Maximum Likelihood Estimation of Markov-Process Blob Boundaries in Noisy Images

Effective and elegant procedures have recently appeared in the published literature for determining by computer a highly variable blob boundary in a noisy image [1]-[3]. In this paper we point out that if the blob boundary is modeled as a Markov process and the additive noise is modeled as a white Gaussian noise field, then maximization of the joint likelihood of the hypothesized blob boundary and all of the image data results in roughly the same blob boundary determination as does one of the aforementioned deterministic formulations [2]. However, the formulation in this paper provides insights into and optimal parameter values for the functions involved and reveals suboptimalities in some of the formulations appearing in the literature. More generally, we agree that maximization of the joint likelihood of the hypothesized blob boundary and of the entire picture function is a fundamental approach to boundary estimation or the estimation of linear features (roads, rivers, etc.) in images, and provides a powerful mechanism for designing sequential, parallel, or other boundary estimation algorithms. The ripple filter, an advanced form of region growing, is briefly introduced and illustrates one of a number of alternative algorithms for maximizing the likelihood function. Hence, this likelihood maximization approach provides a unified view for seemingly different approaches, such as sequential boundary finding and region growing. Bounds on the accuracy of boundary estimation are readily derived with this formulation and are presented.