Jose L. Marroquin

An accurate and efficient Bayesian method for automatic segmentation of brain MRI

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.

Hidden Markov measure field models for image segmentation

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.

DEMODULATION OF A SINGLE INTERFEROGRAM BY USE OF A TWO-DIMENSIONAL REGULARIZED PHASE-TRACKING TECHNIQUE

We present a two-dimensional regularized phase-tracking technique that is capable of demodulating a single fringe pattern with either open or closed fringes. The proposed regularized phase-tracking system gives the detected phase continuously so that no further unwrapping is needed over the detected phase.

Quadratic regularization functionals for phase unwrapping

The problem of unwrapping a noisy principal-value phase field or, equivalently, reconstructing an unwrapped phase field from noisy and possibly incomplete phase differences may be considered ill-posed in the sense of Hadamard. We apply the Thikonov regularization theory to find solutions that correspond to minimizers of positive-definite quadratic cost functionals. These methods may be considered generalizations of the classical least-squares solution to the unwrapping problem; the introduction of the regularization term permits the reduction of noise (even if this noise does not generate integration-path inconsistencies) and the interpolation of the solution over regions with missing data in a stable and controlled way, with a minimum increase of computational complexity. Algorithms for finding direct solutions with transform methods and implementations of iterative procedures are discussed as well. Experimental results on synthetic test images are presented to illustrate the performance of these methods.

Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms

An algorithm for phase demodulation of a single interferogram that may contain closed fringes is presented. This algorithm uses the regularized phase-tracker system as a robust phase estimator, together with a new scanning technique that estimates the phase that initially follows the bright zones of the interferogram. The combination of these two elements constitutes a powerful new method, the fringe-follower regularized phase tracker, that makes it possible to correctly demodulate complex, single-image interferograms for which traditional methods fail.

Fixed Queries Array: A Fast and Economical Data Structure for Proximity Searching

Pivot-based algorithms are effective tools for proximity searching in metric spaces. They allow trading space overhead for number of distance evaluations performed at query time. With additional search structures (that pose extra space overhead) they can also reduce the amount of side computations. We introduce a new data structure, the Fixed Queries Array (FQA), whose novelties are (1) it permits sublinear extra CPU time without any extra data structure; (2) it permits trading number of pivots for their precision so as to make better use of the available memory. We show experimentally that the FQA is an efficient tool to search in metric spaces and that it compares favorably against other state of the art approaches. Its simplicity converts it into a simple yet effective tool for practitioners seeking for a black-box method to plug in their applications.

PHASE UNWRAPPING THROUGH DEMODULATION BY USE OF THE REGULARIZED PHASE-TRACKING TECHNIQUE

Most interferogram demodulation techniques give the detected phase wrapped owing to the arctangent function involved in the final step of the demodulation process. To obtain a continuous detected phase, an unwrapping process must be performed. Here we propose a phase-unwrapping technique based on a regularized phase-tracking (RPT) system. Phase unwrapping is achieved in two steps. First, we obtain two phase-shifted fringe patterns from the demodulated wrapped phase (the sine and the cosine), then demodulate them by using the RPT technique. In the RPT technique the unwrapping process is achieved simultaneously with the demodulation process so that the final goal of unwrapping is therefore achieved. The RPT method for unwrapping the phase is compared with the technique of least-squares integration of wrapped phase differences to outline the substantial noise robustness of the RPT technique.

Local frequency representations for robust multimodal image registration

Automatic registration of multimodal images involves algorithmically estimating the coordinate transformation required to align the data sets. Most existing methods in the literature are unable to cope with registration of image pairs with large nonoverlapping field of view (FOV). We propose a robust algorithm, based on matching dominant local frequency image representations, which can cope with image pairs with large nonoverlapping FOV The local frequency representation naturally allows for processing the data at different scales/resolutions, a very desirable property from a computational efficiency view point. Our algorithm involves minimizing-over all rigid/affine transformations-the integral of the squared error (ISE or L/sub 2/E) between a Gaussian model of the residual and its true density function. The residual here refers to the difference between the local frequency representations of the transformed (by an unknown transformation) source and target data. We present implementation results for image data sets, which are misaligned magnetic resonance (MR) brain scans obtained using different image acquisition protocols as well as misaligned MR-computed tomography scans. We experimently show that our L/sub 2/E-based scheme yields better accuracy over the normalized mutual information.

General n-dimensional quadrature transform and its application to interferogram demodulation

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

WAVE-FRONT RECOVERY FROM TWO ORTHOGONAL SHEARED INTERFEROGRAMS

We present a new technique for using the information of two orthogonal lateral-shear interferograms to estimate an aspheric wave front. The wave-front estimation from sheared inteferometric data may be considered an ill-posed problem in the sense of Hadamard. We apply Thikonov regularization theory to estimate the wave front that has produced the lateral sheared interferograms as the minimizer of a positive definite-quadratic cost functional. The introduction of the regularization term permits one to find a well-defined and stable solution to the inverse shearing problem over the wave-front aperture as well as to reduce wave-front noise as desired.