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arXiv:2502.16709

FedDA-TSformer: Federated Domain Adaptation with Vision TimeSformer for Left Ventricle Segmentation on Gated Myocardial Perfusion SPECT Image

Background and Purpose: Functional assessment of the left ventricle using gated myocardial perfusion (MPS) single-photon emission computed tomography relies on the precise extraction of the left ventricular contours while simultaneously ensuring the security of patient data. Methods: In this paper, we introduce the integration of Federated Domain Adaptation with TimeSformer, named 'FedDA-TSformer' for left ventricle segmentation using MPS. FedDA-TSformer captures spatial and temporal features in gated MPS images, leveraging spatial attention, temporal attention, and federated learning for improved domain adaptation while ensuring patient data security. In detail, we employed Divide-Space-Time-Attention mechanism to extract spatio-temporal correlations from the multi-centered MPS datasets, ensuring that predictions are spatio-temporally consistent. To achieve domain adaptation, we align the model output on MPS from three different centers using local maximum mean discrepancy (LMMD) loss. This approach effectively addresses the dual requirements of federated learning and domain adaptation, enhancing the model's performance during training with multi-site datasets while ensuring the protection of data from different hospitals. Results: Our FedDA-TSformer was trained and evaluated using MPS datasets collected from three hospitals, comprising a total of 150 subjects. Each subject's cardiac cycle was divided into eight gates. The model achieved Dice Similarity Coefficients (DSC) of 0.842 and 0.907 for left ventricular (LV) endocardium and epicardium segmentation, respectively. Conclusion: Our proposed FedDA-TSformer model addresses the challenge of multi-center generalization, ensures patient data privacy protection, and demonstrates effectiveness in left ventricular (LV) segmentation.

arXiv:2407.20387

Two-Phase Segmentation Approach for Accurate Left Ventricle Segmentation in Cardiac MRI using Machine Learning

Accurate segmentation of the Left Ventricle (LV) holds substantial importance due to its implications in disease detection, regional analysis, and the development of complex models for cardiac surgical planning. CMR is a golden standard for diagnosis of serveral cardiac diseases. LV in CMR comprises of three distinct sections: Basal, Mid-Ventricle, and Apical. This research focuses on the precise segmentation of the LV from Cardiac MRI (CMR) scans, joining with the capabilities of Machine Learning (ML). The central challenge in this research revolves around the absence of a set of parameters applicable to all three types of LV slices. Parameters optimized for basal slices often fall short when applied to mid-ventricular and apical slices, and vice versa. To handle this issue, a new method is proposed to enhance LV segmentation. The proposed method involves using distinct sets of parameters for each type of slice, resulting in a two-phase segmentation approach. The initial phase categorizes images into three groups based on the type of LV slice, while the second phase aims to segment CMR images using parameters derived from the preceding phase. A publicly available dataset (Automated Cardiac Diagnosis Challenge (ACDC)) is used. 10-Fold Cross Validation is used and it achieved a mean score of 0.9228. Comprehensive testing indicates that the best parameter set for a particular type of slice does not perform adequately for the other slice types. All results show that the proposed approach fills a critical void in parameter standardization through a two-phase segmentation model for the LV, aiming to not only improve the accuracy of cardiac image analysis but also contribute advancements to the field of LV segmentation.

arXiv:2310.10756

Deep Conditional Shape Models for 3D cardiac image segmentation

Delineation of anatomical structures is often the first step of many medical image analysis workflows. While convolutional neural networks achieve high performance, these do not incorporate anatomical shape information. We introduce a novel segmentation algorithm that uses Deep Conditional Shape models (DCSMs) as a core component. Using deep implicit shape representations, the algorithm learns a modality-agnostic shape model that can generate the signed distance functions for any anatomy of interest. To fit the generated shape to the image, the shape model is conditioned on anatomic landmarks that can be automatically detected or provided by the user. Finally, we add a modality-dependent, lightweight refinement network to capture any fine details not represented by the implicit function. The proposed DCSM framework is evaluated on the problem of cardiac left ventricle (LV) segmentation from multiple 3D modalities (contrast-enhanced CT, non-contrasted CT, 3D echocardiography-3DE). We demonstrate that the automatic DCSM outperforms the baseline for non-contrasted CT without the local refinement, and with the refinement for contrasted CT and 3DE, especially with significant improvement in the Hausdorff distance. The semi-automatic DCSM with user-input landmarks, while only trained on contrasted CT, achieves greater than 92% Dice for all modalities. Both automatic DCSM with refinement and semi-automatic DCSM achieve equivalent or better performance compared to inter-user variability for these modalities.

