FCM Clustering Algorithms for Segmentation of Brain MR Images

The study of brain disorders requires accurate tissue segmentation of magnetic resonance (MR) brain images which is very important for detecting tumors, edema, and necrotic tissues. Segmentation of brain images, especially into three main tissue types: Cerebrospinal Fluid (CSF), Gray Matter (GM), and White Matter (WM), has important role in computer aided neurosurgery and diagnosis. Brain images mostly contain noise, intensity inhomogeneity, and weak boundaries. Therefore, accurate segmentation of brain images is still a challenging area of research. This paper presents a review of fuzzy c-means (FCM) clustering algorithms for the segmentation of brain MR images. The review covers the detailed analysis of FCM based algorithms with intensity inhomogeneity correction and noise robustness. Different methods for the modification of standard fuzzy objective function with updating of membership and cluster centroid are also discussed

Compressed Sensing in Resource-Constrained Environments: From Sensing Mechanism Design to Recovery Algorithms

Compressed Sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. It is promising that CS can be utilized in environments where the signal acquisition process is extremely difficult or costly, e.g., a resource-constrained environment like the smartphone platform, or a band-limited environment like visual sensor network (VSNs). There are several challenges to perform sensing due to the characteristic of these platforms, including, for example, needing active user involvement, computational and storage limitations and lower transmission capabilities. This dissertation focuses on the study of CS in resource-constrained environments. First, we try to solve the problem on how to design sensing mechanisms that could better adapt to the resource-limited smartphone platform. We propose the compressed phone sensing (CPS) framework where two challenging issues are studied, the energy drainage issue due to continuous sensing which may impede the normal functionality of the smartphones and the requirement of active user inputs for data collection that may place a high burden on the user. Second, we propose a CS reconstruction algorithm to be used in VSNs for recovery of frames/images. An efficient algorithm, NonLocal Douglas-Rachford (NLDR), is developed. NLDR takes advantage of self-similarity in images using nonlocal means (NL) filtering. We further formulate the nonlocal estimation as the low-rank matrix approximation problem and solve the constrained optimization problem using Douglas-Rachford splitting method. Third, we extend the NLDR algorithm to surveillance video processing in VSNs and propose recursive Low-rank and Sparse estimation through Douglas-Rachford splitting (rLSDR) method for recovery of the video frame into a low-rank background component and sparse component that corresponds to the moving object. The spatial and temporal low-rank features of the video frame, e.g., the nonlocal similar patches within the single video frame and the low-rank background component residing in multiple frames, are successfully exploited

Noise Estimation, Noise Reduction and Intensity Inhomogeneity Correction in MRI Images of the Brain

Rician noise and intensity inhomogeneity are two common types of image degradation that manifest in the acquisition of magnetic resonance imaging (MRI) system images of the brain. Many noise reduction and intensity inhomogeneity correction algorithms are based on strong parametric assumptions. These parametric assumptions are generic and do not account for salient features that are unique to specific classes and different levels of degradation in natural images. This thesis proposes the 4-neighborhood clique system in a layer-structured Markov random field (MRF) model for noise estimation and noise reduction. When the test image is the only physical system under consideration, it is regarded as a single layer Markov random field (SLMRF) model, and as a double layer MRF model when the test images and classical priors are considered. A scientific principle states that segmentation trivializes the task of bias field correction. Another principle states that the bias field distorts the intensity but not the spatial attribute of an image. This thesis exploits these two widely acknowledged scientific principles in order to propose a new model for correction of intensity inhomogeneity. The noise estimation algorithm is invariant to the presence or absence of background features in an image and more accurate in the estimation of noise levels because it is potentially immune to the modeling errors inherent in some current state-of-the-art algorithms. The noise reduction algorithm derived from the SLMRF model does not incorporate a regularization parameter. Furthermore, it preserves edges, and its output is devoid of the blurring and ringing artifacts associated with Gaussian and wavelet based algorithms. The procedure for correction of intensity inhomogeneity does not require the computationally intensive task of estimation of the bias field map. Furthermore, there is no requirement for a digital brain atlas which will incorporate additional image processing tasks such as image registration

