Monotonic Tree of Images and Its Application in Image Processing

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 be reduced. The reduced monotonic tree can also be used as a hierarchical representation of image structures in image processing. In particular, we demonstrate its application on image smoothing and texture retrieval. Experiments show that our smoothing scheme is successful in both noise reduction and texture retrieval.