Monotonic Tree

Contour trees have been used in geographic information systems (GIS) and medical imaging to display scalar data. Contours are only defined for continuous functions. For an image represented by discrete data, a continuous function is first defined as an interpolation of the data. Then the contour tree is defined on this continuous function. In this paper, we introduce a new concept termed monotonic line, which is directly defined on discrete data. All monotonic lines in an image form a tree, called monotonic tree. As compared with contour trees, monotonic trees avoid the step of interpolation, thus can be computed more efficiently. Monotonic tree can also be used as a hierarchical representation of image structures in computer imagery.