Parametric image segmentation consists of finding a label field that defines a partition of an image into a set of nonoverlapping regions and the parameters of the models that describe the variation of some property within each region. A new Bayesian formulation for the solution of this problem is presented, based on the key idea of using a doubly stochastic prior model for the label field, which allows one to find exact optimal estimators for both this field and the model parameters by the minimization of a differentiable function. An efficient minimization algorithm and comparisons with existing methods on synthetic images are presented, as well as examples of realistic applications to the segmentation of Magnetic Resonance volumes and to motion segmentation.
Automatic 3D segmentation of the brain from MR scans is a challenging problem that has received enormous amount of attention lately. Of the techniques reported in literature, very few are fully automatic. In this paper, we present an efficient and accurate, fully automatic 3D segmentation procedure for brain MR scans. It has several salient features namely, (1) instead of a single multiplicative bias field that affects all tissue intensities, separate parametric smooth models are used for the intensity of each class. This may be a more realistic model and avoids the need for a logarithmic transformation. (2) A brain atlas is used in conjunction with a robust registration procedure to find a nonrigid transformation that maps the standard brain to the specimen to be segmented. This transformation is then used to: segment the brain from non-brain tissue; compute prior probabilities for each class at each voxel location and find an appropriate automatic initialization. (3) Finally, a novel algorithm is presented which is a variant of the EM procedure, that incorporates a fast and accurate way to find optimal segmentations, given the intensity models along with the spatial coherence assumption. Experimental results with both synthetic and real data are included, as well as comparisons of the performance of our algorithm with that of other published methods.
Automatic three-dimensional (3-D) segmentation of the brain from magnetic resonance (MR) scans is a challenging problem that has received an enormous amount of attention lately. Of the techniques reported in the literature, very few are fully automatic. In this paper, we present an efficient and accurate, fully automatic 3-D segmentation procedure for brain MR scans. It has several salient features; namely, the following. 1) Instead of a single multiplicative bias field that affects all tissue intensities, separate parametric smooth models are used for the intensity of each class. 2) A brain atlas is used in conjunction with a robust registration procedure to find a nonrigid transformation that maps the standard brain to the specimen to be segmented. This transformation is then used to: segment the brain from nonbrain tissue; compute prior probabilities for each class at each voxel location and find an appropriate automatic initialization. 3) Finally, a novel algorithm is presented which is a variant of the expectation-maximization procedure, that incorporates a fast and accurate way to find optimal segmentations, given the intensity models along with the spatial coherence assumption. Experimental results with both synthetic and real data are included, as well as comparisons of the performance of our algorithm with that of other published methods.
This paper shows a generalization of the classic isotropic plasticity
theory to be applied to orthotropic or anisotropic materials. This approach
assumes the existence of a real anisotropic space, and other fictitious
isotropic space where a mapped fictitious problem is solved. Both spaces are
related by means of a linear transformation using a fourth order
transformation tensor that contains all the information concerning the real
anisotropic material. The paper describes the basis of the spaces
transformation proposed and the expressions of the resulting secant and
tangent constitutive equations. Also details of the numerical integration of
the constitutive equation are provided. Examples of application showing the
good performance of the model for analysis of orthotropic materials and
fibre‐reinforced composites are given.
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