A Variational Level Set Model Combined with FCMS for Image Clustering Segmentation
TL;DR: A new variational level set model combined with FCMS for image clustering segmentation is proposed, which can get smooth cluster boundaries and closed cluster regions due to the use of level set scheme and has a better performance for the images contaminated by different noise levels.
Abstract: The fuzzy C means clustering algorithm with spatial constraint (FCMS) is effective for image segmentation. However, it lacks essential smoothing constraints to the cluster boundaries and enough robustness to the noise. Samson et al. proposed a variational level set model for image clustering segmentation, which can get the smooth cluster boundaries and closed cluster regions due to the use of level set scheme. However it is very sensitive to the noise since it is actually a hard C means clustering model. In this paper, based on Samson’s work, we propose a new variational level set model combined with FCMS for image clustering segmentation. Compared with FCMS clustering, the proposed model can get smooth cluster boundaries and closed cluster regions due to the use of level set scheme. In addition, a block-based energy is incorporated into the energy functional, which enables the proposed model to be more robust to the noise than FCMS clustering and Samson’s model. Some experiments on the synthetic and real images are performed to assess the performance of the proposed model. Compared with some classical image segmentation models, the proposed model has a better performance for the images contaminated by different noise levels.
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TL;DR: A novel application of FCM clustering is presented by using Firefly algorithm with a chaotic map to initialize the population of fireflies and tune the absorption coefficient, for increasing the global search mobility.
26 citations
TL;DR: The proposed model is a promising model for image denoising applications and uses an alternating iterative algorithm that combines the gradient descent algorithm and the alternating direction method of multipliers to numerically solve the model.
16 citations
TL;DR: The function of curve evolution and original model of level set based on region and edge are derived, respectively, which are good at handling complex topologies and capturing boundary.
Abstract: Level set is one of active contour models, which is good at handling complex topologies and capturing boundary. The level set methods are specially used in image with intensity inhomogeneity, such as medical image, SAR image, etc. There are many methods based on level set, which are classified into region-based and edge-based. This article firstly derives the function of curve evolution and original model of level set based on region and edge, respectively. Level set methods over the past decade are summed up and categorized. Some typical models and their improvement are introduced in detail. Some level set methods are employed for comparison. The disadvantages and future work are also discussed.
15 citations
01 Nov 2015
TL;DR: The proposed algorithm is evaluated with accuracy index in performing it on artificial synthesized images, and the results show the superior accuracy compared to some other state of the art FCM-based segmentation methods.
Abstract: Image segmentation with clustering approach is widely used in biomedical application. Fuzzy c-means (FCM) clustering is able to preserve the information between tissues in image, but not taking spatial information into account, makes segmentation results of the standard FCM sensitive to noise. To overcome the above shortcoming, a modified FCM algorithm for MRI brain image segmentation is presented in this paper. The algorithm is realized by incorporating the spatial neighborhood information into the standard FCM algorithm and modifying the membership weighting of each cluster by smoothing it by Total Variation (TV) denoising. The proposed algorithm is evaluated with accuracy index in performing it on artificial synthesized images, and the results show the superior accuracy compared to some other state of the art FCM-based segmentation methods.
6 citations
Cites methods from "A Variational Level Set Model Combi..."
...In order to have better segmentation results in the clusters boundaries, Tang [6] proposed to combine variational level set with FCMS....
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TL;DR: A novel geometric active contour model is developed, which include an external energy based on transition region and fractional order edge indicator function that is used to drive the zero level set toward the desired image features, such as object boundaries.
Abstract: 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.
5 citations
Cites methods from "A Variational Level Set Model Combi..."
...To solve the limitation of variational level set method, many researchers try to propose efficient schemes combined with other methods [16]....
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References
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TL;DR: A new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets is proposed, which can detect objects whose boundaries are not necessarily defined by the gradient.
Abstract: We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.
10,404 citations
"A Variational Level Set Model Combi..." refers methods in this paper
...Recently, some improved models are proposed, such as piecewise constant model [6] proposed byChan andVese (CV) and region-based active contour model [7] (RBACM) proposed by Zhang et al....
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TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.
