A spatially variant finite mixture model is proposed for pixel labeling and image segmentation. For the case of spatially varying mixtures of Gaussian density functions with unknown means and variances, an expectation-maximization (EM) algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities, An a priori density function is formulated for the spatially variant mixture weights. A generalized EM algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived. This algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent. Gaussian densities have been used for simplicity, but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities. The accuracy of the algorithm is quantitatively evaluated through Monte Carlo simulation, and its performance is qualitatively assessed via experimental images from computerized tomography (CT) and magnetic resonance imaging (MRI).

Practical applications of estimating an objects motion from an image sequence must address the occlusion of feature points. A sequential algorithm for estimating an object's motion and structure based upon minimizing a conditional least squares criterion is formulated. In comparison to a batch least squares solution based upon twenty image frames, this structure achieved a 98.7 fold reduction in computation time at the cost of an overall 3% increase in estimation error.

A computationally efficient, easily implementable algorithm for MAP restoration of images degraded by blur and additive correlated Gaussian noise using Gibbs prior density functions is derived. This algorithm is valid for a variety of complete data spaces. The constraints upon the complete data space arising from the Gaussian image formation model are analyzed and a motivation is provided for the choice of the complete data, based upon the ease of computation of the resulting EM algorithms. The overlooked role of the null space of the blur operator in image restoration is introduced. An examination of this role reveals an important drawback to the use of the simulated annealing algorithm in maximizing a specific class of functionals. An alternative iterative method for computing the nullspace component of a vector is given. The ability of a simple Gibbs prior density function to enable partial recovery of the component of an image within the nullspace of the blur operator is demonstrated.

The class of noninverse problems versus inverse problems is discussed. A general optimization approach to solving certain constrained noninverse problems is presented. This approach is applied in the area of single photon emission computed tomography to estimate the patient outer contour directly from the photo-peak projection data. The resulting algorithm is fully automated, fast, and the determined 3-D patient contour satisfies smoothness constraints. The accuracy and reliability of the algorithm is evaluated through Monte Carlo simulations, patient studies, and an experimental validation study.

Gibbs distributions are widely used as a priori density functions for Bayesian image restoration. When a Gibbs distribution prior is formulated to incorporate a line or edge process, Bayesian image restoration additionally yields the edges in the image. We interpret these a priori and density function as themselves being edge detectors. We formulate a density function that is more effective in this regard. This work explores the use of higher order Markov random fields that hold rich potential for varied applications.>

In single photon emission computed tomography (SPECT), every reconstruction algorithm must use some model for the response of the gamma camera to emitted gamma-rays. The true camera response is both spatially variant and object dependent. These two properties result from the effects of scatter, septal penetration, and attenuation, and they forestall determination of the true response with any precision. This motivates the investigation of the performance of reconstruction algorithms when there are errors between the camera response used in the reconstruction algorithm and the true response of the gamma camera. In this regard, the authors compare the filtered backprojection algorithm, the expectation-maximization maximum likelihood algorithm, and the generalized expectation maximization (GEM) maximum a posteriori (MAP) algorithm, a Bayesian algorithm which uses a Markov random field prior.

A widely used approach to restoration of images degraded by Poisson noise has been to represent the degraded image as a linear transformation of the intact image plus zero-mean, uncorrelated additive noise. The explicit Poisson model is retained and the authors formulate maximum a posteriori (MAP) image restoration using homogeneous, isotropic Markov random field priors. For this purpose, a deterministic algorithm based upon the expectation maximization (EM) method of optimization is derived. The performance of candidate priors is compared.>