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Segmentation of Touching Cell Nuclei Using a Two-Stage Graph Cut Model

Methods based on combinatorial graph cut algorithms received a lot of attention in the recent years for their robustness as well as reasonable computational demands. These methods are built upon an underlying Maximum a Posteriori estimation of Markov Random Fields and are suitable to solve accurately many different problems in image analysis, including image segmentation. In this paper we present a two-stage graph cut based model for segmentation of touching cell nuclei in fluorescence microscopy images. In the first stage voxels with very high probability of being foreground or background are found and separated by a boundary with a minimal geodesic length. In the second stage the obtained clusters are split into isolated cells by combining image gradient information and incorporated a priori knowledge about the shape of the nuclei. Moreover, these two qualities can be easily balanced using a single user parameter. Preliminary tests on real data show promising results of the method.

Heterogeneity in the kinetics of nuclear proteins and trajectories of substructures associated with heterochromatin.

BackgroundProtein exchange kinetics correlate with the level of chromatin condensation and, in many cases, with the level of transcription. We used fluorescence recovery after photobleaching (FRAP) to analyse the kinetics of 18 proteins and determine the relationships between nuclear arrangement, protein molecular weight, global transcription level, and recovery kinetics. In particular, we studied heterochromatin-specific heterochromatin protein 1β (HP1β) B lymphoma Mo-MLV insertion region 1 (BMI1), and telomeric-repeat binding factor 1 (TRF1) proteins, and nucleolus-related proteins, upstream binding factor (UBF) and RNA polymerase I large subunit (RPA194). We considered whether the trajectories and kinetics of particular proteins change in response to histone hyperacetylation by histone deacetylase (HDAC) inhibitors or after suppression of transcription by actinomycin D.ResultsWe show that protein dynamics are influenced by many factors and events, including nuclear pattern and transcription activity. A slower recovery after photobleaching was found when proteins, such as HP1β, BMI1, TRF1, and others accumulated at specific foci. In identical cells, proteins that were evenly dispersed throughout the nucleoplasm recovered more rapidly. Distinct trajectories for HP1β, BMI1, and TRF1 were observed after hyperacetylation or suppression of transcription. The relationship between protein trajectory and transcription level was confirmed for telomeric protein TRF1, but not for HP1β or BMI1 proteins. Moreover, heterogeneity of foci movement was especially observed when we made distinctions between centrally and peripherally positioned foci.ConclusionBased on our results, we propose that protein kinetics are likely influenced by several factors, including chromatin condensation, differentiation, local protein density, protein binding efficiency, and nuclear pattern. These factors and events likely cooperate to dictate the mobility of particular proteins.

A Two-Phase Segmentation of Cell Nuclei Using Fast Level Set-Like Algorithms

An accurate localization of a cell nucleus boundary is inevitable for any further quantitative analysis of various subnuclear structures within the cell nucleus. In this paper, we present a novel approach to the cell nucleus segmentation in fluorescence microscope images exploiting the level set framework. The proposed method works in two phases. In the first phase, the image foreground is separated from the background using a fast level set-like algorithm by Nilsson and Heyden [1]. A binary mask of isolated cell nuclei as well as their clusters is obtained as a result of the first phase. A fast topology-preserving level set-like algorithm by Maska and Matula [2] is applied in the second phase to delineate individual cell nuclei within the clusters. The potential of the new method is demonstrated on images of DAPI-stained nuclei of a lung cancer cell line A549 and promyelocytic leukemia cell line HL60.

A fast level set-like algorithm for region-based active contours

Implicit active contours are widely employed in image processing and related areas. Their implementation using the level set framework brings several advantages over parametric snakes. In particular, a parameterization independence, topological flexibility, and straightforward extension into higher dimensions have led to their popularity. On the other hand, a numerical solution of associated partial differential equations (PDEs) is very time-consuming, especially for large 3D images. In this paper, we modify a fast level set-like algorithm by Nilsson and Heyden [14] intended for tracking gradient-based active contours in order to obtain a fast algorithm for tracking region-based active contours driven by the Chan-Vese model. The potential of the proposed algorithm and its comparison with two other fast methods minimizing the Chan-Vese model are demonstrated on both synthetic and real image data.

A Simple Topology Preserving Max-Flow Algorithm for Graph Cut Based Image Segmentation

In this paper, we propose a modification to the Boykov-Kolmogorov maximum flow algorithm in order to make the algorithm preserve the topology of an initial interface. This algorithm is being widely used in computer vision and image processing fields for its efficiency and speed when dealing with problems such as graph cut based image segmentation. Using our modification we are able to incorporate a topology prior into the algorithm allowing us to apply it in situations in which the inherent topological flexibility of graph cuts is inconvenient (e.g., biomedical image segmentation). Our approach exploits the simple point concept from digital geometry and is simpler and more straightforward to implement than previously introduced methods. Due to the NP-completeness of the topology preserving problem our algorithm is only an approximation and is initialization dependent. However, promising results are demonstrated on graph cut based segmentation of both synthetic and real image data.

An improved riemannian metric approximation for graph cuts

Boykov and Kolmogorov showed that it is possible to find globally minimal contours and surfaces via graph cuts by embedding an appropriate metric approximation into the graph edge weights and derived the requisite formulas for Euclidean and Riemannian metrics [3]. In [9] we have proposed an improved Euclidean metric approximation that is invariant under (horizontal and vertical) mirroring, applicable to grids with anisotropic resolution and with a smaller approximation error. In this paper, we extend our method to general Riemannian metrics that are essential for graph cut based image segmentation or stereo matching. It is achieved by the introduction of a transformation reducing the Riemannian case to the Euclidean one and adjusting the formulas from [9] to be able to cope with non-orthogonal grids. We demonstrate that the proposed method yields smaller approximation errors than the previous approaches both in theory and practice.

On Euclidean Metric Approximation via Graph Cuts

The graph cut framework presents a popular energy minimization tool. In order to be able to minimize contour length dependent energy terms an appropriate metric approximation has to be embedded into the graph such that the cost of every cut approximates the length of a corresponding contour under a given metric. Formulas giving a good approximation have been introduced by Boykov and Kolmogorov for both Euclidean and Riemannian metrics. In this paper, we improve their method and obtain a better approximation in case of the Euclidean metric. In our approach, we combine the well-known Cauchy-Crofton formulas with Voronoi diagrams theory to devise a general method with straightforward extension from 2D to 3D space. Our edge weight formulas are invariant to mirroring and directly applicable to grids with anisotropic node spacing. Finally, we show that our approach yields smaller metrication errors in both the isotropic and anisotropic case and demonstrate an application of the derived formulas to biomedical image segmentation.