A gray-level image can be represented by a component tree, based on the inclusion relation of connected regions obtained by threshold decomposition. The great advantage of this structure is the efficient determination of a set of attributes for each component of the image, being widely used in morphological filtering (for instance, area as attribute to the area opening). This paper describes the computation of new statistical attributes determined incrementally from this tree construction in quasi-linear time, defining variations of anti-extensive operators as region-based contrast restriction an region-based adaptive thresholding.