arXiv:2310.10095

A Multi-Scale Spatial Transformer U-Net for Simultaneously Automatic Reorientation and Segmentation of 3D Nuclear Cardiac Images

Accurate reorientation and segmentation of the left ventricular (LV) is essential for the quantitative analysis of myocardial perfusion imaging (MPI), in which one critical step is to reorient the reconstructed transaxial nuclear cardiac images into standard short-axis slices for subsequent image processing. Small-scale LV myocardium (LV-MY) region detection and the diverse cardiac structures of individual patients pose challenges to LV segmentation operation. To mitigate these issues, we propose an end-to-end model, named as multi-scale spatial transformer UNet (MS-ST-UNet), that involves the multi-scale spatial transformer network (MSSTN) and multi-scale UNet (MSUNet) modules to perform simultaneous reorientation and segmentation of LV region from nuclear cardiac images. The proposed method is trained and tested using two different nuclear cardiac image modalities: 13N-ammonia PET and 99mTc-sestamibi SPECT. We use a multi-scale strategy to generate and extract image features with different scales. Our experimental results demonstrate that the proposed method significantly improves the reorientation and segmentation performance. This joint learning framework promotes mutual enhancement between reorientation and segmentation tasks, leading to cutting edge performance and an efficient image processing workflow. The proposed end-to-end deep network has the potential to reduce the burden of manual delineation for cardiac images, thereby providing multimodal quantitative analysis assistance for physicists.

arXiv:2310.00454

SimLVSeg: Simplifying Left Ventricular Segmentation in 2D+Time Echocardiograms with Self- and Weakly-Supervised Learning

Echocardiography has become an indispensable clinical imaging modality for general heart health assessment. From calculating biomarkers such as ejection fraction to the probability of a patient's heart failure, accurate segmentation of the heart structures allows doctors to assess the heart's condition and devise treatments with greater precision and accuracy. However, achieving accurate and reliable left ventricle segmentation is time-consuming and challenging due to different reasons. Hence, clinicians often rely on segmenting the left ventricular (LV) in two specific echocardiogram frames to make a diagnosis. This limited coverage in manual LV segmentation poses a challenge for developing automatic LV segmentation with high temporal consistency, as the resulting dataset is typically annotated sparsely. In response to this challenge, this work introduces SimLVSeg, a novel paradigm that enables video-based networks for consistent LV segmentation from sparsely annotated echocardiogram videos. SimLVSeg consists of self-supervised pre-training with temporal masking, followed by weakly supervised learning tailored for LV segmentation from sparse annotations. We demonstrate how SimLVSeg outperforms the state-of-the-art solutions by achieving a 93.32% (95%CI 93.21-93.43%) dice score on the largest 2D+time echocardiography dataset (EchoNet-Dynamic) while being more efficient. SimLVSeg is compatible with two types of video segmentation networks: 2D super image and 3D segmentation. To show the effectiveness of our approach, we provide extensive ablation studies, including pre-training settings and various deep learning backbones. We further conduct an out-of-distribution test to showcase SimLVSeg's generalizability on unseen distribution (CAMUS dataset). The code is publicly available at https://github.com/fadamsyah/SimLVSeg.

arXiv:2210.11291공식 코드 · Papers with Code

Cyclical Self-Supervision for Semi-Supervised Ejection Fraction Prediction from Echocardiogram Videos

