Θℜ-string: A geometry-based representation for efficient and effective retrieval of images by spatial similarity

A spatial similarity algorithm assesses the degree to which the spatial relationships among the domain objects in a database image conform to those specified in the query image. In this paper, we propose a geometry-based structure for representing the spatial relationships in the images and an associated spatial similarity algorithm. The proposed algorithm recognizes both translation, scale, and rotation variants of an image, and variants of the image generated by an arbitrary composition of translation, scale, and rotation transformations. The algorithm has Θ(n log n) time complexity in terms of the number of objects common to the database and query images. The retrieval effectiveness of the proposed algorithm is evaluated using the TESSA image collection