29.9CRJul 26, 2023
Unveiling Security, Privacy, and Ethical Concerns of ChatGPTXiaodong Wu, Ran Duan, Jianbing Ni
This paper delves into the realm of ChatGPT, an AI-powered chatbot that utilizes topic modeling and reinforcement learning to generate natural responses. Although ChatGPT holds immense promise across various industries, such as customer service, education, mental health treatment, personal productivity, and content creation, it is essential to address its security, privacy, and ethical implications. By exploring the upgrade path from GPT-1 to GPT-4, discussing the model's features, limitations, and potential applications, this study aims to shed light on the potential risks of integrating ChatGPT into our daily lives. Focusing on security, privacy, and ethics issues, we highlight the challenges these concerns pose for widespread adoption. Finally, we analyze the open problems in these areas, calling for concerted efforts to ensure the development of secure and ethically sound large language models.
20.5LGMar 1, 2022
When AUC meets DRO: Optimizing Partial AUC for Deep Learning with Non-Convex Convergence GuaranteeDixian Zhu, Gang Li, Bokun Wang et al.
In this paper, we propose systematic and efficient gradient-based methods for both one-way and two-way partial AUC (pAUC) maximization that are applicable to deep learning. We propose new formulations of pAUC surrogate objectives by using the distributionally robust optimization (DRO) to define the loss for each individual positive data. We consider two formulations of DRO, one of which is based on conditional-value-at-risk (CVaR) that yields a non-smooth but exact estimator for pAUC, and another one is based on a KL divergence regularized DRO that yields an inexact but smooth (soft) estimator for pAUC. For both one-way and two-way pAUC maximization, we propose two algorithms and prove their convergence for optimizing their two formulations, respectively. Experiments demonstrate the effectiveness of the proposed algorithms for pAUC maximization for deep learning on various datasets.
13.0LGMar 27, 2022
Benchmarking Deep AUROC Optimization: Loss Functions and Algorithmic ChoicesDixian Zhu, Xiaodong Wu, Tianbao Yang
The area under the ROC curve (AUROC) has been vigorously applied for imbalanced classification and moreover combined with deep learning techniques. However, there is no existing work that provides sound information for peers to choose appropriate deep AUROC maximization techniques. In this work, we fill this gap from three aspects. (i) We benchmark a variety of loss functions with different algorithmic choices for deep AUROC optimization problem. We study the loss functions in two categories: pairwise loss and composite loss, which includes a total of 10 loss functions. Interestingly, we find composite loss, as an innovative loss function class, shows more competitive performance than pairwise loss from both training convergence and testing generalization perspectives. Nevertheless, data with more corrupted labels favors a pairwise symmetric loss. (ii) Moreover, we benchmark and highlight the essential algorithmic choices such as positive sampling rate, regularization, normalization/activation, and optimizers. Key findings include: higher positive sampling rate is likely to be beneficial for deep AUROC maximization; different datasets favors different weights of regularizations; appropriate normalization techniques, such as sigmoid and $\ell_2$ score normalization, could improve model performance. (iii) For optimization aspect, we benchmark SGD-type, Momentum-type, and Adam-type optimizers for both pairwise and composite loss. Our findings show that although Adam-type method is more competitive from training perspective, but it does not outperform others from testing perspective.
2.8CVOct 25, 2023
Trust, but Verify: Robust Image Segmentation using Deep LearningFahim Ahmed Zaman, Xiaodong Wu, Weiyu Xu et al.
We describe a method for verifying the output of a deep neural network for medical image segmentation that is robust to several classes of random as well as worst-case perturbations i.e. adversarial attacks. This method is based on a general approach recently developed by the authors called "Trust, but Verify" wherein an auxiliary verification network produces predictions about certain masked features in the input image using the segmentation as an input. A well-designed auxiliary network will produce high-quality predictions when the input segmentations are accurate, but will produce low-quality predictions when the segmentations are incorrect. Checking the predictions of such a network with the original image allows us to detect bad segmentations. However, to ensure the verification method is truly robust, we need a method for checking the quality of the predictions that does not itself rely on a black-box neural network. Indeed, we show that previous methods for segmentation evaluation that do use deep neural regression networks are vulnerable to false negatives i.e. can inaccurately label bad segmentations as good. We describe the design of a verification network that avoids such vulnerability and present results to demonstrate its robustness compared to previous methods.
