Two thresholds are better than one

The concept of the Bayesian optimal single threshold is a well established and widely used classification technique. In this paper, we prove that when spatial cohesion is assumed for targets, a better classification result than the "optimal" single threshold classification can be achieved. Under the assumption of spatial cohesion and certain prior knowledge about the target and background, the method can be further simplified as dual threshold classification. In core-dual threshold classification, spatial cohesion within the target core allows "continuation" linking values to fall between the two thresholds to the target core; classical Bayesian classification is employed beyond the dual thresholds. The core-dual threshold algorithm can be built into a Markov random field model (MRF). From this MRF model, the dual thresholds can be obtained and optimal classification can be achieved. In some practical applications, a simple method called symmetric subtraction may be employed to determine effective dual thresholds in real time. Given dual thresholds, the quasi-connected component algorithm is shown to be a deterministic implementation of the MRF core-dual threshold model combining the dual thresholds, extended neighborhoods and efficient connected component computation.