Similarity retrieval based on group bounding and angle sequence matching in shape database systems

Abstract

In this paper, a new method for retrieving similar shapes from a shape database is proposed. The shapes in the database are indexed by their CPA-strings. When a query shape is submitted to the system, it is converted to a CPA-string from which both the lower and the upper bounds of the locations of the potentially matched shapes are computed. This will restrict the search space to a reasonable small proportion of the whole database. At the second stage, an angle sequence matching algorithm is invoked to compute the Weighted Levensthein Distances between the query CPA-string and the selected database CPA-strings. The shapes that have distances less than a given threshold are finally retrieved. Experimental results show that our approach is robust, accurate and efficient in terms of finding the desired shapes within a reasonable time, even if the shapes are rotated, scaled, and may have boundary noise.

Introduction

Similarity retrieval is one of the most important functions in image database systems. Techniques of using spatial relations among objects for similarity retrieval have been widely studied in the past few years (Chang et al., 1987, Chang et al., 1988; Lee et al., 1989; Lee and Hsu, 1992; Huang and Jean, 1994, Huang and Jean, 1996). There are many image database applications where an image contains only a single object. Typical examples include target shapes in defense applications; part or tool shapes in manufacturing applications; and shape of body parts, medical tools, and biomedical signals in medical applications (Mehrotra and Gary, 1995). In such applications, shape feature becomes the most important information used to discriminate objects. The shape of an object is described through an image or drawing. Large collections of object images or drawings are called shape databases. The process of selecting a subset of objects' images or drawings, which are visually similar to the query shape, is called shape similarity retrieval.

There are three important issues involved in shape similarity retrieval: (1) how to represent a shape in an abstract and efficient way while still preserving important shape feature; (2) what are the measures for evaluating both the difference and similarity between shapes?; (3) how to index and organize the shapes in the database so that searching effort for desired shapes can be reduced?

The shape of an object can be described quantitatively using numeric shape descriptors such as roundness, curveness, rectangularity, compactness, direction, elongatedness and eccentricity (Sonka et al., 1993). These shape descriptors provide a global description of object shape, but lack detailed variations. On the other hand, shape feature can be extracted from critical points because the main information of a shape is concentrated at those points with high curvature. Existing critical points detection techniques were summarized in (Fu and Yan, 1997).

Methods of shape similarity retrieval depend on the shape representation schemes used. So far, there is no technique of general validity to measure shape similarity. Evaluating diversities among an unpredictably wide range of shapes probably requires complete shape descriptions about objects. In despite of such difficulties, Mehrotra and Gary (1995) proposed a shape indexing method by transforming a sequence of critical points of a shape into a single point in a multidimensional space. All points in this multidimensional space are then organized into a dynamic structure such as K–D–B tree (Robinson, 1981). Searching for desired shapes in a K–D–B tree is much more efficient than exhaustive search. However, this method is very sensitive to noises on shapes. It is also difficult to determine the dimension of a suitable K–D–B tree because of varieties of shapes. Besides, the implementation cost of a K–D–B tree is extremely high. Another method of shape similarity measuring is to compute the string distance by applying a string-matching technique directly to chain-coded contours (Abe and Sugita, 1982; Cortelazzo et al., 1994). This method is also too sensitive for non-smooth parts of contours which are not the real `features' of the shapes.

In this paper, we present a robust and efficient method for retrieving similar shapes from a shape database. Our approach is robust because it can discriminate objects by measuring their similarities even if objects are rotated, scaled and have noise on the boundary. It is also efficient because the search area for locating potentially matched shapes is controlled within two bounds, which can be dynamically calculated according to the shape feature of the query object. The effectiveness of our approach has been well demonstrated by an experimental system implemented in C⁺⁺ on IBM compatible PC.

The remainder of this paper is organized as follows. In Section 2, we present our method for extracting and representing the shape feature of an object. In Section 3, we describe how to extend the Weighted Levensthein Distance (WLD) method (Okuda et al., 1976) to become a similarity (or dissimilarity) measure for shape recognition and retrieval. In Section 4, we show the method of organizing the shape database and mapping a shape query into a specific area of the shape database by computing the lower bound and upper bound for that area. The results demonstrating the performance of our experimental system are shown in Section 5. Finally, conclusions are given in Section 6.