4.8IVOct 8, 2022
A deep learning network with differentiable dynamic programming for retina OCT surface segmentationHui Xie, Weiyu Xu, Xiaodong Wu
Multiple-surface segmentation in Optical Coherence Tomography (OCT) images is a challenge problem, further complicated by the frequent presence of weak image boundaries. Recently, many deep learning (DL) based methods have been developed for this task and yield remarkable performance. Unfortunately, due to the scarcity of training data in medical imaging, it is challenging for DL networks to learn the global structure of the target surfaces, including surface smoothness. To bridge this gap, this study proposes to seamlessly unify a U-Net for feature learning with a constrained differentiable dynamic programming module to achieve an end-to-end learning for retina OCT surface segmentation to explicitly enforce surface smoothness. It effectively utilizes the feedback from the downstream model optimization module to guide feature learning, yielding a better enforcement of global structures of the target surfaces. Experiments on Duke AMD (age-related macular degeneration) and JHU MS (multiple sclerosis) OCT datasets for retinal layer segmentation demonstrated very promising segmentation accuracy.
12.2ETMar 11
Report for NSF Workshop on Algorithm-Hardware Co-design for Medical ApplicationsPeipei Zhou, Zheng Dong, Insup Lee et al.
This report summarizes the discussions and recommendations from the NSF Workshop on Algorithm-Hardware Co-design for Medical Applications, held on September 26-27, 2024, in Pittsburgh, PA. The workshop assembled an interdisciplinary cohort of researchers, clinicians, and industry leaders to examine foundational challenges and develop a strategic roadmap for algorithm-hardware co-design in medical computing. The workshop focuses on four thematic areas: (1) teleoperations, telehealth, and surgical operations; (2) wearable and implantable medicine, including implantable living pharmacies; (3) home ICU, hospital systems, and elderly care; and (4) medical sensing, imaging, and reconstruction. This report calls for a fundamental shift in how next-generation medical technologies are conceived, designed, validated, and translated into practice. The report recommends that NSF sustain investment in shared standardized data infrastructures and compute infrastructures, develop clinic workflow-aware systems and human-AI collaboration frameworks, promote scalable validation ecosystems grounded in objective, continuous measures, and physics-informed, and enable safe, accountable, and resilient platforms, including virtual-physical healthcare ecosystems, to de-risk translational pathways. The workshop information can be found on the website: https://sites.google.com/view/nsfworkshop.
5.3IVDec 19, 2023
Diagnosis Of Takotsubo Syndrome By Robust Feature Selection From The Complex Latent Space Of DL-based Segmentation NetworkFahim Ahmed Zaman, Wahidul Alam, Tarun Kanti Roy et al.
Researchers have shown significant correlations among segmented objects in various medical imaging modalities and disease related pathologies. Several studies showed that using hand crafted features for disease prediction neglects the immense possibility to use latent features from deep learning (DL) models which may reduce the overall accuracy of differential diagnosis. However, directly using classification or segmentation models on medical to learn latent features opt out robust feature selection and may lead to overfitting. To fill this gap, we propose a novel feature selection technique using the latent space of a segmentation model that can aid diagnosis. We evaluated our method in differentiating a rare cardiac disease: Takotsubo Syndrome (TTS) from the ST elevation myocardial infarction (STEMI) using echocardiogram videos (echo). TTS can mimic clinical features of STEMI in echo and extremely hard to distinguish. Our approach shows promising results in differential diagnosis of TTS with 82% diagnosis accuracy beating the previous state-of-the-art (SOTA) approach. Moreover, the robust feature selection technique using LASSO algorithm shows great potential in reducing the redundant features and creates a robust pipeline for short- and long-term disease prognoses in the downstream analysis.
8.9IVDec 19, 2023
Surf-CDM: Score-Based Surface Cold-Diffusion Model For Medical Image SegmentationFahim Ahmed Zaman, Mathews Jacob, Amanda Chang et al.
