An EM-like relaxation operator

Traditional probabilistic relaxation labeling schemes are critically dependent on the availability of salient and reliable measurements for initialisation purposes. Unfortunately such measurements may not be obtainable within the level-by-level processing philosophy under which the schemes operate. In this paper we present a new Bayesian probabilistic relaxation labeling scheme which overcomes this problem. Salient label measurements are made available at multiple levels of abstraction through a succession of fitting operations on the raw data. Measurement reliability is achieved by feeding the current label probabilities into fitting operations, thereby facilitating the suppression of noise or outliers. By iterating between fitting and labeling modes in a manner analogous to the EM algorithm, improved robust estimation leads, via more reliable measurements, to better labeling and vice versa. At convergence, both the parametric and symbolic image descriptions are compatible. In this way we offer a compromise between conventional relaxation schemes that are either dominated by the prior label model or that rely on static measurement based compatibility relations. We demonstrate the utility of our evidence-combining scheme in relation to the extraction of differential structure from range data.