Variational Level Set Formulation Research Articles

Integrating Feature Direction Information with a Level Set Formulation for Image Segmentation

AbstractA feature-dependent variational level set formulation is proposed for image segmentation. Two second order directional derivatives act as the external constraint in the level set evolution, with the directional derivative across the image features direction playing a key role in contour extraction and another only slightly contributes. To overcome the local gradient limit, we integrate the information from the maximal (in magnitude) second-order directional derivative into a common variational framework. It naturally encourages the level set function to deform (up or down) in opposite directions on either side of the image edges, and thus automatically generates object contours. An additional benefit of this proposed model is that it does not require manual initial contours, and our method can capture weak objects in noisy or intensity-inhomogeneous images. Experiments on infrared and medical images demonstrate its advantages.

Distance regularized two level sets for segmentation of left and right ventricles from cine-MRI

This paper presents a new level set method for segmentation of cardiac left and right ventricles. We extend the edge based distance regularized level set evolution (DRLSE) model in Li et al. (2010) to a two-level-set formulation, with the 0-level set and k-level set representing the endocardium and epicardium, respectively. The extraction of endocardium and epicardium is obtained as a result of the interactive curve evolution of the 0 and k level sets derived from the proposed variational level set formulation. The initialization of the level set function in the proposed two-level-set DRLSE model is generated from roughly located endocardium, which can be performed by applying the original DRLSE model. Experimental results have demonstrated the effectiveness of the proposed two-level-set DRLSE model.

Simultaneous vector-valued image segmentation and intensity nonuniformity correction using variational level set combined with Markov random field modeling

Object quantification requires an image segmentation to make measurements about size, material composition and morphology of the object. In vector-valued or multispectral images, each image channel has its signal characteristics and provides special information that may improve the results of image segmentation method. This paper presents a region-based active contour model for vector-valued image segmentation with a variational level set formulation. In this model, the local image intensities are characterized using Gaussian distributions with different means and variances. Furthermore, by utilizing Markov random field, the spatial correlation between neighboring pixels and voxels is modeled. With incorporation of intensity nonuniformity model, our method is able to deal with brain tissue segmentation from multispectral magnetic resonance (MR) images. Our experiments on synthetic images and multispectral cerebral MR images with different noise and bias level show the advantages of the proposed method.

Active contours driven by local and global intensity fitting energies based on local entropy

This paper proposes an improved region-based active contour model. A novel region-scalable fitting energy term which based on the local entropy deriving from a grey level distribution of image is defined. Simultaneously, an intensity fitting term that drives the motion of the active contour globally is added to the energy. The combination of these two terms is then incorporated into a variational level set formulation with two extra regularization terms that are necessary for accurate computation in the corresponding level set method. The resulting evolution of the level set function is the gradient flow that minimizes the overall energy functional. The proposed method has been tested on synthetic and real images, and the experiment results show that our method is efficient and robust for segmenting images with noisy and intensity inhomogeneity.

Active contours driven by localizing region and edge-based intensity fitting energy with application to segmentation of the left ventricle in cardiac CT images

Dual source CT of the heart is a well-known and accepted method for detection of cardiac disease. However, weak edges, touching characters, intensity inhomogeneities and complex background lead LV segmentation to leakage and false boundary, in cardiac CT images. This difficult task is accomplished in this work by establishing a new active contour model in a variational level set formulation. Its external energy functional incorporates an edge-based information fitting term, which is an adaptive diffusion flow (ADF), and responsible for extracting object boundaries, especially segmenting the weak and missing borders, and a localizing region intensity fitting, which localizes the Chan–Vese external energy against intensity inhomogeneity and complex background to improve the robustness of the proposed method. For improving the adaptability of the model, the weighted parameter between them is then designed according to the gradient information of image. Besides, the regularity of the level set function is intrinsically preserved by the length regularization term to ensure the curve smooth. Experimental results demonstrate desirable performance of our extension method for real-world dual source cardiac CT images.

Active contours driven by local likelihood image fitting energy for image segmentation

Accurate image segmentation is an essential step in image analysis and understanding, where active contour models play an important part. Due to the noise, low contrast and intensity inhomogeneity in images, many segmentation algorithms suffer from limited accuracy. This paper presents a novel region-based active contour model for image segmentation by using the variational level set formulation. In this model, we construct the local likelihood image fitting (LLIF) energy functional by describing the neighboring intensities with local Gaussian distributions. The means and variances of local intensities in the LLIF energy functional are spatially varying functions, which can be iteratively estimated during an energy minimization process to guide the contour evolving toward object boundaries. To address diverse image segmentation needs, we also expand this model to the multiphase level set, multi-scale Gaussian kernels and narrowband formulations. The proposed model has been compared with several state-of-the-art active contour models on images with different modalities. Our results indicate that the proposed LLIF model achieves superior performance in image segmentation.

Local and Global Region-Based Curve Evolutions for Image Segmentation

In this paper, we propose a novel region-based active contour model in a variational level set formulation. The energy functional for the proposed model consists of two terms, i.e., global term, local term. Therefore, the combination of these two forces allows for flexible initialization of the contours. This energy is then incorporated into a level set for- mulation with a level set regularization term that is necessary for accurate computation in the corresponding level set method. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase formulation. Finally, experiments on some synthetic and real images have demonstrated the efficiency and robustness of our model. Moreover, comparisons with recent popular local image fitting (LIF) model also show that our model is less sensitive to the location of initial contour.

A novel active contour model driven by local and global intensity fitting energies

In this paper, we propose a novel hybrid active contour model for image segmentation. In our model, we define a new region-scalable fitting (RSF) energy functional which combines the local and the global image information. The RSF energy functional can not only attract the contour toward object boundaries, but also improve the robustness to initialization of the contours. In order to segment the image fast and accurately, the length term and regularization term is incorporated into the variational level set formulation. Finally, by adopting gradient descent method, the minimization of the energy equation can be given. Due to the new kernel function we defined, our model can cope with intensity inhomogeneity images and less sensitive to the initialization of the contour when compared with the other models. Experimental results demonstrated that the proposed model can also segment both the real and medical images accurately.

Split Bregman Method for Minimization of Fast Multiphase Image Segmentation Model for Inhomogeneous Images

In this paper, we present a fast multiphase image segmentation model in a variational level set formulation. The proposed model is mainly used for images with inhomogeneity. The newly defined energy functional combines the local intensity information, the global intensity information, and the edge information to deal with the inhomogeneity. We use a weight function varying with locations to control the force of the local and global information dynamically. The special structure of the new energy functional ensures that the split Bregman method can be used for fast minimization. We apply the split Bregman method to minimize the new energy functional and summarize important results in several theorems. Theoretical evidences for these results are given. Several numerical results are also presented.

ACTIVE CONTOURS DRIVEN BY LOCAL INTENSITY AND LOCAL GRADIENT FITTING ENERGIES

This paper presents a new local region-based and local gradient-based active contour model in a variational level set formulation for image segmentation. The model consists of three parts: the local region term, the local gradient term and the regularization term. The local region term is insensitive to noise, while the local gradient term has better capability of localization than the local region. The energy minimization is achieved by the level set evolution in an iterative strategy. In each iteration, the local intensity and local gradient are updated and fed into the level set evolution. Comparative experiments show that our model achieves the better performance on the ultrasound images with noise and low signal-to-noise ratio than the local binary fitting (LBF) energy model.

A Local Statistical Information Active Contour Model for Image Segmentation

This paper presents a local statistical information (LSI) active contour model. Assuming that the distribution of intensity belonging to each region is a Gaussian distribution with spatially varying statistical information, and defining an energy function, the authors integrate the entire image domain. Then, this energy is incorporated into a variational level set formulation. Finally, by minimizing the energy functional, a curve evolution equation can be obtained. Because the image local information is considered, the proposed model can effectively deal with the image with intensity inhomogeneity. Experimental results on synthetic and real images demonstrate that the proposed model can effectively segment the image with intensity inhomogeneity.

A variational level set segmentation formulation based on signal model for images in the presence of intensity inhomogeneity

ABSTRACTBiological images with significant intensity inhomogeneity are considerably difficult for the tissue segmentation. To overcome the difficulties caused by the intensity inhomogeneity, this study presents a variational level set method to simultaneous bias field estimation and tissue segmentation for images in the presence of intensity inhomogeneity. An energy function is defined in terms of two data fitting terms which incorporate the local clustering properties into the global region information. First, depended on the observed image mode, the local cluster property based on the observed signal is simplified to a criterion function which is similar to the Mumford‐Shah model. The local criterion energy is then integrated with a global region measure, which is based on intensity difference of the true signal. The energy is minimized in a variational level set formulation with a regularity term, thus avoiding the expensive computation of the level set reinitialization and keeping the curve close to the signal distance function. Experiment results on biological images show desirable performance and demonstrate the effectiveness of the proposed algorithm.

New region-scalable discriminant and fitting energy functional for driving geometric active contours in medical image segmentation.

We propose a novel region-based geometric active contour model that uses region-scalable discriminant and fitting energy functional for handling the intensity inhomogeneity and weak boundary problems in medical image segmentation. The region-scalable discriminant and fitting energy functional is defined to capture the image intensity characteristics in local and global regions for driving the evolution of active contour. The discriminant term in the model aims at separating background and foreground in scalable regions while the fitting term tends to fit the intensity in these regions. This model is then transformed into a variational level set formulation with a level set regularization term for accurate computation. The new model utilizes intensity information in the local and global regions as much as possible; so it not only handles better intensity inhomogeneity, but also allows more robustness to noise and more flexible initialization in comparison to the original global region and regional-scalable based models. Experimental results for synthetic and real medical image segmentation show the advantages of the proposed method in terms of accuracy and robustness.

Active Contour Driven by Local Region Statistics and Maximum A Posteriori Probability for Medical Image Segmentation

This paper presents a novel active contour model in a variational level set formulation for simultaneous segmentation and bias field estimation of medical images. An energy function is formulated based on improved Kullback-Leibler distance (KLD) with likelihood ratio. According to the additive model of images with intensity inhomogeneity, we characterize the statistics of image intensities belonging to each different object in local regions as Gaussian distributions with different means and variances. Then, we use the Gaussian distribution with bias field as a local region descriptor in level set formulation for segmentation and bias field correction of the images with inhomogeneous intensities. Therefore, image segmentation and bias field estimation are simultaneously achieved by minimizing the level set formulation. Experimental results demonstrate desirable performance of the proposed method for different medical images with weak boundaries and noise.

A new efficient active contour model without local initializations for salient object detection

Abstract In this paper, we propose a fast and effective polarity-based active contour for salient object detection in grey-level images and color images. The adopted variational level set formulation forces the level set function to be close to a signed distance function and therefore completely eliminates the need of the re-initialization procedure and speeds up the curve evolution. Moreover, instead of the classical and widely used gradient-based stopping function, depending on the image gradient, to stop the curve evolution, we use a polarity-based stopping function. In fact, comparatively to the gradient information, the polarity information accurately distinguishes the boundaries or edges of the salient objects in images. One other nice result of the use of polarity information is that the ad hoc manual and local initializations of the evolving curves inside and outside the image objects can be avoided. Therefore, one trivial and global initialization of the evolving curve can be performed to detect image salient objects. We also investigate the multi-spectral polarity information to generalize the proposed active contour to color images. Experiments are performed on several grey-level images and color images to show the advantage and the effectiveness of our new active contour model.

