Image segmentation and selective smoothing based on p-harmonic Mumford–Shah functional

Image segmentation and image denoising are two important and fundamental topics in the field of image processing. Geometric active contour model based on level set method can deal with the problem of image segmentation, but it does not consider the problem of image denoising. In this paper, a new diffusion equation model for noisy image segmentation is proposed by incorporating some classical diffusion equation denoising models into the segmental process. An assumption about the connection between the image intensity and level set function is given firstly. Some classical denoising models are employed to describe the evolution of level set function secondly. The final nonlinear diffusion equation model for noisy image segmentation is built thirdly. Then image segmentation and image denoising are combined in a united framework. The segmental results can be presented by level set function. Experimental results show that the new model has the advantage of noise resistance and is superior to traditional segmentation model.

Image segmentation is one of the crucial tasks in medical image processing and computer vision. The goal for image segmentation is to separate the pixels in the image into its constituent parts. Variational model in image segmentation involves formulating image segmentation as an optimization problem. The models seeking a partition of the image into meaningful regions by minimizing or maximizing an energy functional. These models often use geometric information to represent object boundaries. The models involve techniques such as active contours and level set methods. In this paper, the generalized mean model for image segmentation is investigated and modified. The model is a 2D region-based model which utilizes the fuzzy level set method. The model is compared with the active contour without edges model also known as the Chan-Vese for three types of images: without noise, with noise and with sinusoidal intensity inhomogeneity. Based on the numerical results, the generalized mean model obtained higher accuracy, Dice similarity measure, Jaccard and Kappa Index, comparedto the Chan-Vese model based on the tested images.The model is useful in medical imaging for disease detection, diagnosis, and treatment planning.

HomeRadiology: Imaging CancerVol. 2, No. 2 Previous Research HighlightsFree AccessA New Approach for Automated Image Segmentation of Organs at Risk in Cervical CancerMeredith Jones, Lacey R. McNallyMeredith Jones, Lacey R. McNallyMeredith JonesLacey R. McNallyPublished Online:Mar 27 2020https://doi.org/10.1148/rycan.2020204010MoreSectionsPDF ToolsImage ViewerAdd to favoritesCiteTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Take-Away Points■ Major Focus: Development of an automated multiclass image segmentation model to identify organs at risk (OARs) on CT scans in patients with locally advanced cervical cancer, prior to radiation therapy.■ Key Results: The convolutional neural network model outperformed model-based, intensity-based, and atlas-based segmentation algorithms, with comparable results to other deep learning segmentation models while also decreasing the time needed for image segmentation by several thousand-fold.■ Impact: Reduction of intra- and interuser variability imposed by manual OAR delineation can lead to more accurate and efficient radiation therapy planning.The recent article by Liu et al developed an automated multiclass image segmentation model to identify organs at risk (OARs) on CT scans. To plan effective and safe radiation therapy in the context of cervical cancer, a CT scan is often acquired prior to the first treatment. Currently, a radiation oncologist will segment the CT images by hand, which is a time-consuming process, subject to intra- and interobserver variability, to identify OARs. To overcome these potential limitations and biases, automated image segmentation techniques can be utilized to improve accuracy and speed of annotating each image. A major problem in creation of deep learning image segmentation models for medical images is the lack of available datasets for model training and validation. Liu et al developed a two-dimensional image segmentation model based off the established convolutional neural network architecture, U-Net. U-Net was utilized because it is feasible to train from scratch with a small training set.This study looked at the CT scans of 105 patients with locally advanced cervical cancer. OAR segmentation for cervical cancer is a particularly challenging problem due to variability in organ size and frequent unclear boundaries. Even an experienced radiologist will have trouble. Seven organs were identified as OARs for cervical cancer radiation therapy: bladder, bone marrow, femoral head left, femoral head right, rectum, small intestine, and spinal cord.The model uses context aggregation blocks where U-Net has convolution layers. These context aggregation blocks use dilation convolution layers with different dilated rates and normal convolution layers with different kernel sizes to yield a low false-positive rate and accurate feature extraction in a large receptive field. A squeeze-extract block was used to ensure proper consideration of organs that are small. A class-weighted cross-entropy loss function was also used to overcome the imbalance in the datasets created by the differences in size and shape of each OAR.A ground truth was available based on the radiation oncologist’s annotations, allowing a Dice similarity coefficient (DSC) and 95th Hausdorff distance (HD) to be calculated and used as an evaluation metric. The DSC and the HD metrics indicated a comparable performance to other deep learning image segmentation models in most of the organs analyzed; inferior results were seen in the rectum and superior results in the intestines. All results were analyzed by an oncologist who determined that greater than 90% of results produced by this model were highly acceptable to be used during radiation therapy planning. To make the model more robust and generalizable, it is necessary to acquire a larger dataset with scans from different sources. Translation of this model to three dimensional may ultimately improve clinical translation.Highlighted ArticleLiu Z, Liu X, Xiao B, et al. Segmentation of organs-at-risk in cervical cancer CT images with a convolutional neural network. Physica Medica 2020;69:184-191. doi: https://doi.org/10.1016/j.ejmp.2019.12.008Highlighted ArticleLiu Z, Liu X, Xiao B, et al. Segmentation of organs-at-risk in cervical cancer CT images with a convolutional neural network. Physica Medica 2020;69:184-191. doi: https://doi.org/10.1016/j.ejmp.2019.12.008 Crossref, Medline, Google ScholarArticle HistoryPublished online: Mar 27 2020 FiguresReferencesRelatedDetailsCited ByJournal of Biomimetics, Biomaterials and Biomedical Engineering, Vol. 49Mathematical Problems in Engineering, Vol. 2020Recommended Articles nnU-Net: Further Automating Biomedical Image AutosegmentationRadiology: Imaging Cancer2021Volume: 3Issue: 1Deep Learning: A Primer for RadiologistsRadioGraphics2017Volume: 37Issue: 7pp. 2113-2131Generative Adversarial Networks: A Primer for RadiologistsRadioGraphics2021Volume: 41Issue: 3pp. 840-857Current Applications and Future Impact of Machine Learning in RadiologyRadiology2018Volume: 288Issue: 2pp. 318-328Deep Generative Adversarial Networks: Applications in Musculoskeletal ImagingRadiology: Artificial Intelligence2021Volume: 3Issue: 3See More RSNA Education Exhibits A Multidisciplinary Approach for Program Development with Artificial Intelligence in Pancreatic Cancer: How We Fit InDigital Posters2019Abnormal Changes After Radiation Therapy: What Radiologists Should KnowDigital Posters2018Artificial Intelligence in Diagnostic Imaging: Current Applications and Future PerspectiveDigital Posters2019 RSNA Case Collection Acute Radiation EnteropathyRSNA Case Collection2021Small Bowel LymphomaRSNA Case Collection2021Hirschsprung DiseaseRSNA Case Collection2021 Vol. 2, No. 2 Metrics Downloaded 310 times Altmetric Score

