Medical Image Segmentation Based on Wavelet Transformation and Level set method

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.

Image segmentation is one of the most fundamental and important areas in the field of image processing and computer vision. The traditional level set methods need initialize the level set function as a distance function. If the initial contour is selected inappropriate, we may not get the desired ideal segmentation result. In order to solve the problem of level set automation initial, we proposed a new image segmentation algorithm based on level set and marker extraction. First, we extract the internal mark as level set initial curve by using Extended-minima transform. And then, through using the local binary fitting active contour model, we evolve the labeled image to get the final segmentation result. The simulation results show that this method has low computing complexity than the traditional level set method requirements, and can effectively solve the initialization problem of level set.

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).

Regional level set method is a popular approach for image segmentation that uses inside and outside information of contour to extract object boundary. Unfortunately, in many cases, such method is not adequate to model complex textured objects. In this paper, we propose a natural texture image segmentation method which incorporates the pixel-level feature into region-level feature. The multiscale local structure operation is proposed as pixel-level feature to describe the texture structure of image. So the problems of multi-scale and rotation invariance of inhomogeneous texture are addressed by introducing multi-scale local structure operation into level set energy functional. Then, the global intensity information is extracted as the region-level feature and integrated with multi-scale local structure operation. Further, we propose a so-called vector level set method to obtain the segmentation results. Here, we extend the traditional regional level set model into the vector formulation so that the multi-scale local structure operation can be suitably combined with the global intensity information to achieve the more superior image segmentation performance than that of the traditional segmentation methods for texture images. Experiments on some synthesis texture images and real natural scene images demonstrate the excellent performance of the proposed method which successfully combines local structure information and global intensity information to extract the object boundary.

Images captured under non uniform lightening and illumination conditions consist of unwanted shadow regions. Segmentation of these images using conventional level set methods show improper results which is a major problem in many real time applications such as medical imaging, pattern recognition etc. In this paper we propose an adaptive Level set model by introducing a new adaptive force function on the level sets evolution based on reflectance & illumination present in the image. This method is proved to be successful in segmentation of images by excluding the shadow regions present in the images.

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.

Vascular segmentation plays an important role in medical image analysis. A novel technique for the automaticextraction of vascular trees from 2D medical images is presented, which combines Hessian-based multiscale filtering and a modified level set method. In the proposed algorithm, the morphological top-hat transformation is firstly adopted to attenuate background. Then Hessian-based multiscale filtering is used to enhance vascular structures by combining Hessian matrix with Gaussian convolution to tune the filtering response to the specific scales. Because Gaussian convolution tends to blur vessel boundaries, which makes scale selection inaccurate, an improved level set method is finally proposed to extract vascular structures by introducing an external constrained term related to the standard deviation of Gaussian function into the traditional level set. Our approach was tested on synthetic images with vascular-like structures and 2D slices extracted from real 3D abdomen magnetic resonance angiography (MRA) images along the coronal plane. The segmentation rates for synthetic images are above 95%. The results for MRA images demonstrate that the proposed method can extract most of the vascular structures successfully and accurately in visualization. Therefore, the proposed method is effective for the vascular tree extraction in medical images.

Technology is proliferating. Many methods are used for medical imaging. The important methods used here are fast marching and fast level set in comparison with the watershed transform. Since watershed algorithm was applied to an image has over clusters in segmentation. Both methods are applied to segment the medical images. First, fast marching method is used to extract the rough contours. Then fast level set method is utilized to finely tune the initial boundary. Moreover, Traditional fast marching method was modified by the use of watershed transform. The method is feasible in medical imaging and deserves further research. In the future, we will integrate level set method with statistical shape analysis to make it applicable to more kinds of medical images and have better robustness to noise.

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.

