We propose a constrained version of Mumford and Shah's (1989) segmentation model with an information-theoretic point of view in order to devise a systematic procedure to segment brain magnetic resonance imaging (MRI) data for parametric T1-Map and T1-weighted images, in both 2-D and 3D settings. Incorporation of a tuning weight in particular adds a probabilistic flavor to our segmentation method, and makes the 3-tissue segmentation possible. Moreover, we proposed a novel method to jointly segment the T1-Map and calibrate RF Inhomogeneity (JSRIC). This method assumes the average T1 value of white matter is the same across transverse slices in the central brain region, and JSRIC is able to rectify the flip angles to generate calibrated T1-Maps. In order to generate an accurate T1-Map, the determination of optimal flip-angles and the registration of flip-angle images are examined. Our JSRIC method is validated on two human subjects in the 2D T1-Map modality and our segmentation method is validated by two public databases, BrainWeb and IBSR, of T1-weighted modality in the 3D setting.

In this paper we propose to jointly segment and register objects of interest in layered images. Layered imaging refers to imageries taken from different perspectives and possibly by different sensors. Registration and segmentation are therefore the two main tasks which contribute to the bottom level, data alignment, of the multisensor data fusion hierarchical structures. Most exploitations of two layered images assumed that scanners are at very high altitudes and that only one transformation ties the two images. Our data are however taken at mid-range and therefore requires segmentation to assist us examining different object regions in a divide-and-conquer fashion. Our approach is a combination of multiphase active contour method with a joint segmentation-registration technique (which we called MPJSR) carried out in a local moving window prior to a global optimization. To further address layered video sequences and tracking objects in frames, we propose a simple adaptation of optical flow calculations along the active contours in a pair of layered image sequences. The experimental results show that the whole integrated algorithm is able to delineate the objects of interest, align them for a pair of layered frames and keep track of the objects over time.

Let S(G σ ) be the skew-adjacency matrix of an oriented graph G σ with n vertices, and let λ 1 , λ 2 , . . . , λ n be all eigenvalues of S(G σ ). The skew-spectral radius ρ s (G σ ) of G σ is defined as max{|λ 1 |, |λ 2 |, . . . , |λ n |}. A connected graph, in which the number of edges equals the number of vertices, is called a unicyclic graph. In this paper, the structure of oriented unicyclic graphs whose skew-spectral radius does not exceed 2 is investigated. We order all the oriented unicyclic graphs with n vertices whose skew-spectral radius is bounded by 2. MSC: 05C50; 15A18

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In this paper we propose a constrained version of segmentation with an information-theoretic point of view [2] in order to devise a systematic procedure to segment brain MRI data for two modalities of parametric T 1 -Map and T 1 -weighted images in both 2-D and 3-D settings. The incorporation of a tuning weight in particular adds a probabilistic ƀavor to our segmentation method, and makes the three-tissue segmentation possible. Our method uses region based active contours which have proven to be robust. The method is validated by two real objects which were used to generate T 1 -Maps and also by two simulated brains of T 1 -weighted data from the BrainWeb[3] public database.