Contour trees and small seed sets for isosurface traversal
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Concepts of use in contour map processing
Communications of the ACM
Geometry of Digital Spaces
Trekking in the Alps Without Freezing or Getting Tired
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Very large scale multidimensional data management and retrieval for USGS and NIMA imagery
dg.o '04 Proceedings of the 2004 annual national conference on Digital government research
3D Edge Detection by Selection of Level Surface Patches
Journal of Mathematical Imaging and Vision
Object recognition using multiresolution trees
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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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.