Left-ventricular ejection fraction (LVEF) is an important indicator of heart failure. Existing methods for LVEF estimation from video require large amounts of annotated data to achieve high performance, e.g. using 10,030 labeled echocardiogram videos to achieve mean absolute error (MAE) of 4.10. Labeling these videos is time-consuming however and limits potential downstream applications to other heart diseases. This paper presents the first semi-supervised approach for LVEF prediction. Unlike general video prediction tasks, LVEF prediction is specifically related to changes in the left ventricle (LV) in echocardiogram videos. By incorporating knowledge learned from predicting LV segmentations into LVEF regression, we can provide additional context to the model for better predictions. To this end, we propose a novel Cyclical Self-Supervision (CSS) method for learning video-based LV segmentation, which is motivated by the observation that the heartbeat is a cyclical process with temporal repetition. Prediction masks from our segmentation model can then be used as additional input for LVEF regression to provide spatial context for the LV region. We also introduce teacher-student distillation to distill the information from LV segmentation masks into an end-to-end LVEF regression model that only requires video inputs. Results show our method outperforms alternative semi-supervised methods and can achieve MAE of 4.17, which is competitive with state-of-the-art supervised performance, using half the number of labels. Validation on an external dataset also shows improved generalization ability from using our method. Our code is available at https://github.com/xmed-lab/CSS-SemiVideo.

arXiv:2207.02549공식 코드 · Papers with Code

Light-weight spatio-temporal graphs for segmentation and ejection fraction prediction in cardiac ultrasound

Accurate and consistent predictions of echocardiography parameters are important for cardiovascular diagnosis and treatment. In particular, segmentations of the left ventricle can be used to derive ventricular volume, ejection fraction (EF) and other relevant measurements. In this paper we propose a new automated method called EchoGraphs for predicting ejection fraction and segmenting the left ventricle by detecting anatomical keypoints. Models for direct coordinate regression based on Graph Convolutional Networks (GCNs) are used to detect the keypoints. GCNs can learn to represent the cardiac shape based on local appearance of each keypoint, as well as global spatial and temporal structures of all keypoints combined. We evaluate our EchoGraphs model on the EchoNet benchmark dataset. Compared to semantic segmentation, GCNs show accurate segmentation and improvements in robustness and inference runtime. EF is computed simultaneously to segmentations and our method also obtains state-of-the-art ejection fraction estimation. Source code is available online: https://github.com/guybenyosef/EchoGraphs.

arXiv:2010.08952

Shape Constrained CNN for Cardiac MR Segmentation with Simultaneous Prediction of Shape and Pose Parameters

Semantic segmentation using convolutional neural networks (CNNs) is the state-of-the-art for many medical segmentation tasks including left ventricle (LV) segmentation in cardiac MR images. However, a drawback is that these CNNs lack explicit shape constraints, occasionally resulting in unrealistic segmentations. In this paper, we perform LV and myocardial segmentation by regression of pose and shape parameters derived from a statistical shape model. The integrated shape model regularizes predicted segmentations and guarantees realistic shapes. Furthermore, in contrast to semantic segmentation, it allows direct calculation of regional measures such as myocardial thickness. We enforce robustness of shape and pose prediction by simultaneously constructing a segmentation distance map during training. We evaluated the proposed method in a fivefold cross validation on a in-house clinical dataset with 75 subjects containing a total of 1539 delineated short-axis slices covering LV from apex to base, and achieved a correlation of 99% for LV area, 94% for myocardial area, 98% for LV dimensions and 88% for regional wall thicknesses. The method was additionally validated on the LVQuan18 and LVQuan19 public datasets and achieved state-of-the-art results.

arXiv:2007.10665

Segmentation of the Left Ventricle by SDD double threshold selection and CHT

Automatic and robust segmentation of the left ventricle (LV) in magnetic resonance images (MRI) has remained challenging for many decades. With the great success of deep learning in object detection and classification, the research focus of LV segmentation has changed to convolutional neural network (CNN) in recent years. However, LV segmentation is a pixel-level classification problem and its categories are intractable compared to object detection and classification. In this paper, we proposed a robust LV segmentation method based on slope difference distribution (SDD) double threshold selection and circular Hough transform (CHT). The proposed method achieved 96.51% DICE score on the test set of automated cardiac diagnosis challenge (ACDC) which is higher than the best accuracy reported in recently published literatures.

arXiv:2005.13643

Segmentation of the Myocardium on Late-Gadolinium Enhanced MRI based on 2.5 D Residual Squeeze and Excitation Deep Learning Model