Diffusion models have shown impressive performance for image generation, often times outperforming other generative models. Since their introduction, researchers have extended the powerful noise-to-image denoising pipeline to discriminative tasks, including image segmentation. In this work we propose a conditional score-based generative modeling framework for medical image segmentation which relies on a parametric surface representation for the segmentation masks. The surface re-parameterization allows the direct application of standard diffusion theory, as opposed to when the mask is represented as a binary mask. Moreover, we adapted an extended variant of the diffusion technique known as the "cold-diffusion" where the diffusion model can be constructed with deterministic perturbations instead of Gaussian noise, which facilitates significantly faster convergence in the reverse diffusion. We evaluated our method on the segmentation of the left ventricle from 65 transthoracic echocardiogram videos (2230 echo image frames) and compared its performance to the most popular and widely used image segmentation models. Our proposed model not only outperformed the compared methods in terms of segmentation accuracy, but also showed potential in estimating segmentation uncertainties for further downstream analyses due to its inherent generative nature.
3.9CVDec 7, 2023
gcDLSeg: Integrating Graph-cut into Deep Learning for Binary Semantic SegmentationHui Xie, Weiyu Xu, Ya Xing Wang et al.
Binary semantic segmentation in computer vision is a fundamental problem. As a model-based segmentation method, the graph-cut approach was one of the most successful binary segmentation methods thanks to its global optimality guarantee of the solutions and its practical polynomial-time complexity. Recently, many deep learning (DL) based methods have been developed for this task and yielded remarkable performance, resulting in a paradigm shift in this field. To combine the strengths of both approaches, we propose in this study to integrate the graph-cut approach into a deep learning network for end-to-end learning. Unfortunately, backward propagation through the graph-cut module in the DL network is challenging due to the combinatorial nature of the graph-cut algorithm. To tackle this challenge, we propose a novel residual graph-cut loss and a quasi-residual connection, enabling the backward propagation of the gradients of the residual graph-cut loss for effective feature learning guided by the graph-cut segmentation model. In the inference phase, globally optimal segmentation is achieved with respect to the graph-cut energy defined on the optimized image features learned from DL networks. Experiments on the public AZH chronic wound data set and the pancreas cancer data set from the medical segmentation decathlon (MSD) demonstrated promising segmentation accuracy, and improved robustness against adversarial attacks.
4.6LGJun 23, 2024
Feature compression is the root cause of adversarial fragility in neural network classifiersJingchao Gao, Ziqing Lu, Raghu Mudumbai et al.
In this paper, we uniquely study the adversarial robustness of deep neural networks (NN) for classification tasks against that of optimal classifiers. We look at the smallest magnitude of possible additive perturbations that can change a classifier's output. We provide a matrix-theoretic explanation of the adversarial fragility of deep neural networks for classification. In particular, our theoretical results show that a neural network's adversarial robustness can degrade as the input dimension $d$ increases. Analytically, we show that neural networks' adversarial robustness can be only $1/\sqrt{d}$ of the best possible adversarial robustness of optimal classifiers. Our theories match remarkably well with numerical experiments of practically trained NN, including NN for ImageNet images. The matrix-theoretic explanation is consistent with an earlier information-theoretic feature-compression-based explanation for the adversarial fragility of neural networks.
Provable Multi-instance Deep AUC Maximization with Stochastic PoolingDixian Zhu, Bokun Wang, Zhi Chen et al.
This paper considers a novel application of deep AUC maximization (DAM) for multi-instance learning (MIL), in which a single class label is assigned to a bag of instances (e.g., multiple 2D slices of a CT scan for a patient). We address a neglected yet non-negligible computational challenge of MIL in the context of DAM, i.e., bag size is too large to be loaded into {GPU} memory for backpropagation, which is required by the standard pooling methods of MIL. To tackle this challenge, we propose variance-reduced stochastic pooling methods in the spirit of stochastic optimization by formulating the loss function over the pooled prediction as a multi-level compositional function. By synthesizing techniques from stochastic compositional optimization and non-convex min-max optimization, we propose a unified and provable muli-instance DAM (MIDAM) algorithm with stochastic smoothed-max pooling or stochastic attention-based pooling, which only samples a few instances for each bag to compute a stochastic gradient estimator and to update the model parameter. We establish a similar convergence rate of the proposed MIDAM algorithm as the state-of-the-art DAM algorithms. Our extensive experiments on conventional MIL datasets and medical datasets demonstrate the superiority of our MIDAM algorithm.