ACTIVE CONTOUR BASED ON 3D STRUCTURE TENSOR APPLIED IN MEDICAL IMAGE SEGMENTATION

The paper presents an improved tensor-based active contour model in a variational level set formulation for medical image segmentation. In it, a new energy function is defined with a local intensity fitting term in intensity inhomogeneity of the image, and with a global intensity fitting term in intensity homogeneity domain. Weighting factor is chosen to balance these two intensity fitting terms, which can be calculated automatically by local entropy. The level set regularization term is to replace contour curve to find the minimum of the energy function. Particularly, structure tensor is applied to describe the image, which overcomes the disadvantage of image feature without structure information. The experimental results show that our proposed method can segment image efficiently whether it presents intensity inhomogeneity or not and wherever the initial contour is. Moreover, compared with the Chan–Vese model and local binary fitting model, our proposed model not only handles better intensity inhomogeneity, but also is less sensitive to the location of initial contour.

Active Contours Driven by the Salient Edge Energy Model

In this brief, we present a new indicator, i.e., salient edge energy, for guiding a given contour robustly and precisely toward the object boundary. Specifically, we define the salient edge energy by exploiting the higher order statistics on the diffusion space, and incorporate it into a variational level set formulation with the local region-based segmentation energy for solving the problem of curve evolution. In contrast to most previous methods, the proposed salient edge energy allows the curve to find only significant local minima relevant to the object boundary even in the noisy and cluttered background. Moreover, the segmentation performance derived from our new energy is less sensitive to the size of local windows compared with other recently developed methods, owing to the ability of our energy function to suppress diverse clutters. The proposed method has been tested on various images, and experimental results show that the salient edge energy effectively drives the active contour both qualitatively and quantitatively compared to various state-of-the-art methods.

Active contour driven by local divergence energies for ultrasound image segmentation

In this study, a new local region-based active contour model in a variational level set formulation for ultrasound image segmentation is proposed. The energy function is formulated based on the local divergence with likelihood ratio. The proposed model can handle blurry boundaries and noise problems. In addition, the regularity of the level set function is intrinsically preserved by the level set regularisation term to ensure accurate computation. The authors only adopt a level set function to define the partition of image domain into two disjoined regions. Experimental results demonstrate desirable performance of the authors’ method for synthetic images with different level noise and ultrasound images with weak boundaries and noise.

EFFICIENT ACTIVE CONTOUR MODEL FOR MULTIPHASE SEGMENTATION WITH APPLICATION TO BRAIN MR IMAGES

In this paper, we propose an efficient active contour model for multiphase image segmentation in a variational level set formulation. By incorporating the globally convex segmentation idea and the split Bregman method into the multiphase formulation of the local and global intensity fitting energy model, our new model improved the original local and global intensity fitting energy model in the following aspects. First, we propose a new energy functional using the globally convex segmentation method to guarantee fast convergence. Second, we incorporate information from the edge into the energy functional by using a non-negative edge detector function to detect boundaries more easily. Third, instead of a constant value to control the influence of the local and global intensity fitting terms, we use a weight function varying with the locations of the image to balance the weights between the local and the global fitting terms dynamically. Lastly, the special structure of our energy functional enables us to apply the split Bregman method to minimize the energy much more efficiently. We have applied our model to synthetic images and real brain MR images with promising results. Experimental results demonstrate the efficiency and superiority of our model.

Adaptive segmentation of magnetic resonance images with intensity inhomogeneity using level set method

It is a big challenge to segment magnetic resonance (MR) images with intensity inhomogeneity. The widely used segmentation algorithms are region based, which mostly rely on the intensity homogeneity, and could bring inaccurate results. In this paper, we propose a novel region-based active contour model in a variational level set formulation. Based on the fact that intensities in a relatively small local region are separable, a local intensity clustering criterion function is defined. Then, the local function is integrated around the neighborhood center to formulate a global intensity criterion function, which defines the energy term to drive the evolution of the active contour locally. Simultaneously, an intensity fitting term that drives the motion of the active contour globally is added to the energy. In order to segment the image fast and accurately, we utilize a coefficient to make the segmentation adaptive. Finally, the energy is incorporated into a level set formulation with a level set regularization term, and the energy minimization is conducted by a level set evolution process. Experiments on synthetic and real MR images show the effectiveness of our method.