Cardiac left ventricular (LV) segmentation from short-axis MRI acquired 10 minutes after the injection of a contrast agent (LGE-MRI) is a necessary step in the processing allowing the identification and diagnosis of cardiac diseases such as myocardial infarction. However, this segmentation is challenging due to high variability across subjects and the potential lack of contrast between structures. Then, the main objective of this work is to develop an accurate automatic segmentation method based on deep learning models for the myocardial borders on LGE-MRI. To this end, 2.5 D residual neural network integrated with a squeeze and excitation blocks in encoder side with specialized convolutional has been proposed. Late fusion has been used to merge the output of the best trained proposed models from a different set of hyperparameters. A total number of 320 exams (with a mean number of 6 slices per exam) were used for training and 28 exams used for testing. The performance analysis of the proposed ensemble model in the basal and middle slices was similar as compared to intra-observer study and slightly lower at apical slices. The overall Dice score was 82.01% by our proposed method as compared to Dice score of 83.22% obtained from the intra observer study. The proposed model could be used for the automatic segmentation of myocardial border that is a very important step for accurate quantification of no-reflow, myocardial infarction, myocarditis, and hypertrophic cardiomyopathy, among others.

arXiv:1912.10220

Spatio-Temporal Segmentation in 3D Echocardiographic Sequences using Fractional Brownian Motion

An important aspect for an improved cardiac functional analysis is the accurate segmentation of the left ventricle (LV). A novel approach for fully-automated segmentation of the LV endocardium and epicardium contours is presented. This is mainly based on the natural physical characteristics of the LV shape structure. Both sides of the LV boundaries exhibit natural elliptical curvatures by having details on various scales, i.e. exhibiting fractal-like characteristics. The fractional Brownian motion (fBm), which is a non-stationary stochastic process, integrates well with the stochastic nature of ultrasound echoes. It has the advantage of representing a wide range of non-stationary signals and can quantify statistical local self-similarity throughout the time-sequence ultrasound images. The locally characterized boundaries of the fBm segmented LV were further iteratively refined using global information by means of second-order moments. The method is benchmarked using synthetic 3D+time echocardiographic sequences for normal and different ischemic cardiomyopathy, and results compared with state-of-the-art LV segmentation. Furthermore, the framework was validated against real data from canine cases with expert-defined segmentations and demonstrated improved accuracy. The fBm-based segmentation algorithm is fully automatic and has the potential to be used clinically together with 3D echocardiography for improved cardiovascular disease diagnosis.

arXiv:1906.10486

A Novel Deep Learning Based Approach for Left Ventricle Segmentation in Echocardiography: MFP-Unet

Segmentation of the Left ventricle (LV) is a crucial step for quantitative measurements such as area, volume, and ejection fraction. However, the automatic LV segmentation in 2D echocardiographic images is a challenging task due to ill-defined borders, and operator dependence issues (insufficient reproducibility). U-net, which is a well-known architecture in medical image segmentation, addressed this problem through an encoder-decoder path. Despite outstanding overall performance, U-net ignores the contribution of all semantic strengths in the segmentation procedure. In the present study, we have proposed a novel architecture to tackle this drawback. Feature maps in all levels of the decoder path of U-net are concatenated, their depths are equalized, and up-sampled to a fixed dimension. This stack of feature maps would be the input of the semantic segmentation layer. The proposed network yielded state-of-the-art results when comparing with results from U-net, dilated U-net, and deeplabv3, using the same dataset. An average Dice Metric (DM) of 0.945, Hausdorff Distance (HD) of 1.62, Jaccard Coefficient (JC) of 0.97, and Mean Absolute Distance (MAD) of 1.32 are achieved. The correlation graph, bland-altman analysis, and box plot showed a great agreement between automatic and manually calculated volume, area, and length.

arXiv:1904.00631

TAN: Temporal Affine Network for Real-Time Left Ventricle Anatomical Structure Analysis Based on 2D Ultrasound Videos

With superiorities on low cost, portability, and free of radiation, echocardiogram is a widely used imaging modality for left ventricle (LV) function quantification. However, automatic LV segmentation and motion tracking is still a challenging task. In addition to fuzzy border definition, low contrast, and abounding artifacts on typical ultrasound images, the shape and size of the LV change significantly in a cardiac cycle. In this work, we propose a temporal affine network (TAN) to perform image analysis in a warped image space, where the shape and size variations due to the cardiac motion as well as other artifacts are largely compensated. Furthermore, we perform three frequent echocardiogram interpretation tasks simultaneously: standard cardiac plane recognition, LV landmark detection, and LV segmentation. Instead of using three networks with one dedicating to each task, we use a multi-task network to perform three tasks simultaneously. Since three tasks share the same encoder, the compact network improves the segmentation accuracy with more supervision. The network is further finetuned with optical flow adjusted annotations to enhance motion coherence in the segmentation result. Experiments on 1,714 2D echocardiographic sequences demonstrate that the proposed method achieves state-of-the-art segmentation accuracy with real-time efficiency.