6.1IVMay 19, 2021
Joint Calibrationless Reconstruction and Segmentation of Parallel MRIAniket Pramanik, Xiaodong Wu, Mathews Jacob
The volume estimation of brain regions from MRI data is a key problem in many clinical applications, where the acquisition of data at high spatial resolution is desirable. While parallel MRI and constrained image reconstruction algorithms can accelerate the scans, image reconstruction artifacts are inevitable, especially at high acceleration factors. We introduce a novel image domain deep-learning framework for calibrationless parallel MRI reconstruction, coupled with a segmentation network to improve image quality and to reduce the vulnerability of current segmentation algorithms to image artifacts resulting from acceleration. The combination of the proposed image domain deep calibrationless approach with the segmentation algorithm offers improved image quality, while increasing the accuracy of the segmentations. The novel architecture with an encoder shared between the reconstruction and segmentation tasks is seen to reduce the need for segmented training datasets. In particular, the proposed few-shot training strategy requires only 10% of segmented datasets to offer good performance.
2.3CVJul 2, 2020
Globally Optimal Segmentation of Mutually Interacting Surfaces using Deep LearningHui Xie, Zhe Pan, Leixin Zhou et al.
Segmentation of multiple surfaces in medical images is a challenging problem, further complicated by the frequent presence of weak boundary and mutual influence between adjacent objects. The traditional graph-based optimal surface segmentation method has proven its effectiveness with its ability of capturing various surface priors in a uniform graph model. However, its efficacy heavily relies on handcrafted features that are used to define the surface cost for the "goodness" of a surface. Recently, deep learning (DL) is emerging as powerful tools for medical image segmentation thanks to its superior feature learning capability. Unfortunately, due to the scarcity of training data in medical imaging, it is nontrivial for DL networks to implicitly learn the global structure of the target surfaces, including surface interactions. In this work, we propose to parameterize the surface cost functions in the graph model and leverage DL to learn those parameters. The multiple optimal surfaces are then simultaneously detected by minimizing the total surface cost while explicitly enforcing the mutual surface interaction constraints. The optimization problem is solved by the primal-dual Internal Point Method, which can be implemented by a layer of neural networks, enabling efficient end-to-end training of the whole network. Experiments on Spectral Domain Optical Coherence Tomography (SD-OCT) retinal layer segmentation and Intravascular Ultrasound (IVUS) vessel wall segmentation demonstrated very promising results. All source code is public to facilitate further research at this direction.
2.0IVJul 2, 2020
Globally Optimal Surface Segmentation using Deep Learning with Learnable Smoothness PriorsLeixin Zhou, Xiaodong Wu
Automated surface segmentation is important and challenging in many medical image analysis applications. Recent deep learning based methods have been developed for various object segmentation tasks. Most of them are a classification based approach, e.g. U-net, which predicts the probability of being target object or background for each voxel. One problem of those methods is lacking of topology guarantee for segmented objects, and usually post processing is needed to infer the boundary surface of the object. In this paper, a novel model based on convolutional neural network (CNN) followed by a learnable surface smoothing block is proposed to tackle the surface segmentation problem with end-to-end training. To the best of our knowledge, this is the first study to learn smoothness priors end-to-end with CNN for direct surface segmentation with global optimality. Experiments carried out on Spectral Domain Optical Coherence Tomography (SD-OCT) retinal layer segmentation and Intravascular Ultrasound (IVUS) vessel wall segmentation demonstrated very promising results.
8.5CVMay 19, 2020
Unsupervised anomaly localization using VAE and beta-VAELeixin Zhou, Wenxiang Deng, Xiaodong Wu
Variational Auto-Encoders (VAEs) have shown great potential in the unsupervised learning of data distributions. An VAE trained on normal images is expected to only be able to reconstruct normal images, allowing the localization of anomalous pixels in an image via manipulating information within the VAE ELBO loss. The ELBO consists of KL divergence loss (image-wise) and reconstruction loss (pixel-wise). It is natural and straightforward to use the later as the predictor. However, usually local anomaly added to a normal image can deteriorate the whole reconstructed image, causing segmentation using only naive pixel errors not accurate. Energy based projection was proposed to increase the reconstruction accuracy of normal regions/pixels, which achieved the state-of-the-art localization accuracy on simple natural images. Another possible predictors are ELBO and its components gradients with respect to each pixels. Previous work claimed that KL gradient is a robust predictor. In this paper, we argue that the energy based projection in medical imaging is not as useful as on natural images. Moreover, we observe that the robustness of KL gradient predictor totally depends on the setting of the VAE and dataset. We also explored the effect of the weight of KL loss within beta-VAE and predictor ensemble in anomaly localization.
