Threshold selection using estimates from truncated normal distribution

Two situations in which the image gray-level histogram cannot be used for threshold determination are: (1) the situation in which the background noise by itself has a multimodal distribution; and (2) the situation in which the object is so small that its contribution to the histogram is overwhelmed by the noise portion even if the noise distribution is unimodal. To alleviate these two undesirable conditions, local average, the central limit theorem, and a statistical theory for truncated data analysis are used to: (1) make the noise part of the histogram appear unimodal; and (2) cut off a large portion of the background so that the object portion in the histogram becomes more prominent. The gray-level distributions for the background and the object are then estimated and used to find an optimum threshold