Abstract: : This reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamental problem is to appropriately decompose the domain R of a function g (x,y) of two variables. This problem starts by describing the physical situation which produces images: assume that a three-dimensional world is observed by an eye or camera from some point P and that g1(rho) represents the intensity of the light in this world approaching the point sub 1 from a direction rho. If one has a lens at P focusing this light on a retina or a film-in both cases a plane domain R in which we may introduce coordinates x, y then let g(x,y) be the strength of the light signal striking R at a point with coordinates (x,y); g(x,y) is essentially the same as sub 1 (rho) -possibly after a simple transformation given by the geometry of the imaging syste. The function g(x,y) defined on the plane domain R will be called an image. What sort of function is g? The light reflected off the surfaces Si of various solid objects O sub i visible from P will strike the domain R in various open subsets R sub i. When one object O1 is partially in front of another object O2 as seen from P, but some of object O2 appears as the background to the sides of O1, then the open sets R1 and R2 will have a common boundary (the 'edge' of object O1 in the image defined on R) and one usually expects the image g(x,y) to be discontinuous along this boundary. (JHD)
5,516 citations
TL;DR: A new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations, and validated by numerical results for signal and image denoising and segmentation.
Abstract: We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141–151) and T. Chan and L. Vese (2001. IEEE-IP, 10(2):266–277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies, including triple junctionss in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.
2,649 citations
"A Variational Level Set Model Combi..." refers methods in this paper
...[6] T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 266–277, 2001....
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...[10] L. A. Vese and T. F. Chan, “A multiphase level set framework for image segmentation using the Mumford and Shah model,” International Journal of Computer Vision, vol. 50, no. 3, pp. 271– 293, 2002....
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...Recently, some improved models are proposed, such as piecewise constant model [6] proposed byChan andVese (CV) and region-based active contour model [7] (RBACM) proposed by Zhang et al.....
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...Some multiphase models are proposed, such as Vese and Chan [10] proposed multiphase CV model (MCV), Gao and Yan [11] proposed multiphase local CV model (MLCV) to improve the efficiency for noisy image segmentation....
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...References [1] T. F. Chan, B. Y. Sandberg, and L. A. Vese, “Active contours without edges for vector-valued images,” Journal of Visual Communication and Image Representation, vol. 11, no. 2, pp. 130– 141, 2000....
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20 Jun 2005
TL;DR: A new variational formulation for geometric active contours that forces the level set function to be close to a signed distance function, and therefore completely eliminates the need of the costly re-initialization procedure.
Abstract: In this paper, we present a new variational formulation for geometric active contours that forces the level set function to be close to a signed distance function, and therefore completely eliminates the need of the costly re-initialization procedure. Our variational formulation consists of an internal energy term that penalizes the deviation of the level set function from a signed distance function, and an external energy term that drives the motion of the zero level set toward the desired image features, such as object boundaries. The resulting evolution of the level set function is the gradient flow that minimizes the overall energy functional. The proposed variational level set formulation has three main advantages over the traditional level set formulations. First, a significantly larger time step can be used for numerically solving the evolution partial differential equation, and therefore speeds up the curve evolution. Second, the level set function can be initialized with general functions that are more efficient to construct and easier to use in practice than the widely used signed distance function. Third, the level set evolution in our formulation can be easily implemented by simple finite difference scheme and is computationally more efficient. The proposed algorithm has been applied to both simulated and real images with promising results.
2,005 citations
"A Variational Level Set Model Combi..." refers methods in this paper
...In the traditional variational level set method for image processing, in order to maintain the stability of the level set function during the evolution, the evolving level set function needs periodical reinitialization to keep it close to a signed distance function [22]....
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TL;DR: A novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data and estimation of intensity inhomogeneities using fuzzy logic and the neighborhood effect acts as a regularizer and biases the solution toward piecewise-homogeneous labelings.
Abstract: We present a novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data and estimation of intensity inhomogeneities using fuzzy logic. MRI intensity inhomogeneities can be attributed to imperfections in the radio-frequency coils or to problems associated with the acquisition sequences. The result is a slowly varying shading artifact over the image that can produce errors with conventional intensity-based classification. Our algorithm is formulated by modifying the objective function of the standard fuzzy c-means (FCM) algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel (voxel) to be influenced by the labels in its immediate neighborhood. The neighborhood effect acts as a regularizer and biases the solution toward piecewise-homogeneous labelings. Such a regularization is useful in segmenting scans corrupted by salt and pepper noise. Experimental results on both synthetic images and MR data are given to demonstrate the effectiveness and efficiency of the proposed algorithm.
1,786 citations
"A Variational Level Set Model Combi..." refers background in this paper
...In [15], the authors proposed FCMS clustering to partition the discrete dataset {x j } n j=1 into k clusters....
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...[15] first considered the fuzzy C means with spatial constraints (FCMS), that is, incorporating the spatial information of image into the objective function, to overcome this difficulty....
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