Segmentation algorithms that do not require preselected thresholds and are rapid and automatic for various applications are introduced. The approach is to track how the background graytone distribution varies throughout the image without a priori knowledge. Rectangular image regions are sampled to track background variations. Criteria based on statistical theory are used to determine the homogeneity of regions and to distinguish between background-homogeneous and object-homogeneous regions. The criteria include upper and lower bounds to account for practical situations which arise when the underlying assumptions become invalid. Segmentation is focused on non-homogeneous regions. The background graytone distribution throughout the image is estimated from regions where it is measurable. Knowledge of the local background distribution throughout the entire image is then used to preserve the local brightness relationship of object pixels to the background. Rather than simply mapping the graytone image into an object-background binary image, more information is retained by determining additional thresholds and mapping pixels into object brightness relative to background and into uncertainty. Image regions made up of uncertainty labelled pixels assist in identifying image regions that require further processing.