ALGORITHMS FOR MATCHING RELATIONAL STRUCTURES AND THEIR APPLICATIONS TO IMAGE PROCESSING
Abstract
Two major problems need to be considered in image analysis and understanding. One is how to represent or model objects and images, the other is how to recognize objects in images. To answer the first question, we must decide what are suitable data structures for representing objects and images. Graph representation (relational structure) not only can keep sufficient information of the image but is still flexible enough to tolerate noise. Unlike other approaches where there exists close interaction between control structure and low level processing, here the recognition process can be formulated as a purely mathematical task--finding matchings between relational structures. The matching can be either discrete or probabilistic (fuzzy). Based on whether the mapping is one--one or not, we can further subdivide it into five categories--graph isomorphism, subgraph isomorphism, common subgraph isomorphism, homomorphism, and maximal matches. We have proposed a fast subgraph isomorphism algorithm using resolution, and also modified the updating rule for fuzzy model which was proposed by Rosenfeld so that it is more suitable for image understanding. The main contributions of this paper are the observation of the difference between the topological mapping and embedded mapping, and the idea of the star structure which has several advantages over the conventional node structures. In applications to real pictures the objects are embedded in the picture plane. The spatial relationship among the primitives of the object is fixed. Spatial orderings as well as the measurements of numerical attributes among primitives are essential clues for narrowing the search space in the search tree. The mappings which make use of these clues to eliminate several mappings which are topologically possible but practically impossible are called embedded mappings. The idea of star structure is made possible by the use of embedded mapping which eliminates a large number of impossible topological mappings and saves storage for star structure. It has more refinement power in the search process than the conventional node structure and there is no need to store a large compatibility table which involves four variables if we use the node structure. Finally, we provide four application examples, two in image understanding and two in image registration. Both objects with straight-line boundaries and those with curvilinear boundaries are considered.
Degree
Ph.D.
Subject Area
Electrical engineering|Computer science
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.