Costly Re-initialization Procedure Research Articles

Fast Hybrid Level Set Model for Non-homogenous Image Segmentation Solving by Algebraic Multigrid

A novel hybrid fitting energy based active contours model in the level set framework is proposed. The method fuses the local image fitting term and the global image fitting term to drive the contour evolution, and a special extra term that penalizes the deviation of the level set function from a signed distance function is also included in our method, so the complex and costly re-initialization procedure is completely eliminated. Our model can efficiently segment the images with intensity inhomogeneity no matter where the initial curve is located in the image. In its numerical implementation, the Algebraic Multigrid (AMG) is used for breaking the restrictions on time step, compared with the traditional schemes, the AMG strategy can shorten the time consumption of the evolution process, this allows the level set to quickly reach the true target location. The extensive and promising experimental results on numerous synthetic and real images have shown that our method can efficiently improve the image segmentation performance, in terms of accuracy, efficiency, and robustness.

Local average fitting active contour model with thresholding for noisy image segmentation

In this paper, an active contours model using neighborhood average fitting with thresholding is proposed for noisy images segmentation. Energy of the proposed model is formulated according to the difference between the local average and global region information. For images corrupted by noise, the neighborhood average method is capable of denoising at the expense of blurring images to some extent. However, problems that appear with average method can be settled by thresholding in this work. Minimization of the energy associated with the active contour model is then implemented in a variational level set framework. Moreover, to eliminate the need for costly re-initialization procedure, a reaction-diffusion method is adopted to regularize the level set function for stability. Experimental results on synthetic and real images validate the effectiveness of the proposed approach.

Application of radial basis functions to evolution equations arising in image segmentation

In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method.

A Diffusion-Augmented Level Set Method with Efficient Two Step Implementation

The level set method was devised by Osher and Sethian [2] in as a simple and versatile method for computing and analyzing the motion of an interface Γ in two or three dimensions. Γ bounds a region Ω. The goal is to compute and analyze the subsequent motion of Γ under a velocity field v [1]. This velocity can depend on position, time, the geometry of the interface and the external physics. The interface is captured for later time as the zero level set of a smooth function ϕ(x, t), i.e., Γ (t) = {x|ϕ(x, t) = 0}. ϕ is positive inside Ω, negative outside Ω and is zero on Γ (t) [1]. This paper presents a reaction-diffusion method used to describe a physicochemical phenomenon that comprises two elements, namely chemical reactions and diffusion for implicit active contours[21][37][39][40], which is completely free of the costly re-initialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in a diffusion-augmented level set method with efficient two step implementation. First we iteratively solve the diffusion term and then iteratively solve the level set equation. By solving equation in two steps we can stabilize the level set function without re-initialization. This is also called two step splitting method for image segmentation.

An improved level set method for vertebra CT image segmentation

BackgroundClinical diagnosis and therapy for the lumbar disc herniation requires accurate vertebra segmentation. The complex anatomical structure and the degenerative deformations of the vertebrae makes its segmentation challenging.MethodsAn improved level set method, namely edge- and region-based level set method (ERBLS), is proposed for vertebra CT images segmentation. By considering the gradient information and local region characteristics of images, the proposed model can efficiently segment images with intensity inhomogeneity and blurry or discontinuous boundaries. To reduce the dependency on manual initialization in many active contour models and for an automatic segmentation, a simple initialization method for the level set function is built, which utilizes the Otsu threshold. In addition, the need of the costly re-initialization procedure is completely eliminated.ResultsExperimental results on both synthetic and real images demonstrated that the proposed ERBLS model is very robust and efficient. Compared with the well-known local binary fitting (LBF) model, our method is much more computationally efficient and much less sensitive to the initial contour. The proposed method has also applied to 56 patient data sets and produced very promising results.ConclusionsAn improved level set method suitable for vertebra CT images segmentation is proposed. It has the flexibility of segmenting the vertebra CT images with blurry or discontinuous edges, internal inhomogeneity and no need of re-initialization.

