An optimal graph theoretic approach to data clustering: theory andits application to image segmentation
Wu, Z.
Leahy, R.
Dept. of Radiol., Pennsylvania Univ., Philadelphia, PA;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Nov 1993
Volume: 15,
Issue: 11
On page(s): 1101-1113
ISSN: 0162-8828
References Cited: 25
CODEN: ITPIDJ
INSPEC Accession Number: 4580744
Digital Object Identifier: 10.1109/34.244673
Current Version Published: 2002-08-06
Abstract
A novel graph theoretic approach for data clustering is presented
and its application to the image segmentation problem is demonstrated.
The data to be clustered are represented by an undirected adjacency
graph 𝒢 with arc capacities assigned to reflect the similarity
between the linked vertices. Clustering is achieved by removing arcs of
𝒢 to form mutually exclusive subgraphs such that the largest
inter-subgraph maximum flow is minimized. For graphs of moderate size (~
2000 vertices), the optimal solution is obtained through partitioning a
flow and cut equivalent tree of 𝒢, which can be efficiently
constructed using the Gomory-Hu algorithm (1961). However for larger
graphs this approach is impractical. New theorems for subgraph
condensation are derived and are then used to develop a fast algorithm
which hierarchically constructs and partitions a partially equivalent
tree of much reduced size. This algorithm results in an optimal solution
equivalent to that obtained by partitioning the complete equivalent tree
and is able to handle very large graphs with several hundred thousand
vertices. The new clustering algorithm is applied to the image
segmentation problem. The segmentation is achieved by effectively
searching for closed contours of edge elements (equivalent to minimum
cuts in 𝒢), which consist mostly of strong edges, while rejecting
contours containing isolated strong edges. This method is able to
accurately locate region boundaries and at the same time guarantees the
formation of closed edge contours
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