A New Variational Level Set Evolving Algorithm for Image Segmentation

We use variational level set method and transition region extraction techniques to achieve image segmentation task. The proposed scheme is done by two steps. We first develop a novel algorithm to extract transition region based on the morphological gradient. After this, we integrate the transition region into a variational level set framework and develop a novel geometric active contour model, which include an external energy based on transition region and fractional order edge indicator function. The external energy is used to drive the zero level set toward the desired image features, such as object boundaries. Due to this external energy, the proposed model allows for more flexible initialization. The fractional order edge indicator function is incorporated into the length regularization term to diminish the influence of noise. Moreover, internal energy is added into the proposed model to penalize the deviation of the level set function from a signed distance function. The results evolution of the level set function is the gradient flow that minimizes the overall energy functional. The proposed model has been applied to both synthetic and real images with promising results.

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.

In conventional level set methods, the slope of the level set function needs to be well controlled to maintain the numerical stability during the topology optimization process. One common solution is to regularize the level set function to be a signed distance function, which is usually achieved by periodically implementing the so called re-initialization scheme to force the level set function to gain the desired signed distance property. However, the re-initialization scheme will bring some unwanted drawbacks to the optimization process, such as zero level set drifting, time consuming etc. In addition, re-initialization is usually implemented outside the optimization loop, which will cause convergence issues. In this paper, a distance regularization functional is introduced to the structural topology optimization objective functional to ensure the signed distance property of the level set function near the structure boundaries. This functional can also keep the level set function to be constant-value at positions far away from the structural boundaries. The radial basis function (RBF) based parameterization technique together with the mathematical programming are utilized to improve the potential capability of handling multiple constraints for the topology optimization. The combination of these two techniques makes the level set based topology optimization be capable of handling complicated multi-constrained problems with higher numerical efficiency, leaving no compromise to multiple drawbacks. To demonstrate the validity of the proposed scheme, benchmark examples on minimum compliance structural optimization are employed. This type of problem is computed by the conventional level set method with the introduced distance regularization functional, the RBF based parametric level set and at last, the distance regularized RBF based parametric level set separately to demonstrate their differences.

The edge-based level set model gives no satisfactory results for images with weak edge, and the region-based model performs poorly for intensity inhomogeneity images. In this paper, we propose an improved region-based level set model that integrates both the gradient information and the region information. The proposed model defines a novel external energy term, which consists of gradient information and signed pressure forces function. In order to eliminate the re-initialization procedure of traditional level set model, an internal energy term is also introduced for the level set function to maintain signed distance function. Compared with traditional models, our model is more robust against images with weak edge and intensity inhomogeneity. Experiments on liver segmentation from abdominal CT images demonstrate the effectiveness and accuracy of the proposed method.

Modeling the growth and interaction of multiple dendrites in solidification using a level set method

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.

High-order level set reinitialization for multiphase flow simulations based on unstructured grids

Distance regularization energy terms in level set image segment model: A survey

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.

3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement

Improving image segmentation by using energy function based on mixture of Gaussian pre-processing

The application of segmentation technology in CT images can not only retain the clear characteristics of CT images, but also have the advantages of high resolution, clear anatomical relationship and clear pathological development. Level set segmentation method combines region and boundary information to solve the problems on complex texture and blurred edge of CT image. Therefore, this paper proposes an algorithm for regional growth and level set interaction for the problem of boundary sensitivity and lack of regional information in level set segmentation. In order to improve the efficiency and reduce the error of segmentation, this algorithm uses Gaussian filter to remove noise. Meaning while it adopts Ostu method to transform the image into a binary image. In addition, this algorithm provides an ideal growth environment for the seed point of the region growing algorithm correspondingly. The results of region growth are accomplished as the initial contour of the level set to modify the initial boundary. The boundary indication function introduces the region information; the level set segmentation algorithm achieves the purpose of accelerating in the pixel similar region and stopping at the target boundary as a result. Comparing the overall improved algorithms with the previous both region growing method and the level set method, the experiment results shows convincingly that the interaction between the level set segmentation and the region growing reduces the number of iterations. Under the condition of weak boundary and high noise, the boundary indicator function can accurately and completely segment the organ region and save the details of the internal organ completely, which improves the segmentation accuracy to a certain extent.

The precision of grinding and positioning by industry robot is influenced by segmentation accuracy of region of interest (ROI). The inherent defects of casting billet including perforation defects, crack defects, surface defects, and the polluted environment of post-processing may cause poor imaging quality which may have adverse effects on image segmentation. Considering the need for localization and identification in casting post-processing production line, this paper proposed a novel active contour algorithm which is suitable for the segmentation of complex images. First of all, the penalty term based on the local gradient information of image was introduced into the energy function, which will modify the deviation between evolution model of level set and Signed Distance Function (SDF) to reduce repeated initialization and improve convergence accuracy. Then, Gaussian pyramid energy term is incorporated into the energy function of geodesic active contour model to further accelerate its convergence speed. Finally, iteratively calculate the energy function of the proposed level set model to realize the evolution of contour curve, which can realize fast robust segmentation of complex image by solving the zero level set of the energy function. The comparative experiments between conventional method and the method proposed in this paper prove that the proposed method has higher processing speed than traditional C-V model on condition that the segmentation precision is guaranteed.

This paper presents an approach tomodel the solvent-excluded surface (SES) of 3D protein molecular structures using the geometric PDE-based level-set method. The level-set method embeds the shape of 3D molecular objects as an isosurface or level set corresponding to some isovalue of a scattered dense scalar field, which is saved as a discretely-sampled, rectilinear grid, i.e., a volumetric grid. Our level-set model is described as a class of tri-cubic tensor product B-spline implicit surface with control point values that are the signed distance function. The geometric PDE is evolved in the discrete volume. The geometric PDE we use is the mean curvature specified flow, which coincides with the definition of the SES and is geometrically intrinsic. The technique of speeding up is achieved by use of the narrow band strategy incorporated with a good initial approximate construction for the SES. We get a very desirable approximate surface for the SES. AMS subject classifications: 65D07, 65D10, 65D17, 65D18

In this paper, we present a robust and accurate algorithm for interactive image segmentation. The level set method is clearly advantageous for image objects with a complex topology and fragmented appearance. Our method integrates discriminative classification models and distance transforms with the level set method to avoid local minima and better snap to true object boundaries. The level set function approximates a transformed version of pixelwise posterior probabilities of being part of a target object. The evolution of its zero level set is driven by three force terms, region force, edge field force, and curvature force. These forces are based on a probabilistic classifier and an unsigned distance transform of salient edges. We further propose a technique that improves the performance of both the probabilistic classifier and the level set method over multiple passes. It makes the final object segmentation less sensitive to user interactions. Experiments and comparisons demonstrate the effectiveness of our method.