A Continuous Gibbs Annealer

Virtually all implementations of simulated annealing are simplified by assuming discrete unknowns, yet continuous-parameter annealing has many potential applications to image processing. A wide array of problems such as speech formant tracking, boundary estimation and phase-unwrapping can be approached as global minimization of contour energy function. This thesis proposes to solve such problems by a new continuous simulated annealing method based on the discrete Gibbs sampler. The benefits of simulated annealing in this context are its insensitivity to initial conditions and its ability to solve problems with many local minima. Spline contours are a good fit for Gibbs sampling because each control point affects a limited local neighborhood. The primary challenge of converting the discrete Gibbs model to a continuous domain is to efficiently generate samples from a continuous conditional distribution. Various techniques for such adaptive sampling are explored, ranging from simple heuristics to more complex attempts at a general, motivated solution. The problem remains somewhat open as a definitive, efficient solution has not yet been found. The proposed continuous annealing algorithm is implemented for both a well-defined synthetic problem and speech-formant tracking in spectrograms. Results indicate that the method is highly effective in both domains. Estimation results also show that a relatively simple adaptive sampling heuristic is capable of performing nearly as well as much more complex approaches, reducing processing time by at least a factor of four.Continuous simulated annealing is found to be an effective method for ordered contour estimation in images. Further research in the area may further explore the range of application of this method, and shed more light on the strengths and weaknesses of the technique. iv