization techniques – a mixed smoothness/focal method and a level set method – for application to damage imaging via EIT. These new techniques are experimentally validated on two three-dimensional composite components, a carbon black-modified glass fiber/epoxy tube and a carbon fiber/epoxy laminate airfoil subject to multiple damaging impacts. It is shown that both of the new regularization techniques markedly outperform traditional smoothness-only methods. These results are an important step towards adoption of more sophisticated EIT formulations in NDE and transition of EIT from the proof-of-concept phase and into practice for engineered materials.

Transnormal Functions and Focal Varieties on Finsler Manifolds

In this paper, we study transnormal functions and their level sets and focal varieties on complete Finsler manifolds. We prove that the focal varieties of a $$C^{2}$$ transnormal function are smooth submanifolds and each regular level set is a tube over either of the focal varieties.

A Modified 2-D Notch Filter Based on Image Segmentation for RFI Mitigation in Synthetic Aperture Radar

Synthetic aperture radar (SAR), as an active microwave sensor, can inevitably receive radio frequency interference (RFI) generated by various electromagnetic equipment. When the SAR system receives RFI, it will affect SAR imaging and limit the application of SAR images. As a kind of RFI mitigation method, notch filtering method is a classical method with high efficiency and robust performance. However, the notch filtering methods pay no attention to the protection of useful signals. This paper proposed a modified 2-D notch filter based on image segmentation for RFI mitigation with signal-protected capability. (1) The adaptive gamma correction (AGC) approach was utilized to enhance the SAR image with RFI in the range-frequency and azimuth-time domain. (2) The modified selective binary and Gaussian filtering regularized level set (SBGFRLS) model was utilized to further process the image after AGC to accurately extract the contour of the useful signals with interference, which is more conducive to protecting the useful signals without interference. (3) The Generalized Singular Value Thresholding (GSVT) based low-rank sparse decomposition (LRSD) model was utilized to separate the RFI signals and the useful signals. Then, the useful signals were restored to the raw data. The simulation experiments and measured data experiments show that the proposed method can effectively mitigate RFI and protect the useful signals whether there are RFI with single source or multiple sources.

Dynamic iris inner edge location method based on distance-regularized level set

Iris localization is an important part of iris recognition. Aiming at the influence of irregular pupil circle and illumination inequality in dynamic iris localization in actual scene, a dynamic iris inner edge location method based on distance regularized level set model was proposed. According to the geometric features of iris, the pupil and iris are coarsely located through the secondary projection of binary image, and the initial contour of evolution of horizontal set is determined. Accurate positioning of the inner edge of iris is achieved by the improved distance regularized level set model of edge indicator function. Iris images Database were respectively experimented with this paper and another improved distance regularized level set model, and the positioning effect was evaluated by using the Jakard similarity coefficient. The results show that the distance regularized level set model based dynamic iris internal edge localization algorithm proposed in this paper can significantly reduce the number of iterations and positioning time of the localization algorithm on the basis of ensuring the positioning accuracy,which provides a theoretical basis and technical reference for the application of iris recognition technology.

Three-dimensional inversion of knot defects recognition in timber cutting

The comprehensive utilization of wood is the main goal of log cutting, but knot defects increase the difficulty of rationally optimizing cutting. Due to the lack of real shape data of knot defects in logs, it is difficult for detection methods to establish a correlation between signal and defect morphology. An image-processing method is proposed for knot inversion based on distance regularized level set segmentation (DRLSE) and spatial vertex clustering, and with the inversion of the defects existing relative board position in the log, an inversion model of the knot defect is established. First, the defect edges of the top and bottom images of the boards are extracted by DRLSE and ellipse fitting, and the major axes of the ellipses made coplanar by angle correction; second, the coordinate points of the top and bottom ellipse edges are extracted to form a spatial straight line; third, to solve the intersection dispersion of spatial straight lines and the major axis plane, K-medoids clustering is used to locate the vertex. Finally, with the vertex and the large ellipse, a 3D cone model is constructed which can be used to invert the shape of knots in the board. The experiment was conducted on ten defective larch boards, and the experimental results showed that this method can accurately invert the shapes of defects in solid wood boards with the advantages of low cost and easy operation.

Accurate image segmentation based on adaptive distance regularization level set method

Level set method has been widely applied in the field of image segmentation. However, the level set formulation is inevitably affected by the regularization function, in-homogeneity and weak edge in the process of evolution, which often leads to the instability and inaccuracy of image segmentation results. To solve these problems, a new distance regularization term defined by a double-well potential function is proposed to satisfy more ideal characteristics of signed distance property. In addition, a novel edge indicator function is introduced to segment images with uneven intensity or weak edge. Finally, the adaptive adjustment formulas of distance regularization and area parameters are derived to alleviate the difficulty of parameter adjustment. Experimental results show that the proposed model provides better accuracy and versatility, quantitative experiment on Weizmann segmentation evaluation database achieves mean Dice score (96.87%), IoU (94.38%), Hausdorff distance (3.20[Formula: see text]mm), Recall (97.68%) and Precision (96.32%), respectively.

Automated Diagnosis of Autism Spectrum Disorder Condition Using Shape Based Features Extracted from Brainstem.

