Zexuan Ji

A modified possibilistic fuzzy c-means clustering algorithm for bias field estimation and segmentation of brain MR image

A modified possibilistic fuzzy c-means clustering algorithm is presented for fuzzy segmentation of magnetic resonance (MR) images that have been corrupted by intensity inhomogeneities and noise. By introducing a novel adaptive method to compute the weights of local spatial in the objective function, the new adaptive fuzzy clustering algorithm is capable of utilizing local contextual information to impose local spatial continuity, thus allowing the suppression of noise and helping to resolve classification ambiguity. To estimate the intensity inhomogeneity, the global intensity is introduced into the coherent local intensity clustering algorithm and takes the local and global intensity information into account. The segmentation target therefore is driven by two forces to smooth the derived optimal bias field and improve the accuracy of the segmentation task. The proposed method has been successfully applied to 3 T, 7 T, synthetic and real MR images with desirable results. Comparisons with other approaches demonstrate the superior performance of the proposed algorithm. Moreover, the proposed algorithm is robust to initialization, thereby allowing fully automatic applications.

Fuzzy Local Gaussian Mixture Model for Brain MR Image Segmentation

Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited accuracy. In this paper, we assume that the local image data within each voxels neighborhood satisfy the Gaussian mixture model (GMM), and thus propose the fuzzy local GMM (FLGMM) algorithm for automated brain MR image segmentation. This algorithm estimates the segmentation result that maximizes the posterior probability by minimizing an objective energy function, in which a truncated Gaussian kernel function is used to impose the spatial constraint and fuzzy memberships are employed to balance the contribution of each GMM. We compared our algorithm to state-of-the-art segmentation approaches in both synthetic and clinical data. Our results show that the proposed algorithm can largely overcome the difficulties raised by noise, low contrast, and bias field, and substantially improve the accuracy of brain MR image segmentation.

Fuzzy c-means clustering with weighted image patch for image segmentation

Fuzzy c-means (FCM) clustering has been widely used in image segmentation. However, in spite of its computational efficiency and wide-spread prevalence, the FCM algorithm does not take the spatial information of pixels into consideration, and hence may result in low robustness to noise and less accurate segmentation. In this paper, we propose the weighted image patch-based FCM (WIPFCM) algorithm for image segmentation. In this algorithm, we use image patches to replace pixels in the fuzzy clustering, and construct a weighting scheme to able the pixels in each image patch to have anisotropic weights. Thus, the proposed algorithm incorporates local spatial information embedded in the image into the segmentation process, and hence improve its robustness to noise. We compared the novel algorithm to several state-of-the-art segmentation approaches in synthetic images and clinical brain MR studies. Our results show that the proposed WIPFCM algorithm can effectively overcome the impact of noise and substantially improve the accuracy of image segmentations.

A moment-based nonlocal-means algorithm for image denoising

Image denoising is a crucial step to increase image quality and to improve the performance of all the tasks needed for quantitative imaging analysis. The nonlocal (NL) means filter is a very successful technique for denoising textured images. However, this algorithm is only defined up to translation without considering the orientation and scale for each image patch. In this paper, we introduce the Zernike moments into NL-means filter, which are the magnitudes of a set of orthogonal complex moments of the image. The Zernike moments in small local windows of each pixel in the image are computed to obtain the local structure information for each patch, and then the similarities according to this information are computed instead of pixel intensity. For the rotation invariant of the Zernike moments, we can get much more pixels or patches with higher similarity measure and make the similarity of patches translation-invariant and rotation-invariant. The proposed algorithm is demonstrated on real images corrupted by white Gaussian noise (WGN). The comparative experimental results show that the improved NL-means filter achieves better denoising performance.

Robust spatially constrained fuzzy c-means algorithm for brain MR image segmentation

Abstract Objective Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis, and hence has attracted extensive research attention. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited robustness to outliers, over-smoothness for segmentations and limited segmentation accuracy for image details. To further improve the accuracy for brain MR image segmentation, a robust spatially constrained fuzzy c-means (RSCFCM) algorithm is proposed in this paper. Method Firstly, a novel spatial factor is proposed to overcome the impact of noise in the images. By incorporating the spatial information amongst neighborhood pixels, the proposed spatial factor is constructed based on the posterior probabilities and prior probabilities, and takes the spatial direction into account. It plays a role as linear filters for smoothing and restoring images corrupted by noise. Therefore, the proposed spatial factor is fast and easy to implement, and can preserve more details. Secondly, the negative log-posterior is utilized as dissimilarity function by taking the prior probabilities into account, which can further improve the ability to identify the class for each pixel. Finally, to overcome the impact of intensity inhomogeneity, we approximate the bias field at the pixel-by-pixel level by using a linear combination of orthogonal polynomials. The fuzzy objective function is then integrated with the bias field estimation model to overcome the intensity inhomogeneity in the image and segment the brain MR images simultaneously. Results To demonstrate the performances of the proposed algorithm for the images with/without skull stripping, the first group of experiments is carried out in clinical 3T-weighted brain MR images which contain quite serious intensity inhomogeneity and noise. Then we quantitatively compare our algorithm to state-of-the-art segmentation approaches by using Jaccard similarity on benchmark images obtained from IBSR and BrainWeb with different level of noise and intensity inhomogeneity. The comparison results demonstrate that the proposed algorithm can produce higher accuracy segmentation and has stronger ability of denoising, especially in the area with abundant textures and details. Conclusion In this paper, the RSCFCM algorithm is proposed by utilizing the negative log-posterior as the dissimilarity function, introducing a novel factor and integrating the bias field estimation model into the fuzzy objective function. This algorithm successfully overcomes the drawbacks of existing FCM-type clustering schemes and EM-type mixture models. Our statistical results (mean and standard deviation of Jaccard similarity for each tissue) on both synthetic and clinical images show that the proposed algorithm can overcome the difficulties caused by noise and bias fields, and is capable of improving over 5% segmentation accuracy comparing with several state-of-the-art algorithms.