3.3CVMar 26, 2020
Do Deep Minds Think Alike? Selective Adversarial Attacks for Fine-Grained Manipulation of Multiple Deep Neural NetworksZain Khan, Jirong Yi, Raghu Mudumbai et al.
Recent works have demonstrated the existence of {\it adversarial examples} targeting a single machine learning system. In this paper we ask a simple but fundamental question of "selective fooling": given {\it multiple} machine learning systems assigned to solve the same classification problem and taking the same input signal, is it possible to construct a perturbation to the input signal that manipulates the outputs of these {\it multiple} machine learning systems {\it simultaneously} in arbitrary pre-defined ways? For example, is it possible to selectively fool a set of "enemy" machine learning systems but does not fool the other "friend" machine learning systems? The answer to this question depends on the extent to which these different machine learning systems "think alike". We formulate the problem of "selective fooling" as a novel optimization problem, and report on a series of experiments on the MNIST dataset. Our preliminary findings from these experiments show that it is in fact very easy to selectively manipulate multiple MNIST classifiers simultaneously, even when the classifiers are identical in their architectures, training algorithms and training datasets except for random initialization during training. This suggests that two nominally equivalent machine learning systems do not in fact "think alike" at all, and opens the possibility for many novel applications and deeper understandings of the working principles of deep neural networks.
1.8CVJun 11, 2019
Deep Neural Networks for Surface Segmentation Meet Conditional Random FieldsLeixin Zhou, Zisha Zhong, Abhay Shah et al.
Automated surface segmentation is important and challenging in many medical image analysis applications. Recent deep learning based methods have been developed for various object segmentation tasks. Most of them are a classification based approach (e.g., U-net), which predicts the probability of being target object or background for each voxel. One problem of those methods is lacking of topology guarantee for segmented objects, and usually post processing is needed to infer the boundary surface of the object. In this paper, a novel model based on 3-D convolutional neural networks (CNNs) and Conditional Random Fields (CRFs) is proposed to tackle the surface segmentation problem with end-to-end training. To the best of our knowledge, this is the first study to apply a 3-D neural network with a CRFs model for direct surface segmentation. Experiments carried out on NCI-ISBI 2013 MR prostate dataset and Medical Segmentation Decathlon Spleen dataset demonstrated promising segmentation results.
13.0CRMay 25, 2019
Trust but Verify: An Information-Theoretic Explanation for the Adversarial Fragility of Machine Learning Systems, and a General Defense against Adversarial AttacksJirong Yi, Hui Xie, Leixin Zhou et al.
Deep-learning based classification algorithms have been shown to be susceptible to adversarial attacks: minor changes to the input of classifiers can dramatically change their outputs, while being imperceptible to humans. In this paper, we present a simple hypothesis about a feature compression property of artificial intelligence (AI) classifiers and present theoretical arguments to show that this hypothesis successfully accounts for the observed fragility of AI classifiers to small adversarial perturbations. Drawing on ideas from information and coding theory, we propose a general class of defenses for detecting classifier errors caused by abnormally small input perturbations. We further show theoretical guarantees for the performance of this detection method. We present experimental results with (a) a voice recognition system, and (b) a digit recognition system using the MNIST database, to demonstrate the effectiveness of the proposed defense methods. The ideas in this paper are motivated by a simple analogy between AI classifiers and the standard Shannon model of a communication system.
5.1IVMar 26, 2019
Deep segmentation networks predict survival of non-small cell lung cancerStephen Baek, Yusen He, Bryan G. Allen et al.
