Indexing by Shape of Image Databases Based on Extended Grid Files Carlo Combi, Gian Luca Foresti, Massimo Franceschet, Angelo Montanari Department of Mathematics and ComputerScience, University of Udine Via delle Scienze 206, 33100 Udine, Italy {combi,foresti,francesc,montana}@dimi.uniud.it Abstract In this paper, we propose an original indexing by shape of image databases based on extended grid files. We first introduce a recently developed shape description method and tailor it to obtain suitable representation structures for image databases. Then, in order to efficiently support im- age retrieval, we define an indexing structure based on grid files. Since grid files were originally developed to speed up point (exact match) and range (nearest neighbors within a threshold) queries on multidimensional data with a fixed number of attributes, we extend them to cope with data pro- vided with a varying number of attributes and to deal with a new class of queries relevant to image databases, namely, nearest neighbor queries. We give a detailed description of the proposed search algorithms and a systematic anal- ysis of their complexity, and discuss the outcomes of some experimental tests on sample image databases. 1. Introduction Digital image databases are convenient media for rep- resenting and storing information in a variety of domains, including industrial, biomedical, and public administration domains, provided that an efficient automatic procedure for indexing and retrieving images from them is given. Most image databases take a text-based approach to indexing and retrieval, according to which keywords, captions, or free text are associated with each image in the database. However, such an approach suffers from several limitations. First, since automatic extraction of semantic information from images is beyond the capabilities of current machine vision techniques, a human interaction is required to de- scribe the contents of images in terms of keywords and/or captions. This process is quite time-consuming and ex- tremely subjective. Second, certain visual properties of im- ages, such as some textures and shapes, are very difficult or nearly impossible to describe with text. As an alternative, one can work with descriptions based on properties which are inherent to the visual contents of an image: colors, tex- tures, shape, and location of image objects, spatial relation- ships between objects, etc. Most work in image database retrieval has concentrated on a single feature. Color and tex- ture are reliable features only for retrieving generic images (landscapes, outdoor views, etc.); on the contrary, shape is very useful to represent objects, but it requires a large num- ber of attributes. One of the most promising shape-based approaches exploits morphological skeletons to represent images [2]. It encodes a picture as a set of object skele- tons; a sketch picture can then be partially reconstructed and progressively refined back to the original image by di- lating the skeleton function. This approach allows one to reduce ambiguity in similarity retrieval and to reduce mem- ory requirements, but it has two major drawbacks: the mor- phological skeleton is not robust to noise [3] and it requires a huge amount of attributes to represent object shapes. A solution to the first problem has been obtained by introduc- ing the notion of Statistical Morphological Skeleton (SMS) [1]. The second problem is addressed in this paper. When- ever we want to efficiently store data provided with sev- eral attributes, each of them being possibly treated as a primary key, multidimensional data structures are needed. Most techniques for storing and searching these structures hierarchically decompose the multidimensional space into regions. Such a space can be either the data to be stored or the embedding space from which the data is drawn. Grid files adopt the latter solution. They are especially well- suited when the domains over which the attributes take their values are large and linearly ordered, and the attributes are independent. Under such assumptions, grid files guarantee a high data storage utilization, a smooth adaptation to the contents to be stored, fast access to individual records, and efficient processing of range queries [4]. The goal of our work is to provide a compact represen- tation and efficient indexing structures for image databases. In Section 2, we present a method for SMS extraction and approximation. In Section 3, we first propose an efficient indexing technique, based on a suitable extension of grid files; then, we describe the algorithms we developed for