Alterations to the brainstem can hamper cognitive functioning, including audiovisual and behavioral disintegration, leading to individuals with Autism Spectrum Disorder (ASD) face challenges in social interaction. In this study, a process pipeline for the diagnosis of ASD has been proposed, based on geometrical and Zernike moments features, extracted from the brainstem of ASD subjects. The subjects considered for this study are obtained from publicly available data base ABIDE (300 ASD and 300 typically developing (TD)). Distance regularized level set (DRLSE) method has been used to segment the brainstem region from the midsagittal view of MRI data. Similarity measures were used to validate the segmented images against the ground truth images. Geometrical and Zernike moments features were extracted from the segmented images. The significant features were used to train Support vector machine (SVM) classifier to perform classification between ASD and TD subjects. The similarity results show high matching between DRLSE segmented brainstem and ground truth with high similarity index scores of Pearson Heron-II (PH II) = 0.9740 and Sokal and Sneath-II (SS II) = 0.9727. The SVM classifier achieved 70.53% accuracy to classify ASD and TD subjects. Thus, the process pipeline proposed in this study is able to achieve good accuracy in the classification of ASD subjects.

Brain fMRI segmentation under emotion stimuli incorporating attention-based deep convolutional neural networks

Functional magnetic resonance imaging (fMRI) is widely used for clinical examinations, diagnosis, and treatment. By segmenting fMRI images, large-scale medical image data can be processed more efficiently. Most deep learning (DL)-based segmentation typically uses some type of encoding–decoding model. In this study, affective computing (AC) was developed using the brain fMRI dataset generated from an emotion simulation experiment. The brain fMRI dataset was segmented using an attention model, a deep convolutional neural network-32 (DCNN-32) based on Laplacian of Gaussian (LoG) filter, called ADCNN-32-G. For the evaluation of image segmentation, several indices are presented. By comparing the proposed ADCNN-32s-G model to distance regularized level set evolution (DRLSE), single-seeded region growing, and the single segNet full convolutional network model (FCN), the proposed model performs well in segmenting mass fMRI datasets. The proposed method can be applied to the real-time monitoring of patients with depression, and it can effectively advise human mental health.

Rigidity of Beltrami fields with a non-constant proportionality factor

We prove that bounded Beltrami fields are symmetric if a proportionality factor depends on two variables in the cylindrical coordinate and admits a regular level set diffeomorphic to a cylinder or a torus.

Quantitative Sound Speed Imaging of Cortical Bone and Soft Tissue: Results From Observational Data Sets.

This work presents the first quantitative ultrasonic sound speed images of ex vivo limb cross-sections containing both soft tissue and bone using Full Waveform Inversion (FWI) with level set (LS) and travel time regularization. The estimated bulk sound speed of bone and soft tissue are within 10% and 1%, respectively, of ground truth estimates. The sound speed imagery shows muscle, connective tissue and bone features. Typically, ultrasound tomography (UST) using FWI is applied to imaging breast tissue properties (e.g. sound speed and density) that correlate with cancer. With further development, UST systems have the potential to deliver volumetric operator independent tissue property images of limbs with non-ionizing and portable hardware platforms. This work addresses the algorithmic challenges of imaging the sound speed of bone and soft tissue by combining FWI with LS regularization and travel time methods to recover soft tissue and bone sound speed with improved accuracy and reduced soft tissue artifacts when compared to conventional FWI. The value of leveraging LS and travel time methods is realized by evidence of improved bone geometry estimates as well as promising convergence properties and reduced risk of final model errors due to un-modeled shear wave propagation. Ex vivo bulk measurements of sound speed and MRI cross-sections validates the final inversion results.

A Novel Feature Extraction Algorithm and System for Flexible Integrated Circuit Packaging Substrate.

Aiming at the line defect detection of a flexible integrated circuit substrate (FICS) without reference template, there are some problems such as line discontinuity or inaccurate line defect location in the detection results. In order to address these problems, a line feature detection algorithm for extracting an FICS image is proposed. Firstly, FICS image acquisition is carried out by using the appearance defect intelligent detection system independently developed in our lab. Secondly, in the algorithm design of the software system, the binary image of the line image to be segmented is obtained after the color FICS image is classified by K-means, median filtering, morphological filling and closed operation. Finally, for an FICS binary image, an image segmentation model with convexity-preserving indirect regular level set is proposed, which is applied to extract the line features of an FICS image. Experiment results show that, compared with the CV model, LBF model, LCV model, LGIF model, Order-LBF model and RSF model, the proposed model can extract line features with high accuracy, and the line boundary is smooth, which lays an important foundation for high-precision measurement of line width and line distance and high-precision location of defects.

Wavefield Analysis Tools for Wavenumber and Velocities Extraction in Polar Coordinates.

Experimental characterization of Lamb waves in plate-like structures overcomes the intrinsic limits of a priori semianalytical finite element simulations, where material inaccuracies and nonidealities cannot be easily considered. Unfortunately, the experimental extraction of guided wave dispersion curves, and especially their polar representation along different directions of propagation at a given frequency, is not trivial. In nonisotropic materials, such analysis is a key aspect for a reliable and robust characterization of the behavior of waves. In this work, by exploiting scanning laser Doppler vibrometer measurements with narrowband excitation, two different signal processing methods for the extraction of the wavenumber polar representation at the excitation frequency are investigated and characterized. The first method is based on a distance regularized level set (DRLSE) algorithm, widely used in image processing and computer vision but, to the best of the author's knowledge, never used in the Lamb waves' field. The second method is based on the 2-D sparse wavenumber analysis which exploits the wavefield sparse representation in the wavenumber domain. With a precise and reliable extraction of the wavenumber characteristic in the k -space, the polar representations at the excitation frequency of phase and group velocities can be estimated. The former, by exploiting the well-known wavenumber-frequency relation, the latter, instead, by computing numerical derivative among wavenumbers at multiple frequencies. The methodology has been validated on three different composite plates with different degrees of nonisotropy properties. The results show the effectiveness of the two methods, highlighting the advantages and disadvantages of both.