Level set method and Gaussian Mixture model (GMM) are two very valuable tools for natural image segmentation. The former aims to acquire good geometrical continuity of segmentation boundaries, while the latter focuses on analyzing statistical properties of image feature data. Some studies on the integration between them have been reported due to their complementarity in the last 10 years. However, these studies generally supposed that the image-featured data density distribution of every segmented domain is independent with each other and can be separately approximated by Gaussian model or GMM, which conflicts with the fundamental idea of GMM clustering-based image segmentation. To remedy this problem, we give a new insight at image segmentation objective under the combined framework between Bayesian theory and GMM density approximation. Thereby, a novel level set image segmentation method integrated with GMM (GMMLS) is proposed. Then, the theoretical analysis on GMMLS is given, in which some valuable results are demonstrated. At last, several types of natural image segmentation experiments are reported and the corresponding results indicate that GMMLS can obtain better or at least equivalent performance compared with existing relevant methods in almost all cases.

Many medical and real images are suffered from intensity inhomogeneity and weak edges. For higher image segmentation quality, lots of level set-based methods have been proposed. Some of them however cannot take advantage of image gradient information. And severe intensity inhomogeneity and weak edges are not disposed properly. To address these problems, a new level set method integrated with local direction gradient information is presented in this paper. Firstly, according to the two assumptions on image intensity inhomogeneity adopted by many existing methods, a new pixel classification model based on image gradient is introduced. Secondly, we employ variational level set method combined with image spatial information, which improves the anti-noise capability of the proposed method. Finally, considering the gray gradients in homogeneous regions are close to constants, an improved diffusion process is incorporated into the level set function to make the evolving curves stay around true image edges. To verify our method, different testing images including synthetic images, magnetic resonance imaging (MRI) and real-world images are introduced. The image segmentation results demonstrate that our method can deal with the relatively severe intensity inhomogeneity and obtain the comparatively ideal segmentation results efficiently.

