We present new and faster algorithms to search for a 2-dimensional pattern in a 2-dimensional text allowing any rotation of the pattern. This has applications such as image databases and computational biology. We consider the cases of exact and approximate matching under several matching models, using a combinatorial approach that generalizes string matching techniques. We focus on sequential algorithms, where only the pattern can be preprocessed, as well as on indexed algorithms, where the text is preprocessed and an index built on it. On sequential searching we derive average-case lower bounds and then obtain optimal average-case algorithms for all the matching models. At the same time, these algorithms are worst-case optimal. On indexed searching we obtain search time polylogarithmic on the text size, as well as sublinear time in general for approximate searching.

Content-based image retrieval consists in retrieving from an image database the most similar image with respect to a query, according to some similarity measure. This scenario has numerous specific applications that include bioinformatics and medical imaging, among others. However, because the size of image repositories grows very fast, finding patterns in images requires an index to avoid a sequential scan, thus reducing the search time. Considering that small (and high) levels are faster than larger ones in the memory hierarchy, it would be very beneficial to have a compressed representation of the image database that can give fast access and pattern matching functionalities in high memory levels. In this thesis we propose a deep study of searching in compressed image databases, contributing with new algorithms for approximate indexed search based on template matching. Our specific objectives are to determine the feasibility of extending existing approaches for indexed exact template matching to approximate template matching working on compressed image databases, in particular allowing don’t care pixels; to design a similarity measure based on information theory to be used for approximate template matching; and to evaluate the impact on the performance and quality of results, in feature vector based similarity search, when the index is compressed in lossy form. 1