H. Elliott

Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields

This paper presents a new approach to the use of Gibbs distributions (GD) for modeling and segmentation of noisy and textured images. Specifically, the paper presents random field models for noisy and textured image data based upon a hierarchy of GD. It then presents dynamic programming based segmentation algorithms for noisy and textured images, considering a statistical maximum a posteriori (MAP) criterion. Due to computational concerns, however, sub-optimal versions of the algorithms are devised through simplifying approximations in the model. Since model parameters are needed for the segmentation algorithms, a new parameter estimation technique is developed for estimating the parameters in a GD. Finally, a number of examples are presented which show the usefulness of the Gibbsian model and the effectiveness of the segmentation algorithms and the parameter estimation procedures.

Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields

A new image segmentation algorithm is presented, based on recursive Bayes smoothing of images modeled by Markov random fields and corrupted by independent additive noise. The Bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel, given the total noisy image, in a recursive way. The a posteriori distribution together with a criterion of optimality then determine a Bayes estimate of the scene. The algorithm presented is an extension of a 1-D Bayes smoothing algorithm to 2-D and it gives the optimum Bayes estimate for the scene value at each pixel. Computational concerns in 2-D, however, necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm. In particular, the scene (noiseless image) is modeled as a Markov mesh random field, a special class of Markov random fields, and the Bayes smoothing algorithm is applied on overlapping strips (horizontal/vertical) of the image consisting of several rows (columns). It is assumed that the signal (scene values) vector sequence along the strip is a vector Markov chain. Since signal correlation in one of the dimensions is not fully used along the edges of the strip, estimates are generated only along the middle sections of the strips. The overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image. The Bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel (discrete) or continuous random variables.

Global stability of adaptive pole placement algorithms

This paper presents direct and indirect adaptive control schemes for assigning the closed-loop poles of a single-input, single-output system in both the continuous- and discrete-time cases. The resulting closed-loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids. In particular, persistent excitation of the potentially unbounded closed-loop input-output data, and hence convergence of a sequential least-squares identification algorithm is proved. The results are applicable to standard sequential least squares, and least squares with covariance reset.

Paper: Parameterization issues in multivariable adaptive control

This paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems. All algorithms are presented using a unified pole placement approach. Furthermore the emphasis is on parameterization issues such as: types of control structures necessary for implementation, required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem.

Application of the Gibbs distribution to image segmentation

This paper presents a new statistical approach to image segmentation. Making use of Gibbs distribution models of Markov random fields a dynamic programming based segmentation algorithm is developed. The algorithm is described in detail and examples are given.

Adaptive implementation of the internal model principle

A new algorithm which extracts the disturbance model from a minimal plant model having a different signal is given. The minimal model is used for adaptive pole placement incorporating the internal model principle. The closed loop system is shown to reject the disturbances asymptotically. A number of simulated examples are given to demonstrate the performance of the algorithm.

Bayes smoothing algorithms for segmentation of images modeled by Markov random fields

A new image segmentation algorithm is presented, based on recursive Bayes smoothing of images modeled by Markov random fields and corrupted by independent additive noise. The Bayes smoothing algorithm presented is an extension of a 1-D algorithm to 2-D and it yields the a posteriori distribution and the optimum Bayes estimate of the scene value at each pixel, using the total noisy image data. Computational concerns in 2-D, however, necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm. In particular, the scene (noiseless image) is modeled as a Markov mesh random field and the algorithm is applied on (horizontal/vertical) strips of the image. The Bayes smoothing algorithm is applied to segmentation of two level test images and remotely sensed SAR data obtained from SEASAT, yielding remarkably good segmentation results even for very low signal to noise ratios.

Global stability of a direct hybrid adaptive pole placement algorithm

This paper presents a hybrid adaptive control scheme for assigning the closed loop poles of a single-input single-output continuous time linear system. The resulting closed loop system is shown to be globally stable when driven by an external reference signal containing exactly 2n distinct sinusoids where n is the open-loop system order. In particular, persistant excitation of the closed loop input-output data, and hence convergence of a sequential least squares identification algorithm is proven.

Reduced order adaptive pole placement for multivariable systems

A method is suggested for adaptively assigning the closed-loop poles of a continuous time linear multivariable system. The resulting design significantly reduces the complexity in comparison to any other known multivariable scheme. For implementation one needs to know the order of the system and an upper bound on the observability index.

Two-dimensional image boundary estimation by use of likelihood maximization and Kalman filtering

This paper formulates the problem of object boundary estimation in noisy black and white images as a state sequence estimation problem for a discrete-time Markov process. Based upon this formulation and the resulting likelihood function a suboptimal estimation algorithm is developed for elliptically shaped boundaries. Appropriate transition probabilities are calculated by developing a dynamic model for boundary generation and implementing a Kalman filter.