Conservative Level Set Method Without Re-Initialization Process: Application to Multiphase Flows

To describe the interface evolution in multiphase flows, the numerical simulation requires special approaches. The Lagrangian-based methods (front tracking) are not adequate when the interface curvature is sharp and time dependent. The volume of fluid method is numerically prohibitive. The level set method (LSM) presents many advantages, when a very high accuracy in the interface curvature is needed. In this paper, the LSM is treated in more detail. A finite element (FEM ) formulation has been used to model a two-phase flows involving interface propagation. A variational formulation is introduced in order to suppress the costly re-initialization procedure, and a new mass conservation correction method based on penalty factor is proposed.The performance of the method is then presented using several reported cases. The results showed that the accuracy of the proposed approach is drastically improved in comparison with other reported methods. The method is applied to the dam-break and to the rising bubble in water column problems. Good agreements with the reported solutions are presented, which corroborates the accuracy of the method.

Reinitialization-Free Level Set Evolution via Reaction Diffusion

This paper presents a novel reaction-diffusion (RD) method for implicit active contours that is completely free of the costly reinitialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in an RD-LSE equation, from which a piecewise constant solution can be derived. In order to obtain a stable numerical solution from the RD-based LSE, we propose a two-step splitting method to iteratively solve the RD-LSE equation, where we first iterate the LSE equation, then solve the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly reinitialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and partial differential equation-based level set method. The RD-LSE method shows very good performance on boundary antileakage. The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.

A new level set method for topology optimization of distributed compliant mechanisms

SUMMARYA new level set method for topology optimization of distributed compliant mechanism is presented in this study. By taking two types of mean compliance into consideration, several new objective functions are developed and built in the conventional level set method to avoid generating the de facto hinges in the created mechanisms. Aimed at eliminating the costly reinitialization procedure during the evolution of the level set function, an accelerated level set evolution algorithm is developed by adding an extra energy function, which can force the level set function to close to a signed distance function during the evolution. Two widely studied numerical examples in topology optimization of compliant mechanisms are studied to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

An Improved Integrated Active Contour Model without Re-Initialization for Vector-Valued Images Segmentation

In this paper, an improved variational formulation for active contours model is introduced to force level set function to become fast and stably close to signed distance function, which can completely eliminate the need of the costly re-initialization procedure. A restriction item that is a nonlinear heat equation with balanced diffusion rate is attached to variational Integrated Active Contour (IAC) model on the basis of analysis on regions and edges information from all channels of the valued-vector images, so that the level set evolution segmentation process becomes fast and stable. In addition, more efficient discretization method with spatial rotation-invariance gradient and divergence operator is proposed as numerical implementation scheme. Finally, the experiments on some images have demonstrated the efficiency, accuracy and robustness of the proposed method.

A geometric active contour model without re-initialization for color images

A geometric active contour model without re-initialization for color images is proposed in this paper. It combines directional information about edge location based on local squared contrast as a part of driving force, together with the improved geodesic active contour containing Bayes error based statistical region information as well as an extra term that penalizes deviation of the level set function from a signed distance function. All these measures are integrated in a unified frame thus the costly re-initialization procedure can be completely eliminated. Experimental results on real color images have shown that our model can extract contours of objects in images precisely and its performance is much better than the Geodesic-Aided C-V (GACV) model.

Geometric active contours without re-initialization for image segmentation

A geometric active contour model without re-initialization that can be used for grey and color image segmentation is presented in this paper. It combines directional information about edge location based on Cumani operator as a part of driving force, with the improved geodesic active contours containing Bays error based statistical region information. Moreover, an extra term that penalizes the deviation of the level set function from a signed distance function is also included in the model, thus the costly re-initialization procedure can be completely eliminated and all these measures are integrated in a unified frame. Experimental results on real grey and color images have shown that our model can precisely extract contours of images and its performance is much better and faster than the geodesic-aided C-V (GACV) model.