A new binary level set model using L0 regularizer for image segmentation

In this paper, we introduce multi-symplectic Lagrangian variational integrators for solving Chan-Vese active contour models in image segmentation. Energy functionals are discretized firstly, and numerical schemes are derived from discrete Euler-Lagrange equations based on discrete variational principle. Lagrangian variational integrators preserve native differential structure-multi-symplecticity, that makes the numerical methods have a satisfied behavior. Experiments are performed on the benchmark images from literature. We further evaluated the methods in a segmentation database containing 1023 images. It shows that the proposed numerical schemes attain relatively faster convergence rates and better segmentation accuracy. Comparisons with the standard explicit Euler method of the original Chan-Vese model and other fast numerical optimization methods show that the proposed methods have better stability, higher accuracy, and are more robust when dealing with a large number of pictures. This study provides an example for further research to improve the performance of other existing image segmentation methods based on active contour models.

Convolutional neural networks (CNNs), as a typical deep learning technique, have been widely used in image segmentation, but they often require a large amount of annotated data. However, the number of available pixel-wise labeled medical images is extremely small, and this prevents the application of CNNs in many medical image segmentation tasks. We proposed a self-paced learning with diversity SPLD) framework to boost the performances of medical image segmentation models with a limited amount of annotated data. Self-paced learning (SPL) is a learning regime that selects training samples in order from the easiest to the most difficult for model training. In addition, we took the diversity of the data into consideration. The proposed self-paced learning with diversity by query-by-committee (SPLD-QBC) algorithm dynamically and diversely selects the appropriate training data to boost the performance of an image segmentation model. SPLD-QBC incorporates the query-by-committee (QBC) technique for data selection and affinity propagation for optimizing the data diversity. By dynamically selecting the optimal sequence of training samples from different probability distributions, the segmentation models achieved improved performances. To verify the effectiveness of the proposed SPLD-QBC framework, we conducted experiments on three medical image segmentation tasks with five different datasets. The experimental results indicated that the proposed SPLD-QBC algorithm significantly improved upon the segmentation performances of the baseline models and resulted in a higher Dice score, surface distance and mean intersection over union (mIoU). The proposed SPLD significantly boosts the segmentation performances of models and is easily embedded into CNN-based image segmentation models.

Image segmentation can be used in non-destructive testing, tracking and recognition. Level set method for image segmentation has poor performance on efficiency. In this paper, we propose to use max-flow algorithm to optimize a locally improved Chan-Vese model for image segmentation in the presence of intensity inhomogeneity. The energy function of local Chan-Vese model is introduced firstly. This model consists of global term, local term and penalty term and the local term contributes the segmentation for images with intensity inhomogeneity. Then, we convert this energy function to the frame of Graph Cut whose energy function can be efficiently minimized by max-flow algorithm. As a result, the process of optimization of local Chan-Vese model can be accelerated by using max-flow algorithm. The experiments demonstrate that the proposed method can achieve satisfactory segmentation for images with intensity inhomogeneity as well as very high efficiency.

This study proposes a novel local region-based active contour model (ACM) for image segmentation based on fractional calculus with consideration of the Riemann–Liouville operators. The proposed method aims to achieve accurate boundary segmentation in the presence of severe intensity inhomogeneity. The strength of fractional calculus is exploited with Gaussian Kernel namely, Fractional Gaussian Kernel (FGK) that provides an effective method of edge detection and has good noise immunity. An adaptive window mechanism with various sizes and orientations is employ to maintain and enhance image details especially at the object’s boundary and angle. The powerful combination of adaptive window and Fractional Gaussian Kernel (AFGK) provide an efficient way to utilize image information in local regions. Specifically, the fractional differential Heaviside function (FDH) extracts the image gradient and its various intensities for an accurate boundary segmentation outcome. Experiments on both synthetics and medical images demonstrate that the proposed local region-based ACM including fractional calculus realizes accurate boundary segmentation on images even under the most challenging situations, such as severe intensity inhomogeneity interface.

