Topological and Directional Logo Layout Indexing

To evaluate similarity between two images, the layout or configuration of the shapes is an important feature besides geometrical shape similarity. In particular, trademark im- age retrieval is an application domain where layout sim- ilarity is important, and in many cases overlooked. In this paper, we present a graph-based encoding of layout, in which both directional and topological layout informa- tion is stored. A Hermitian matrix is associated to each graph, and contains all the information that is

present in the graph. The spectra of these Hermitian matrices are used for indexing purposes. By obeying several constraints on the construction of the Hermitian matrices, we can mimic the spectral behaviour of Laplacian matrices, which are proven to be successful representations in retrieval environments. Experiments show the improved representational power of the proposed approach over spectral methods using Lapla- cian matrices. KEY WORDS Indexing, image retrieval, trademarks, Laplacian, Hermi- tian, spectra 1. Introduction The key function of any indexing algorithm is to speed up content-based retrieval of objects or models that are stored in a database, by selecting a small set of candidate ob- jects that are either presented to the user, or passed on to a more refined matching unit in the retrieval pipeline. At this matching level, more accurate and more expensive match- ing algorithms can be deployed because of the reduced size of the set of objects that is under inspection. At the in- dexing level however, comparison of objects should be ef- ficient and it must be possible to prune the database, i.e. the database must be partitioned in such a way that simi- lar models are positioned close to each other. Only then objects that are far from the query object can be discarded without further inspection. Naturally, the representation of the objects in the in- dex and the accuracy and efficiency with which non-similar objects can be discarded are closely related. The objects that are under investigation in this work are logo and trade- mark images, or any kind of image in general where the layout of the individual image components (as opposed to their shape characteristics) is important for similarity eval- uation [10]. In content-based trademark image retrieval, layout can play a large role in identifying trademark in- fringement. See for an example Figure 1, where the con- figuration of the individual shapes is one of the most impor- tant properties. Suppose that in all three cases the five cir- cles are returned as a result of image segmentation (which would be the ideal segmentation), it is impossible to distin- guish between the images without any notion of layout in the representation. In this case, indexing algorithms (with- out layout information) will be less efficient because the set of candidate models will be unnecessary large. More importantly, indexing algorithms can be less accurate by ignoring layout. See Figure 2 for an illustration...

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