Non-small-cell lung cancer (NSCLC) represents approximately 80-85% of lung cancer diagnoses and is the leading cause of cancer-related death worldwide. Recent studies indicate that image-based radiomics features from positron emission tomography-computed tomography (PET/CT) images have predictive power on NSCLC outcomes. To this end, easily calculated functional features such as the maximum and the mean of standard uptake value (SUV) and total lesion glycolysis (TLG) are most commonly used for NSCLC prognostication, but their prognostic value remains controversial. Meanwhile, convolutional neural networks (CNN) are rapidly emerging as a new premise for cancer image analysis, with significantly enhanced predictive power compared to other hand-crafted radiomics features. Here we show that CNN trained to perform the tumor segmentation task, with no other information than physician contours, identify a rich set of survival-related image features with remarkable prognostic value. In a retrospective study on 96 NSCLC patients before stereotactic-body radiotherapy (SBRT), we found that the CNN segmentation algorithm (U-Net) trained for tumor segmentation in PET/CT images, contained features having strong correlation with 2- and 5-year overall and disease-specific survivals. The U-net algorithm has not seen any other clinical information (e.g. survival, age, smoking history) than the images and the corresponding tumor contours provided by physicians. Furthermore, through visualization of the U-Net, we also found convincing evidence that the regions of progression appear to match with the regions where the U-Net features identified patterns that predicted higher likelihood of death. We anticipate our findings will be a starting point for more sophisticated non-intrusive patient specific cancer prognosis determination.
6.0CVMar 20, 2019
Robust Image Segmentation Quality AssessmentLeixin Zhou, Wenxiang Deng, Xiaodong Wu
Deep learning based image segmentation methods have achieved great success, even having human-level accuracy in some applications. However, due to the black box nature of deep learning, the best method may fail in some situations. Thus predicting segmentation quality without ground truth would be very crucial especially in clinical practice. Recently, people proposed to train neural networks to estimate the quality score by regression. Although it can achieve promising prediction accuracy, the network suffers robustness problem, e.g. it is vulnerable to adversarial attacks. In this paper, we propose to alleviate this problem by utilizing the difference between the input image and the reconstructed image, which is conditioned on the segmentation to be assessed, to lower the chance to overfit to the undesired image features from the original input image, and thus to increase the robustness. Results on ACDC17 dataset demonstrated our method is promising.
0.9CVMay 22, 2017
Optimal Multi-Object Segmentation with Novel Gradient Vector Flow Based Shape PriorsJunjie Bai, Abhay Shah, Xiaodong Wu
Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing self-intersection or mesh folding. Those problems require complex and expensive algorithms to mitigate. In this paper, we propose a novel shape prior directly embedded in the voxel grid space, based on gradient vector flows of a pre-segmentation. The flexible and powerful prior shape representation is ready to be extended to simultaneously segmenting multiple interacting objects with minimum separation distance constraint. The problem is formulated as a Markov random field problem whose exact solution can be efficiently computed with a single minimum s-t cut in an appropriately constructed graph. The proposed algorithm is validated on two multi-object segmentation applications: the brain tissue segmentation in MRI images, and the bladder/prostate segmentation in CT images. Both sets of experiments show superior or competitive performance of the proposed method to other state-of-the-art methods.
3.1CVMay 19, 2017
Simultaneous Multiple Surface Segmentation Using Deep LearningAbhay Shah, Michael Abramoff, Xiaodong Wu
The task of automatically segmenting 3-D surfaces representing boundaries of objects is important for quantitative analysis of volumetric images, and plays a vital role in biomedical image analysis. Recently, graph-based methods with a global optimization property have been developed and optimized for various medical imaging applications. Despite their widespread use, these require human experts to design transformations, image features, surface smoothness priors, and re-design for a different tissue, organ or imaging modality. Here, we propose a Deep Learning based approach for segmentation of the surfaces in volumetric medical images, by learning the essential features and transformations from training data, without any human expert intervention. We employ a regional approach to learn the local surface profiles. The proposed approach was evaluated on simultaneous intraretinal layer segmentation of optical coherence tomography (OCT) images of normal retinas and retinas affected by age related macular degeneration (AMD). The proposed approach was validated on 40 retina OCT volumes including 20 normal and 20 AMD subjects. The experiments showed statistically significant improvement in accuracy for our approach compared to state-of-the-art graph based optimal surface segmentation with convex priors (G-OSC). A single Convolution Neural Network (CNN) was used to learn the surfaces for both normal and diseased images. The mean unsigned surface positioning errors obtained by G-OSC method 2.31 voxels (95% CI 2.02-2.60 voxels) was improved to $1.27$ voxels (95% CI 1.14-1.40 voxels) using our new approach. On average, our approach takes 94.34 s, requiring 95.35 MB memory, which is much faster than the 2837.46 s and 6.87 GB memory required by the G-OSC method on the same computer system.