In recent years, image segmentation based on level set formulations was encompassed by proficiently implementing various image processing applications, especially in case of reformative models for medical image segmentation. Existing level set methods under this criterion are not up to the mark in terms of noise, weak boundaries, and inhomogeneity. In this paper, we put forward a new formulation for selective segmentation with level set model using optimised fuzzy region clustering and implementation is carried out in two stages. In first, optimised fuzzy region clustering (OFR) is employed in which particle swarm optimisation technique is utilised at the initialisation of FCM clustering to obtain optimal cluster centres and then it is incorporated with region competition. While in second, implementing OFR clustering using level set methods. The proposed formulation is successfully implemented on some contemporary medicinal images. It is capable to identify the weak boundaries and segment the desired components of an image such as white substance, grey substance, cerebrospinal fluid, bone sarcoma, breast cancer and Alzheimer’s disease, etc. The visual results and quantitative analysis show its effectiveness, superiority and accuracy over the existing formulations.

Level set methods (LSMs) have been extensively investigated for medical image segmentation. However, there are a few inherent drawbacks in common level set formulations using image variation or region competition. For example, edge-based LSMs are susceptible to weak or broken boundaries, while region-based ones are often dominated by suboptimal solutions. By incorporating the functional of fuzzy controlling, we propose a new level set model in this paper to combine the merits of edge-based and region-based LSMs while overcoming their drawbacks. It also provides a convenient framework to integrate prior information or knowledge for medical image segmentation. Its performance has been preliminarily verified for medical images of computed tomography (CT) and magnetic resonance imaging (MRI).

The objective of this paper is to evaluate performance of the level set approach applied to segmentation and tracking of noisy 3D images of computer-simulated blood-vessel phantoms and artificial vascular trees. Of particular interest was the segmentation of thin vessels, with diameter smaller that voxel size. Flood fill technique was also explored, for comparison. Quantitative measures of segmentation accuracy were used for the methods evaluation. It was demonstrated, that the level set method provides good segmentation results even for noisy images. This promising result encourages its future application for vascularity modeling based on MR images.

In traditional image segmentation models based on single level set function, only two regions can be identified because different regions are identified by the signs of single level set function. Though several segmentation models with multiple regions have been proposed, but the largest number of regions that can be identified was limited by the number of embedded level set functions in them. Moreover, the more embedded level set functions, the higher the time cost, usually increasing linearly with the increase of embedded level set functions. In this paper, by introducing the segmentation-measure function, a new model for multi-regions image segmentation based on single level set function is proposed. At the same time, a new initialization function for the level set function is also proposed in order to reduce the time cost of the segmentation model. The experiment results show that the new Image segmentation mode with multiple regions proposed in this paper performs well and dramatically reduces the time cost compared with the popular model for multiple regions proposed by Vese and Chan.

This study was to analyze the impacts of the image segmentation model and computed tomography angiography (CTA) on the clinical diagnosis of aortic constriction under the background of artificial intelligence. In this study, 126 patients with congenital aortic constriction (CAC) diagnosed by surgery were selected as the research objects and routine digital subtraction angiography (DSA) and CTA were performed. Then, the traditional active contour model (AC model) was optimized based on the local area information to construct a new image segmentation model for intelligent segmentation and reconstruction of the CTA images of patients. The results revealed that compared with the AC model and the image segmentation model based on region growth (RG model) obtained from angiography segmentation, the algorithm constructed in this study showed a smaller segmentation range for angiography images and more accurate segmentation results. The quantitative data results suggested that the evolution times and running time of the constructed model were less than those of the AC and RG models P < 0.05 . Based on the gold standard of DSA examination results, there were 122 correctly diagnosed cases, 3 missed diagnosed cases, and 1 misdiagnosed by CTA, so the diagnosis coincidence rate was 96.83%. Compared with DSA, the average inner diameter and average pressure difference of patients with precatheter, paracatheter, and postcatheter type were not greatly different in CTA P > 0.05 . The CTA examination suggested there were 154 cases with intracardiac structural abnormalities, with a detection rate of 86.52%; there were 32 cases of cardiac-vascular connection abnormalities, with a detection rate of 100%; and there were 79 extracardiac vascular abnormalities, with the detection rate of 95.18%. It indicated that the optimized image segmentation model based on local area information proposed in this paper has excellent segmentation performance for CT angiography images and has good segmentation effect and efficiency. The CTA based on the artificial intelligence image segmentation model showed a better diagnostic effect on abnormal heart-vascular connection and abnormal extracardiac blood vessels and can be used as an effective examination method for clinical diagnosis of CAC.