Image Structure from Monotonic Dual Graph Contraction

• Authors: Roman Englert;Walter G. Kropatsch
• Venue: AGTIVE '99 Proceedings of the International Workshop on Applications of Graph Transformations with Industrial Relevance
• Year: 1999

The qualitative structure of images is much like the qualitative structure of landscapes. 'Critical points' of a landscape are the summits, the immits, and the saddle points. These points are connected through special curves on the surface of the landscape. The new approach computes this basic qualitative structure of an image or a landscape from the neighborhood structure of a sampled grid by a process called monotonic dual graph contraction (MDGC). The vertices of the graphs store information about gray level or height as attributes. Edges represent surface curves connecting the vertices. MDGC successively removes non-extrema from the original graphs while it preserves the connectivity between extrema and the connectivity level, a new property expressing the least height difference when moving from one extremum to another extremum. Since the graph represents a surface it is planar and the dual graph is well defined. MDGC performs simplifications such that in one graph all local maxima survive and in the dual all local minima survive. Hence we call them 'maximum graph' and 'minimum graph' respectively. The focus in this paper is on the description of the neighborhood and the hierarchy of the local extrema of height. Monotonic properties of the gray level image are preserved during the contraction process. The implementation of the approach is described and experimental results are discussed.