arXiv:1902.11000

3D High-Resolution Cardiac Segmentation Reconstruction from 2D Views using Conditional Variational Autoencoders

Accurate segmentation of heart structures imaged by cardiac MR is key for the quantitative analysis of pathology. High-resolution 3D MR sequences enable whole-heart structural imaging but are time-consuming, expensive to acquire and they often require long breath holds that are not suitable for patients. Consequently, multiplanar breath-hold 2D cine sequences are standard practice but are disadvantaged by lack of whole-heart coverage and low through-plane resolution. To address this, we propose a conditional variational autoencoder architecture able to learn a generative model of 3D high-resolution left ventricular (LV) segmentations which is conditioned on three 2D LV segmentations of one short-axis and two long-axis images. By only employing these three 2D segmentations, our model can efficiently reconstruct the 3D high-resolution LV segmentation of a subject. When evaluated on 400 unseen healthy volunteers, our model yielded an average Dice score of $87.92 \pm 0.15$ and outperformed competing architectures.

arXiv:1810.08753

Left Ventricle Segmentation via Optical-Flow-Net from Short-axis Cine MRI: Preserving the Temporal Coherence of Cardiac Motion

Quantitative assessment of left ventricle (LV) function from cine MRI has significant diagnostic and prognostic value for cardiovascular disease patients. The temporal movement of LV provides essential information on the contracting/relaxing pattern of heart, which is keenly evaluated by clinical experts in clinical practice. Inspired by the expert way of viewing Cine MRI, we propose a new CNN module that is able to incorporate the temporal information into LV segmentation from cine MRI. In the proposed CNN, the optical flow (OF) between neighboring frames is integrated and aggregated at feature level, such that temporal coherence in cardiac motion can be taken into account during segmentation. The proposed module is integrated into the U-net architecture without need of additional training. Furthermore, dilated convolution is introduced to improve the spatial accuracy of segmentation. Trained and tested on the Cardiac Atlas database, the proposed network resulted in a Dice index of 95% and an average perpendicular distance of 0.9 pixels for the middle LV contour, significantly outperforming the original U-net that processes each frame individually. Notably, the proposed method improved the temporal coherence of LV segmentation results, especially at the LV apex and base where the cardiac motion is difficult to follow.

arXiv:1809.10221

Left Ventricle Segmentation and Quantification from Cardiac Cine MR Images via Multi-task Learning

Segmentation of the left ventricle and quantification of various cardiac contractile functions is crucial for the timely diagnosis and treatment of cardiovascular diseases. Traditionally, the two tasks have been tackled independently. Here we propose a convolutional neural network based multi-task learning approach to perform both tasks simultaneously, such that, the network learns better representation of the data with improved generalization performance. Probabilistic formulation of the problem enables learning the task uncertainties during the training, which are used to automatically compute the weights for the tasks. We performed a five fold cross-validation of the myocardium segmentation obtained from the proposed multi-task network on 97 patient 4-dimensional cardiac cine-MRI datasets available through the STACOM LV segmentation challenge against the provided gold-standard myocardium segmentation, obtaining a Dice overlap of $0.849 \pm 0.036$ and mean surface distance of $0.274 \pm 0.083$ mm, while simultaneously estimating the myocardial area with mean absolute difference error of $205\pm198$ mm$^2$.

arXiv:1809.06247

Left Ventricle Segmentation and Volume Estimation on Cardiac MRI using Deep Learning

