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Combining Intra-Image and Inter-Class Semantics for Image Matching

images query similarity ranking

Definition: Both local (intra-image) and global (inter-class) similarities play complementary roles in image matching and ranking, so a simple linear combination scheme has been experimented with significant performance improvement over single image matching schemes.

Given an image retrieval system, the information need of a user can be modeled as the posterior probability of the set of relevant images R given an expression of the information need in the form of query specification q and an image x in the current database, P ( R | q,x ). The objective of the system is to return images with high probabilities of relevance to the user.

In Query By Example, P ( R | q,x ) depends on the similarity between query q and image x . On the other hand, we note that the set of relevant images R does not exist until a query has been specified. However we can construct prior categories of images C k , k = 1, 2, M as some prototypical instances of R and compute the memberships of q and x to these prior categories for contextual similarity (see an article on Semantic Class-Based Image Indexing ).

Both local (intra-image) and global (inter-class) similarities play complementary roles in image matching and ranking. Using a Bayesian formulation, we have:

We observe that P ( q,x ) tends to be small if q and x are similar (i.e. less likely to find similar images than dissimilar pair in a large database). On the other hand, P (q,x | R) tends to be large if q and x are similar with respect to R (i.e. q and x are more likely to co-occur in R if they belong to R ). And P ( R ) is constant for a given query session. Hence P ( R | q,x ) is proportional to the similarity between q and x given R (denoted as µ( q,x )) arid the similarity between q and x in terms of their image contents (denoted as ?( q , x )) i.e.:

For the purpose of retrieval, Equation (2) provides a principled way to rank images x by their probabilities of relevance to the user’s information need as represented by the query example q . When the similarities µ( q,x ) and ?( q,x ) are expressed in the form of probabilistic distance (i.e. inverse of similarity) such as the Kullback-Leibler distance, ordering images from the smallest distance to the largest distance is the manifestation of the minimum cross-entropy principle This echoes the Probability Ranking Principle in text information retrieval ].

To realize local and global semantics, a good choice for ?( q, x ) and µ( q,x ) are Semantic Support Regions (see an article on Semantic Image Representation and Indexing ) and Semantic Support Classes (see an article on Semantic Class-Based Image Indexing ) respectively. Since only ranking matters for practical image retrieval, a simple linear combination scheme has been experimented with significant performance improvement over single image matching schemes. That is, with ? [0,1] and integrated similarity ?( q,x ) replacing P ( R | q,x ):

 

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