Medical image segmentation as an earlier application field in image segmentation is the key technology of medical image analysis and is also a key point and difficulty in clinical application. This paper proposes an accurate and robust active contour model based on the four-phase level set for medical MR images. First we define a new energy functional by combining the data term and the length term, where the data term is defined by transforming the energy functional of the multiplicative intrinsic component optimization (MICO) model into the level set framework after adding an edge detector function. Then, when we minimize the energy functional, we use the split Bregman method to improve the convergence speed. To test the performance of our model, we do lots of experiments according to the different brain MR images, which show that even under the severe influence of bias field or shadows, our model can still segment these images well, and our model is robust to the initial contours and noise. Moreover, our model is compared with the MICO model by experimental results and the numerical values, concluding that our model is better than the MICO model no matter in segmentation accuracy or in correction effect.

Image segmentation plays an important role in computer vision and image processing. Level set model is a classical image segmentation method. During level set evolution, almost all the level set energy minimization of image segmentation are based on the gradient descent method and the finite difference scheme. The speed of evolution is slow and easy to fall into local minima. In this paper, we propose a fast sweeping optimization algorithm to minimize global cosine fitting (GCF) model. When moving a pixel from the one side region to the another side region of evolving contour, the sweeping algorithm calculates the energy change directly and checks whether the cosine fitting energy is decreased. With this, we can avoid solving the Euler-Lagrange equation and the partial differential equation, which usually take a lot of time. Moreover, our proposal is robust to initial level set contour and it automatically handles the topological variety, algorithm automatic termination and no longer requires the reinitialization step, parameter adjustment and the distance regularization term. The experiments on real noise and synthetic images show the effectiveness of the sweeping algorithm.

Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.

The variational level set model for piecewise constant multiphase image segmentation on the plane and the related Split-Augmented-Lagrangian Projection Method (SALPM) are investigated in this paper. On the analysis of the current problems based on the variational level set method for image segmentation, we also design a rapid SALPM method for two-phase image segmentation model, getting the general model of multiple phase level set in order to facilitate the generic design and program. In addition, the concrete formula of the rapid split algorithms for multiphase image segmentation with level set model and the calculation steps are given, and simultaneously taking liver tumor CT image as examples of the multiphase segmentation. Moreover, by comparing with the traditional methods, the experiments show that our algorithm presented in this paper have higher computational efficiency and accuracy, and better the extraction of liver contour.

Image segmentation is the problem of partitioning an image into different subsets, where each subset may have a different characterization in terms of color, intensity, texture, and/or other features. Segmentation is a fundamental component of image processing, and plays a significant role in computer vision, object recognition, and object tracking. Active Contour Models (ACMs) constitute a powerful energy-based minimization framework for image segmentation, which relies on the concept of contour evolution. Starting from an initial guess, the contour is evolved with the aim of approximating better and better the actual object boundary. Handling complex images in an efficient, effective, and robust way is a real challenge, especially in the presence of intensity inhomogeneity, overlap between the foreground/background intensity distributions, objects characterized by many different intensities, and/or additive noise. In this thesis, to deal with these challenges, we propose a number of image segmentation models relying on variational level set methods and specific kinds of neural networks, to handle complex images in both supervised and unsupervised ways. Experimental results demonstrate the high accuracy of the segmentation results, obtained by the proposed models on various benchmark synthetic and real images compared with state-of-the-art active contour models.

Level set methods have previously been successfully implemented in interface propagation for etching and deposition processes. In this article, the authors show that level set methods can be used to model solid phase epitaxial regrowth. The model incorporates orientation dependence of regrowth as found by Csepregi et al. [J. Appl. Phys. 49, 3906 (1978)]. The orientation dependent velocity data are taken from Csepregi’s paper and fitted to a polynomial function to give the growth velocity for level set methods. Simulations show the capability of our model in predicting the pinching of the corners in ⟨111⟩ direction and humplike shape in ⟨100⟩ direction. This is confirmed by the transmission electron microscope pictures from recent papers. This modeling holds special interest because of the different diffusivities of boron in amorphous and crystalline silicon (approximately five orders of magnitude difference) and because of the various defects forming at the pinching corners which could lead to higher leakage current in scaled devices. The level set model is implemented in FLOOPS.