In the United States, heart disease is the leading cause of death for both men and women, accounting for 610,000 deaths each year [1]. Physicians use Magnetic Resonance Imaging (MRI) scans to take images of the heart in order to non-invasively estimate its structural and functional parameters for cardiovascular diagnosis and disease management. The end-systolic volume (ESV) and end-diastolic volume (EDV) of the left ventricle (LV), and the ejection fraction (EF) are indicators of heart disease. These measures can be derived from the segmented contours of the LV; thus, consistent and accurate segmentation of the LV from MRI images are critical to the accuracy of the ESV, EDV, and EF, and to non-invasive cardiac disease detection. In this work, various image preprocessing techniques, model configurations using the U-Net deep learning architecture, postprocessing methods, and approaches for volume estimation are investigated. An end-to-end analytics pipeline with multiple stages is provided for automated LV segmentation and volume estimation. First, image data are reformatted and processed from DICOM and NIfTI formats to raw images in array format. Secondly, raw images are processed with multiple image preprocessing methods and cropped to include only the Region of Interest (ROI). Thirdly, preprocessed images are segmented using U-Net models. Lastly, post processing of segmented images to remove extra contours along with intelligent slice and frame selection are applied, followed by calculation of the ESV, EDV, and EF. This analytics pipeline is implemented and runs on a distributed computing environment with a GPU cluster at the San Diego Supercomputer Center at UCSD.

arXiv:1809.01015

Automated segmentation on the entire cardiac cycle using a deep learning work-flow

The segmentation of the left ventricle (LV) from CINE MRI images is essential to infer important clinical parameters. Typically, machine learning algorithms for automated LV segmentation use annotated contours from only two cardiac phases, diastole, and systole. In this work, we present an analysis work-flow for fully-automated LV segmentation that learns from images acquired through the cardiac cycle. The workflow consists of three components: first, for each image in the sequence, we perform an automated localization and subsequent cropping of the bounding box containing the cardiac silhouette. Second, we identify the LV contours using a Temporal Fully Convolutional Neural Network (T-FCNN), which extends Fully Convolutional Neural Networks (FCNN) through a recurrent mechanism enforcing temporal coherence across consecutive frames. Finally, we further defined the boundaries using either one of two components: fully-connected Conditional Random Fields (CRFs) with Gaussian edge potentials and Semantic Flow. Our initial experiments suggest that significant improvement in performance can potentially be achieved by using a recurrent neural network component that explicitly learns cardiac motion patterns whilst performing LV segmentation.

arXiv:1507.07508

Fast Segmentation of Left Ventricle in CT Images by Explicit Shape Regression using Random Pixel Difference Features

Recently, machine learning has been successfully applied to model-based left ventricle (LV) segmentation. The general framework involves two stages, which starts with LV localization and is followed by boundary delineation. Both are driven by supervised learning techniques. When compared to previous non-learning-based methods, several advantages have been shown, including full automation and improved accuracy. However, the speed is still slow, in the order of several seconds, for applications involving a large number of cases or case loads requiring real-time performance. In this paper, we propose a fast LV segmentation algorithm by joint localization and boundary delineation via training explicit shape regressor with random pixel difference features. Tested on 3D cardiac computed tomography (CT) image volumes, the average running time of the proposed algorithm is 1.2 milliseconds per case. On a dataset consisting of 139 CT volumes, a 5-fold cross validation shows the segmentation error is $1.21 \pm 0.11$ for LV endocardium and $1.23 \pm 0.11$ millimeters for epicardium. Compared with previous work, the proposed method is more stable (lower standard deviation) without significant compromise to the accuracy.

arXiv:1512.07951

A Combined Deep-Learning and Deformable-Model Approach to Fully Automatic Segmentation of the Left Ventricle in Cardiac MRI

Segmentation of the left ventricle (LV) from cardiac magnetic resonance imaging (MRI) datasets is an essential step for calculation of clinical indices such as ventricular volume and ejection fraction. In this work, we employ deep learning algorithms combined with deformable models to develop and evaluate a fully automatic segmentation tool for the LV from short-axis cardiac MRI datasets. The method employs deep learning algorithms to learn the segmentation task from the ground true data. Convolutional networks are employed to automatically detect the LV chamber in MRI dataset. Stacked autoencoders are utilized to infer the shape of the LV. The inferred shape is incorporated into deformable models to improve the accuracy and robustness of the segmentation. We validated our method using 45 cardiac MR datasets taken from the MICCAI 2009 LV segmentation challenge and showed that it outperforms the state-of-the art methods. Excellent agreement with the ground truth was achieved. Validation metrics, percentage of good contours, Dice metric, average perpendicular distance and conformity, were computed as 96.69%, 0.94, 1.81mm and 0.86, versus those of 79.2%-95.62%, 0.87-0.9, 1.76-2.97mm and 0.67-0.78, obtained by other methods, respectively.