In this research, we present a statistical theory, and an algorithm, to identify one-pixel-wide closed object boundaries in gray-scale images. Closed-boundary identification is an important problem because boundaries of objects are major features in images. In spite of this, most statistical approaches to image restoration and texture identification place inappropriate stationary model assumptions on the image domain. One way to characterize the structural components present in images is to identify one-pixel-wide closed boundaries that delineate objects. By defining a prior probability model on the space of one-pixel-wide closed boundary configurations and appropriately specifying transition probability functions on this space, a Markov chain Monte Carlo algorithm is constructed that theoretically converges to a statistically optimal closed boundary estimate. Moreover, this approach ensures that any approximation to the statistically optimal boundary estimate will have the necessary property of closure.