RETRACTED: A framework with modified fast FCM for brain MR images segmentation

Intensity inhomogeneity, noise and partial volume (PV) effect render a challenging task for segmentation of brain magnetic resonance (MR) images. Most of the current MR image segmentation methods focus on only one or two of the effects listed above. In this paper, a framework with modified fast fuzzy c-means for brain MR images segmentation is proposed to take all these effects into account simultaneously and improve the accuracy of image segmentations. Firstly, we propose a new automated method to determine the initial values of the centroids. Secondly, an adaptive method to incorporate the local spatial continuity is proposed to overcome the noise effectively and prevent the edge from blurring. The intensity inhomogeneity is estimated by a linear combination of a set of basis functions. Meanwhile, a regularization term is added to reduce the iteration steps and accelerate the algorithm. The weights of the regularization terms are all automatically computed to avoid the manually tuned parameter. Synthetic and real MR images are used to test the proposed framework. Improved performance of the proposed algorithm is observed where the intensity inhomogeneity, noise and PV effect are commonly encountered. The experimental results show that the proposed method has stronger anti-noise property and higher segmentation precision than other reported FCM-based techniques.

Generalized rough fuzzy c-means algorithm for brain MR image segmentation

Fuzzy sets and rough sets have been widely used in many clustering algorithms for medical image segmentation, and have recently been combined together to better deal with the uncertainty implied in observed image data. Despite of their wide spread applications, traditional hybrid approaches are sensitive to the empirical weighting parameters and random initialization, and hence may produce less accurate results. In this paper, a novel hybrid clustering approach, namely the generalized rough fuzzy c-means (GRFCM) algorithm is proposed for brain MR image segmentation. In this algorithm, each cluster is characterized by three automatically determined rough-fuzzy regions, and accordingly the membership of each pixel is estimated with respect to the region it locates. The importance of each region is balanced by a weighting parameter, and the bias field in MR images is modeled by a linear combination of orthogonal polynomials. The weighting parameter estimation and bias field correction have been incorporated into the iterative clustering process. Our algorithm has been compared to the existing rough c-means and hybrid clustering algorithms in both synthetic and clinical brain MR images. Experimental results demonstrate that the proposed algorithm is more robust to the initialization, noise, and bias field, and can produce more accurate and reliable segmentations.

Interval-valued possibilistic fuzzy C-means clustering algorithm

Type-2 fuzzy sets have drawn increasing research attentions in the pattern recognition community, since it is capable of modeling various uncertainties that cannot be appropriately managed by usual fuzzy sets. Although it has been introduced to data clustering, most widely used clustering approaches based on type-2 fuzzy sets still suffer from inherent drawbacks, such as the sensitiveness to outliers and initializations. In this paper, we incorporate the interval-valued fuzzy sets into the hybrid fuzzy clustering scheme, and thus propose the interval-valued possibilistic fuzzy c-means (IPFCM) clustering algorithm. We use both fuzzy memberships and possibilistic typicalities to model the uncertainty implied in the data sets, and develop solutions to overcome the difficulties caused by type-2 fuzzy sets, such as the construction of footprint of uncertainty, type-reduction and defuzzification. We compare the proposed algorithm with five fuzzy clustering approaches, including the FCM, PCM, PFCM, IFCM and IPCM, on two-dimensional Gaussian data sets and four multi-dimensional benchmark data sets. We also apply these clustering techniques to segment the brain magnetic resonance images and natural images. Our results show that the proposed IPFCM algorithm is more robust to outliers and initializations and can produce more accurate clustering results.

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.

Adaptive scale fuzzy local Gaussian mixture model for brain MR image segmentation

The Gaussian mixture model (GMM) has been widely used in brain magnetic resonance (MR) image segmentation. However, due to the MR bias field effect, the implied stochastic assumption that the intensities of each tissue type are sampled from an identical distribution may not be valid. In this paper, we propose a novel adaptive scale fuzzy local GMM (AS-FLGMM) algorithm for accurate and robust brain MR image segmentation. We assume that the local image data within the neighborhood of each pixel follow the GMM, in which the difference of variance among Gaussian components can be ignored. Based on this assumption, we develop a local scale estimation method to adaptively calculate the variance in each distribution. The segmentation is then performed under the fuzzy clustering framework and the objective is defined as the integration of the weighted GMM energy of each pixel. The AS-FLGMM algorithm has been compared to five state-of-the-art segmentation approaches in both synthetic and clinical MR images. Our results show that the proposed algorithm can produce more accurate segmentation results and its performance is more robust to initialization.