ContactPerson: azhang@cse.buffalo.edu
### Begin Citation ### Do not delete this line ###
%R 2001-12
%U /projects/azhang/papers/Song/monotree/monotree.pdf
%A Song, Yuqing and Zhang, Aidong
%T Monotonic Tree of Images and Its Application in Image Processing
%D August 29, 2001
%I Department of Computer Science and Engineering, SUNY Buffalo
%K Image retrieval
%Y Image processing
%X 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.