In this paper, 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.

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A wide range of computer vision applications require an accurate solution of a particular Hamilton- Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of the point, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.

We propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region-of-interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels. We follow the most conventional approaches in that initial images and desired maps of regions are described by a joint Markov-Gibbs random field (MGRF) model of independent image signals and interdependent region labels. However, our focus is on more accurate model identification. To better specify region borders, each empirical distribution of image signals is precisely approximated by a linear combination of Gaussians (LCG) with positive and negative components. We modify an expectation-maximization (EM) algorithm to deal with the LCGs and also propose a novel EM-based sequential technique to get a close initial LCG approximation with which the modified EM algorithm should start. The proposed technique identifies individual LCG models in a mixed empirical distribution, including the number of positive and negative Gaussians. Initial segmentation based on the LCG models is then iteratively refined by using the MGRF with analytically estimated potentials. The convergence of the overall segmentation algorithm at each stage is discussed. Experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms.

Most of the shape from shading (SFS)