In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extrem...In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extremely popular and dramatically improved in the past two decades. On one hand, many models have been proposed for nearly all kinds of applications. On the other hand, a lot of models can be globally optimized and also many computation tools have been introduced. Under the variational framework, we focus on two basic problems in medical imaging： image restoration and segmentation, which are core components for kinds of specific tasks. For image restoration, we discuss some models on both additive and multiplicative noises. For image segmentation, we review some models on both whole image segmentation and specific target delineation, with the later being a key step in computer aided surgery. Additionally, we present some models on liver delineation and give their applications to living donor liver transplantation.展开更多
This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind o...This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind of image segmentation is still a challenging task.The proposed method uses both the region and boundary information to achieve accurate segmentation results.The region information can help to identify rough region of interest and prevent the boundary leakage problem.It makes use of normalized nonlocal comparisons between pairs of patches in each region,and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation.The boundary information can help to detect the precise location of the target object,it makes use of the geodesic active contour model to obtain the target boundary.The corresponding variational segmentation problem is implemented by a level set formulation.We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function.At last,experimental results on synthetic images and real images are shown in the paper with promising results.展开更多
In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the （1 ＋ n）-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyp...In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the （1 ＋ n）-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n =2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem; while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.展开更多
Accurate pancreas segmentation is critical for the diagnosis and management of diseases of the pancreas. It is challenging to precisely delineate pancreas due to the highly variations in volume, shape and location. In...Accurate pancreas segmentation is critical for the diagnosis and management of diseases of the pancreas. It is challenging to precisely delineate pancreas due to the highly variations in volume, shape and location. In recent years, coarse-to-fine methods have been widely used to alleviate class imbalance issue and improve pancreas segmentation accuracy. However,cascaded methods could be computationally intensive and the refined results are significantly dependent on the performance of its coarse segmentation results. To balance the segmentation accuracy and computational efficiency, we propose a Discriminative Feature Attention Network for pancreas segmentation, to effectively highlight pancreas features and improve segmentation accuracy without explicit pancreas location. The final segmentation is obtained by applying a simple yet effective post-processing step. Two experiments on both public NIH pancreas CT dataset and abdominal BTCV multi-organ dataset are individually conducted to show the effectiveness of our method for 2 D pancreas segmentation. We obtained average Dice Similarity Coefficient(DSC) of 82.82±6.09%, average Jaccard Index(JI) of 71.13± 8.30% and average Symmetric Average Surface Distance(ASD) of 1.69 ± 0.83 mm on the NIH dataset. Compared to the existing deep learning-based pancreas segmentation methods, our experimental results achieve the best average DSC and JI value.展开更多
Automatic segmentation of the liver and hepatic lesions from abdominal 3D comput-ed tomography(CT)images is fundamental tasks in computer-assisted liver surgery planning.However,due to complex backgrounds,ambiguous bo...Automatic segmentation of the liver and hepatic lesions from abdominal 3D comput-ed tomography(CT)images is fundamental tasks in computer-assisted liver surgery planning.However,due to complex backgrounds,ambiguous boundaries,heterogeneous appearances and highly varied shapes of the liver,accurate liver segmentation and tumor detection are stil-1 challenging problems.To address these difficulties,we propose an automatic segmentation framework based on 3D U-net with dense connections and globally optimized refinement.First-ly,a deep U-net architecture with dense connections is trained to learn the probability map of the liver.Then the probability map goes into the following refinement step as the initial surface and prior shape.The segmentation of liver tumor is based on the similar network architecture with the help of segmentation results of liver.In order to reduce the infuence of the surrounding tissues with the similar intensity and texture behavior with the tumor region,during the training procedure,I x liverlabel is the input of the network for the segmentation of liver tumor.By do-ing this,the accuracy of segmentation can be improved.The proposed method is fully automatic without any user interaction.Both qualitative and quantitative results reveal that the pro-posed approach is efficient and accurate for liver volume estimation in clinical application.The high correlation between the automatic and manual references shows that the proposed method can be good enough to replace the time-consuming and non-reproducible manual segmentation method.展开更多
Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to...Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.展开更多
This paper presents a relevance vector regression(RVR) based on parametric approach to the bias field estimation in brain magnetic resonance(MR) image segmentation. Segmentation is a very important and challenging tas...This paper presents a relevance vector regression(RVR) based on parametric approach to the bias field estimation in brain magnetic resonance(MR) image segmentation. Segmentation is a very important and challenging task in brain analysis,while the bias field existed in the images can significantly deteriorate the performance.Most of current parametric bias field correction techniques use a pre-set linear combination of low degree basis functions, the coefficients and the basis function types of which completely determine the field. The proposed RVR method can automatically determine the best combination for the bias field, resulting in a good segmentation in the presence of noise by combining with spatial constrained fuzzy C-means(SCFCM)segmentation. Experiments on simulated T1 images show the efficiency.展开更多
基金Supported by the National Natural Science Foundation of China (11101365)a National Science and Technology Project during the twelfth five-year plan of China (2012BAI10B04)
文摘In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extremely popular and dramatically improved in the past two decades. On one hand, many models have been proposed for nearly all kinds of applications. On the other hand, a lot of models can be globally optimized and also many computation tools have been introduced. Under the variational framework, we focus on two basic problems in medical imaging： image restoration and segmentation, which are core components for kinds of specific tasks. For image restoration, we discuss some models on both additive and multiplicative noises. For image segmentation, we review some models on both whole image segmentation and specific target delineation, with the later being a key step in computer aided surgery. Additionally, we present some models on liver delineation and give their applications to living donor liver transplantation.
基金supported in part by the National Natural Science Foundation of China(11626214,11571309)the General Research Project of Zhejiang Provincial Department of Education(Y201635378)+3 种基金the Zhejiang Provincial Natural Science Foundation of China(LY17F020011)J.Peng is supported by the National Natural Science Foundation of China(11771160)the Research Promotion Program of Huaqiao University(ZQN-PY411)Natural Science Foundation of Fujian Province(2015J01254)
文摘This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind of image segmentation is still a challenging task.The proposed method uses both the region and boundary information to achieve accurate segmentation results.The region information can help to identify rough region of interest and prevent the boundary leakage problem.It makes use of normalized nonlocal comparisons between pairs of patches in each region,and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation.The boundary information can help to detect the precise location of the target object,it makes use of the geodesic active contour model to obtain the target boundary.The corresponding variational segmentation problem is implemented by a level set formulation.We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function.At last,experimental results on synthetic images and real images are shown in the paper with promising results.
基金Supported by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)
文摘In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the （1 ＋ n）-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n =2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem; while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.
基金Supported by the Ph.D. Research Startup Project of Minnan Normal University(KJ2021020)the National Natural Science Foundation of China(12090020 and 12090025)Zhejiang Provincial Natural Science Foundation of China(LSD19H180005)。
文摘Accurate pancreas segmentation is critical for the diagnosis and management of diseases of the pancreas. It is challenging to precisely delineate pancreas due to the highly variations in volume, shape and location. In recent years, coarse-to-fine methods have been widely used to alleviate class imbalance issue and improve pancreas segmentation accuracy. However,cascaded methods could be computationally intensive and the refined results are significantly dependent on the performance of its coarse segmentation results. To balance the segmentation accuracy and computational efficiency, we propose a Discriminative Feature Attention Network for pancreas segmentation, to effectively highlight pancreas features and improve segmentation accuracy without explicit pancreas location. The final segmentation is obtained by applying a simple yet effective post-processing step. Two experiments on both public NIH pancreas CT dataset and abdominal BTCV multi-organ dataset are individually conducted to show the effectiveness of our method for 2 D pancreas segmentation. We obtained average Dice Similarity Coefficient(DSC) of 82.82±6.09%, average Jaccard Index(JI) of 71.13± 8.30% and average Symmetric Average Surface Distance(ASD) of 1.69 ± 0.83 mm on the NIH dataset. Compared to the existing deep learning-based pancreas segmentation methods, our experimental results achieve the best average DSC and JI value.
基金Supported by the National Natural Science Foundation of China(12090020,12090025)Zhejiang Provin-cial Natural Science Foundation of China(LSD19H180005)。
文摘Automatic segmentation of the liver and hepatic lesions from abdominal 3D comput-ed tomography(CT)images is fundamental tasks in computer-assisted liver surgery planning.However,due to complex backgrounds,ambiguous boundaries,heterogeneous appearances and highly varied shapes of the liver,accurate liver segmentation and tumor detection are stil-1 challenging problems.To address these difficulties,we propose an automatic segmentation framework based on 3D U-net with dense connections and globally optimized refinement.First-ly,a deep U-net architecture with dense connections is trained to learn the probability map of the liver.Then the probability map goes into the following refinement step as the initial surface and prior shape.The segmentation of liver tumor is based on the similar network architecture with the help of segmentation results of liver.In order to reduce the infuence of the surrounding tissues with the similar intensity and texture behavior with the tumor region,during the training procedure,I x liverlabel is the input of the network for the segmentation of liver tumor.By do-ing this,the accuracy of segmentation can be improved.The proposed method is fully automatic without any user interaction.Both qualitative and quantitative results reveal that the pro-posed approach is efficient and accurate for liver volume estimation in clinical application.The high correlation between the automatic and manual references shows that the proposed method can be good enough to replace the time-consuming and non-reproducible manual segmentation method.
基金Supported in part by the NNSF of China(11301129,11271323,91330105,11326033)the Zhejiang Provincial Natural Science Foundation of China(LQ13A010025,LZ13A010002)
文摘Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.
基金National Natural Science Foundation of Chinagrant number:10971190+1 种基金National Natural Science Foundation of Chinagrant number:11001239 and 11101365
文摘This paper presents a relevance vector regression(RVR) based on parametric approach to the bias field estimation in brain magnetic resonance(MR) image segmentation. Segmentation is a very important and challenging task in brain analysis,while the bias field existed in the images can significantly deteriorate the performance.Most of current parametric bias field correction techniques use a pre-set linear combination of low degree basis functions, the coefficients and the basis function types of which completely determine the field. The proposed RVR method can automatically determine the best combination for the bias field, resulting in a good segmentation in the presence of noise by combining with spatial constrained fuzzy C-means(SCFCM)segmentation. Experiments on simulated T1 images show the efficiency.