Sparse and low-rank techniques for the efficient restoration of images

Image reconstruction is a key problem in numerous applications of computer vision and medical imaging. By removing noise and artifacts from corrupted images, or by enhancing the quality of low-resolution images, reconstruction methods are essential to provide high-quality images for these applications. Over the years, extensive research efforts have been invested toward the development of accurate and efficient approaches for this problem. Recently, considerable improvements have been achieved by exploiting the principles of sparse representation and nonlocal self-similarity. However, techniques based on these principles often suffer from important limitations that impede their use in high-quality and large-scale applications. Thus, sparse representation approaches consider local patches during reconstruction, but ignore the global structure of the image. Likewise, because they average over groups of similar patches, nonlocal self-similarity methods tend to over-smooth images. Such methods can also be computationally expensive, requiring a hour or more to reconstruct a single image. Furthermore, existing reconstruction approaches consider either local patch-based regularization or global structure regularization, due to the complexity of combining both regularization strategies in a single model. Yet, such combined model could improve upon existing techniques by removing noise or reconstruction artifacts, while preserving both local details and global structure in the image. Similarly, current approaches rarely consider external information during the reconstruction process. When the structure to reconstruct is known, external information like statistical atlases or geometrical priors could also improve performance by guiding the reconstruction. This thesis addresses limitations of the prior art through three distinct contributions. The first contribution investigates the histogram of image gradients as a powerful prior for image reconstruction. Due to the trade-off between noise removal and smoothing, image reconstruction techniques based on global or local regularization often over-smooth the image, leading to the loss of edges and textures. To alleviate this problem, we propose a novel prior for preserving the distribution of image gradients modeled as a histogram. This prior is combined with low-rank patch regularization in a single efficient model, which is then shown to improve reconstruction accuracy for the problems of denoising and deblurring. The second contribution explores the joint modeling of local and global structure regularization for image restoration. Toward this goal, groups of similar patches are reconstructed simultaneously using an adaptive regularization technique based on the weighted nuclear norm. An innovative strategy, which decomposes the image into a smooth component and a sparse residual, is proposed to preserve global image structure. This strategy is shown to better exploit the property of structure sparsity than standard techniques like total variation. The proposed model is evaluated on the problems of completion and super-resolution, outperforming state-of-the-art approaches for these tasks. Lastly, the third contribution of this thesis proposes an atlas-based prior for the efficient reconstruction of MR data. Although popular, image priors based on total variation and nonlocal patch similarity often over-smooth edges and textures in the image due to the uniform regularization of gradients. Unlike natural images, the spatial characteristics of medical images are often restricted by the target anatomical structure and imaging modality. Based on this principle, we propose a novel MRI reconstruction method that leverages external information in the form of an probabilistic atlas. This atlas controls the level of gradient regularization at each image location, via a weighted total-variation prior. The proposed method also exploits the redundancy of nonlocal similar patches through a sparse representation model. Experiments on a large scale dataset of T1-weighted images show this method to be highly competitive with the state-of-the-art

Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling

In this thesis, we focus on the image labeling problem which is the task of performing unique pixel-wise label decisions to simplify the image while reducing its redundant information. We build upon a recently introduced geometric approach for data labeling by assignment flows [ APSS17 ] that comprises a smooth dynamical system for data processing on weighted graphs. Hereby we pursue two lines of research that give new application and theoretically-oriented insights on the underlying segmentation task. We demonstrate using the example of Optical Coherence Tomography (OCT), which is the mostly used non-invasive acquisition method of large volumetric scans of human retinal tis- sues, how incorporation of constraints on the geometry of statistical manifold results in a novel purely data driven geometric approach for order-constrained segmentation of volumetric data in any metric space. In particular, making diagnostic analysis for human eye diseases requires decisive information in form of exact measurement of retinal layer thicknesses that has be done for each patient separately resulting in an demanding and time consuming task. To ease the clinical diagnosis we will introduce a fully automated segmentation algorithm that comes up with a high segmentation accuracy and a high level of built-in-parallelism. As opposed to many established retinal layer segmentation methods, we use only local information as input without incorporation of additional global shape priors. Instead, we achieve physiological order of reti- nal cell layers and membranes including a new formulation of ordered pair of distributions in an smoothed energy term. This systematically avoids bias pertaining to global shape and is hence suited for the detection of anatomical changes of retinal tissue structure. To access the perfor- mance of our approach we compare two different choices of features on a data set of manually annotated 3 D OCT volumes of healthy human retina and evaluate our method against state of the art in automatic retinal layer segmentation as well as to manually annotated ground truth data using different metrics. We generalize the recent work [ SS21 ] on a variational perspective on assignment flows and introduce a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in J. Math. Imaging & Vision 58(2), 2017. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with re- spect to a nonconvex potential. We devise an entropy-regularized difference-of-convex-functions (DC) decomposition of this potential and show that the basic geometric Euler scheme for inte- grating the assignment flow is equivalent to solving the G-PDE by an established DC program- ming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments